a developed production control and scheduling model in the semiconductor manufacturing systems with...

ORIGINAL ARTICLE

A developed production control and scheduling modelin the semiconductor manufacturing systems with hybridmake-to-stock/make-to-order products

H. Eivazy & M. Rabbani & M. Ebadian

Received: 9 September 2008 /Accepted: 18 March 2009 /Published online: 2 April 2009# Springer-Verlag London Limited 2009

Abstract Semiconductor manufacturing systems are one ofthe most complex production systems and this complexityincreases when these systems produce both make-to-stock(MTS) and make-to-order (MTO) products in order toimprove the production system utilization. To deal with thiscomplexity, we present a dynamic production control andscheduling model for a semiconductor shop (fab) withhybrid MTS/MTO production environment. The proposedmodel encompasses two major modules: release moduleand dispatching module. The release module deals with twoissues: prioritizing the MTS and MTO products in the jobpool and determining when and which products can bereleased into the shop floor. The only considered issue ofdispatching module is to prioritize the MTS and MTOproducts in the queue of each workstation whenever amachine becomes idle. To evaluate the proposed model,different performance measures for MTS and MTOproducts are considered. Moreover, a number of numericalexperiments have been conducted by simulation studies.Simulation studies indicate that the proposed model out-performs other related well-known production control andscheduling policies in the literature.

Keywords Semiconductor manufacturing systems .

Hybrid make-to-stock (MTS) and make-to-order (MTO) .

Production control and scheduling .

Workload control (WLC) approach . Simulation

1 Introduction

Semiconductor manufacturing is the process of making theintegrated circuits on wafer. The manufacturing shop,which is called fab, usually includes several workstationswith parallel identical machines. Fab is the clean shopwhere the main part of very-large-scale-integration circuitmanufacturing is performed and is considered as a set of Mworkstations, each having mi (i=1, 2...,M) identical parallelmachines [11, 12]. These workstations manufacture theproducts either in series processing or in batch processing.

The general manufacturing operations (steps) performedon the semiconductor products incorporate the waferfabrication, probe or electrical die sorting, assembly, andfinal test. The process route of a typical semiconductorproduct is often comprised of 500 steps usually includingthe photolithography, etching, thin filming, and diffusion.Some steps are repeated several times until the respectiveprocess route is completed. Thus, semiconductor productsmay reenter a workstation like photolithography worksta-tion several times before being completed. These steps canbe grouped into several layers. Each layer incorporatessome steps beginning from the first step after photolithog-raphy step and ending with the next photolithography step.It is noteworthy that the first layer for each product beginsfrom the head step, i.e., the first operation, and the last layerends at the last operation in the process route.

Int J Adv Manuf Technol (2009) 45:968–986DOI 10.1007/s00170-009-2028-5

H. Eivazy :M. Rabbani (*)Department of Industrial Engineering, College of Engineering,University of Tehran,Tehran, Irane-mail: [email protected]

M. EbadianDepartment of Wood Science, University of British Columbia,2424 Main Mall,Vancouver, BC V6T-1Z4, Canada

Semiconductor manufacturing is one of the most complexproduction systems due to the existence of reentrancycharacteristic, capital-intensive equipment, long process routeof each product, product variety, uncertainty (e.g., machinebreakdown), constant device miniaturization, and changingtechnologies [11, 12]. Among these complexities, reentrancyfeature has a profound role in complicating the productioncontrol and scheduling of semiconductor products. Asmentioned above, there are a few workstations that a productreenters to them several times in its process route likephotolithography workstation. Moreover, the semiconductormanufacturing is one of the highly capital-technology-intensive industries [37]. Thus, increasing the utilization inthe fab to decrease the production costs is another challengein production control and scheduling models of such produc-tion systems.

The production of both make-to-stock (MTS) and make-to-order (MTO) items is another issue which makes theproduction system of the semiconductor manufacturing morecomplicated. This complexity stems from different character-istics of MTS and MTO manufacturing systems. Since thearriving orders in MTO systems are customer-based, on-timedelivery and short and reliable cycle time are the maincompetitive factors to win the market share while in MTSsystems, the high utilization rate, the throughput rate, and theproduction achievement ratio are the major competitivefactors. In seasons that the demand for MTS products inintegrated device plants decreases, the production systemaccepts the MTO products to increase the plant revenue anddecline the low utilization costs [6]. For the same reasons,foundry plants switch to the combined MTS/MTO produc-tion system during the low MTO order demands. In suchcases, the production systems strive for meeting themanagement objectives of MTS and MTO products. There-fore, in the combined production environment, productioncontrol and scheduling turns into a formidable and compli-cated task as the total capacity of the plant is limited andshared between MTS and MTO products.

In summary, to handle the aforementioned issues insemiconductor manufacturing including the existence ofreentrancy, high utilization of the production system, and thefulfillment of management objectives for bothMTS andMTOproducts, the production managers need to a dynamicproduction control and scheduling system. In this regard, wepropose a comprehensive production control and schedulingmodel including release and dispatching modules for a hybridMTS/MTO semiconductor manufacturing system. To dem-onstrate the advantages of the model, a suite of simulation isapplied. The obtained results show the efficiency of the modelin managing the production of MTO and MTS products andalso the utilization of the production system.

This paper is organized as follows: Section 2 reviews therelated literature on production control and scheduling

models in the semiconductor manufacturing and the hybridMTS/MTO production environment. The proposed produc-tion control and scheduling model is described in detail inSection 3. This section elaborates on different steps of themodel. The validation of the proposed model via simulationstudies is demonstrated in the Section 4. The concludingremarks and future research directions are presented inSection 5.

2 Literature review

Regarding the application of production control andscheduling systems in semiconductor companies, there aretwo types of policies for production control of a semicon-ductor fab: open-loop control and closed-loop control.Open-loop control policies release a new lot of productinto fab without taking into account the dynamic shop floorstate such as workload congestion of shop. Uniformreleasing is an overt open-loop control policy that releasesa new lot into the shop periodically. In contrast, the closed-loop control policies send a new product lot into the shopby continuously monitoring the dynamic work-in-progress(WIP) situation in the shop floor. Constant WIP (CONWIP)[16, 40], starvation avoidance (SA) [11, 12], load-orientedmanufacturing control [2, 43], drum–buffer–rope [14], twoboundary [26, 27], workload regulating [42, 45], fixed WIP[5, 35], constant load (CONLOAD) [36], and target balance[23] are the closed-loop control methods developed forreleasing a new product lot into the shop. The mainobjective of closed-loop control policies is to keep WIPswithin an optimal level in the shop or bottleneck work-stations [33]. Generally, the closed-loop control policyoutperforms the open loop control policy in terms ofcontrolling the production system [30].

Besides the type of production control policy, anotherimportant factor which should be considered in theproduction system is the dispatching mechanism. Asmentioned before, there are two types of workstations inthe fab: batch workstation and series workstation. Althoughvarious dispatching mechanisms for series machines havebeen proposed by Lu et al. [29], Glassey and Resende [11,12], Lu and Kumar [28], Kim et al. [19], Yoon and Lee[46], Lee et al. [24], Dabbas and Fowler [7], and Wu et al.[45], a few studies have been conducted in batch dispatch-ing problems such as Glassey and Weng [10]. A compre-hensive review of job shop dispatching mechanisms hasbeen discussed in the work of Blackstone et al. [4].

As mentioned before, semiconductor systems are work-ing in a combined MTS/MTO production environment.Thus, the various issues considered in pure MTO or pureMTS systems arise in these hybrid MTS/MTO productionsystems. As a result, the production control and scheduling in

Int J Adv Manuf Technol (2009) 45:968–986 969

such systems would be much more difficult. It is obvious thatthe semiconductor manufacturing literature has not paid to thevarying issues ofMTS/MTO systems the attention it deserves.Several studies have investigated the different aspects ofcombined MTS/MTO production systems such as Adan andvan deWal [1], Federgruen and Katalan [9], Kerkkänen [18],Nguyen [31], Soman et al. [39], and Tsubone et al. [41].However, they have not dealt with the specific aspects of thesemiconductor industry. Only a few studies have developed aproduction control and scheduling model for hybrid MTS/MTO semiconductor production environment such as Changet al. [6] and Wu et al. [44].

Chang et al. [6] have proposed a production control andscheduling model for hybrid MTS/MTO semiconductorproduction environment. Their model includes three decisionmaking modules: bottleneck identification module, orderrelease module, and dispatching module. They have used SAmethod for releasing products into the fab. Their releasemodule ensures timely release of MTO orders and thedispatching module expedites late orders to allow timelydelivery. However, their model releases MTS products to fillup remaining capacity after the MTO orders have beenplanned without disturbing the released MTO orders. In asimilar study, Wu et al. [44] have developed a schedulingmethod for the hybrid MTS/MTO semiconductor productionenvironment. In their model, they have exploited the releasemethod presented by Chang et al. [6] with minor modifica-tions by considering the machine-dedication characteristic.Also, to dispatch the products, MTS products are dispatchedbefore MTO products if none of MTO orders are deliveredlate with respect to their planned due date in its current step.In both models proposed by Chang et al. [6] and Wu et al.[44], the release date of MTO products has been predeter-mined and MTS products are released into the shop onlyafter releasing all MTO products. In fact, their proposedmodels do not take into consideration a strict plan forproducing MTS products. In other words, their models planMTO products at first and do not present a clear prioritiza-tion policy for MTS products in release and dispatchingmodules. Also, these models do not try to plan the releaseand dispatch of MTS products in the right time. It is worthnoting that the predetermined release date for MTO ordersprevents the production system from performing in a real-time manner, in that it is hardly possible to predict when andhow the MTO products will be distributed among variousworkstations within the planning horizon.

The two aforementioned studies have exploited the theoryof constraint (TOC) approach to manage the productionsystem. Based on TOC, throughput, WIP, and due date can becontrolled by only controlling the utilization of bottleneckresources [13]. The proposed models in the works of Changet al. [6] and Wu et al. [44] control the production andworkload of the shop by controlling the utilization of only

bottleneck workstations. They have assumed that thebottleneck workstations are known or can be determinedexactly. This assumption is not practical in that the locationof the bottleneck workstation(s) may shift in the shop floor,especially due to the high dynamics in this productionenvironment if the workload of all workstations is notcontrolled.

As stated by Kingsman [21], due to the present dynam-ics, stochastic nature, and present irregularities in hybridMTS/MTO semiconductor plants such as stochastic de-mand for MTS products, rush orders, dynamic changingproduct mix, high routing variety of process route of eachMTO product, unique process route for each product lot,stochastic arrival of MTO products, and reentrancy charac-teristic, the methods based on TOC approach cannot beeffective for production control in these environments if itis the only used production control method in the system.The main reason is that these methods do not control theworkload of all workstations in the shop strictly; thus,the dynamics can create the imbalanced shop resulting inthe bottleneck shifting issue. Moreover, due to these dy-namics and irregularities, determining how and when theMTO and MTS products will be distributed among variousworkstations in the shop floor over planning horizon is veryhard or impossible [20].

As a conclusion, the suitable production control andscheduling model should be dynamic to deal with thesedynamics. On the other hand, the inappropriate productiontiming of a MTO product incurs costs such as the tardinesspenalty and holding inventory cost. Also, excessiveproduction or backorders of a MTS product causes costssuch as high holding cost and lost sale, respectively. It isnoted that the excessive production of a MTS productutilize the capital-intensive facilities in the fab withoutadding value to the whole system while they can be used bymore profitable MTO products. Therefore, the suitableproduction control and scheduling model in this environ-ment should be strict for controlling the production of bothMTS and MTO products.

To improve the performance of production system insemiconductor manufacturing, we propose a productioncontrol and scheduling model for a semiconductor fab withhybrid MTS/MTO production environment. The proposedmodel includes two major decision making modules:release and dispatching modules. The release module iscomprised of two main tasks: prioritizing the MTS andMTO products in the job pool and determining when andwhich products can be released into the fab. The onlyconsidered issue of dispatching module is to prioritize theMTS and MTO products in the queue of each workstationwhen a machine gets idle. The applied production controlpolicy to control the workload in the production system isworkload control (WLC).

970 Int J Adv Manuf Technol (2009) 45:968–986

WLC is an input–output control policy which has beenmostly applied to MTO production environment. In thispaper, this release mechanism is applied to release bothMTS and MTO products because both of them areconsidered as workload in WLC logic. Thus, we employWLC policy that absorbs the dynamics in the system byforming the job pool and controlling the workload of eachworkstation in the fab. Absorption of dynamics hinders thebottleneck shifting. Bechte [2] stated that confining andbalancing the WIP on a level as low as possible forobtaining maximum utilization and minimum cycle time ofproducts are the core idea of WLC. On the other hand,workload balancing function has the most important role inachieving the short and stable queue in all workstations[22]. Also, as semiconductor manufacturing system is amanufacturing environment without dominant flow direc-tion, WLC can be more effective [32]. Besides using WLC,in this model, we apply TOC approach. In this regard, asone of release conditions, we control the workload ofpotential bottleneck workstation to prevent this workloadfrom becoming less than a predetermined value.

To evaluate the proposed model, the suitable performancemeasures are used for MTO and MTS products. Also, aperformance measure which is critical in supply chainmanagement, i.e., “inventory turns”, is examined. The highinventory turns values show the strength of a manufacturingsystem in the supply chain.

In summary, the main advantages of the proposedproduction control and scheduling model are as follows:

& The proposed production control and scheduling modelworks in the dynamic manner and controls the produc-tion of both MTS and MTO products strictly, while inthe related previous studies such as Chang et al. [6] andWu et al. [44], the proposed production control andscheduling models consider a predetermined date forreleasing products to shop floor. This cannot lead to thecontrol of dynamics such as stochastic MTO productsentry and the dynamic change of the demand of MTSproducts. On the other hand, they present productioncontrol and scheduling for only MTO products strictlyand no rigid plan for production control and schedulingof MTS products. For example, they release MTSproducts after releasing of all MTO products while inthis paper, production of both MTS and MTO productsare planned and controlled strictly.

& The proposed model applies the TOC reasonably alongwith WLC approach in this complex manufacturingsystem. For applying TOC effectively, the location ofbottleneck resources should be known. Also, thelocation of these bottleneck resources should not shiftin the course of time. As WLC policy absorbs presentdynamics in the production system by forming the job

pool and controls the workload of all workstations inthe fab, it can guarantee that the position of potentialbottleneck workstations does not shift, while previousstudies such as Chang et al. [6] and Wu et al. [44]proposed their models based on only TOC to managethe production system. Their models do not guaranteethat the bottleneck workstations in the shop do not shift.

& The proposed model is superior to the previous modelsin terms of a critical performance measure in supplychain management, i.e., inventory turns.

& To calculate total workload (TWL) for each worksta-tion, a new adjusted dynamic workload conversioncoefficient is applied. This conversion coefficient showsmore actual representation of dynamic state of the fabworkload than previous proposed conversion coefficientversions.

& The proposed model applies the WLC method in con-trolling the workload of the hybrid MTS/MTO produc-tion environment. WLC is a simple method that hasbeen mostly applied to MTO production environments,while in this paper, this release mechanism is applied torelease both MTS and MTO products.

3 The proposed production control and schedulingmodel

In this section, we elaborate on a novel production controland scheduling model for a typical semiconductor fab withhybrid MTS/MTO production system. The productionsystem is assumed to be job shop with reentrancycharacteristics. All products have unlimited access tocommon raw materials, here wafers. Since the monetaryvalue of wafers is less than the finished products, shop floormanagers try to keep a large amount of these materials instorages and release them only when they are required formanufacturing of final products. The buffer capacity ofeach workstation is assumed to be infinite. Machines ineach workstation have two states: idle and busy. At eachworkstation, a released wafer lot of product is first placed inthe buffer. When a machine becomes idle, a wafer lot ofproduct is chosen from buffer for processing based on thedispatching mechanism. When the process is completed,the product is transported to the next required workstation.Here, we assume that the transportation time is negligible.

The proposed model controls the production of bothMTS and MTO products strictly. In this regard, the modelprioritizes both MTS and MTO products for release anddispatching and then attempts to release and dispatchproducts at the right time. In order to tackle dynamics andcomplexities of the hybrid MTS/MTO semiconductormanufacturing environments, WLC approach is applied to


control the total workload of the shop floor. WLC controlsthe workload of each workstation to prevent from starvationor congestion of the shop floor and also the lead timesyndrome phenomenon [34]. Lead time syndrome stemsfrom updating lead times in response to changing workloadlevels which leads to erratic ordering behavior, resulting ineven larger variability in WIP and flow times. Thisphenomenon hinders production system from meeting themanagement objectives of both MTS and MTO products.The main advantages of WLC are reduction in waiting timein the queue of workstations and buffering the shop fromexternal dynamics. The external dynamics such as MTOproducts entry fluctuations and dynamic change of MTSproducts demand is absorbed by forming the job pool forall products waiting for release. With the existence of thejob pool in the production system, products are not releasedinto the shop floor immediately. In fact, the job pool is a listof MTS and MTO products that the production systeminitiates their production in future.

Due to highly stochastic circumstances of the hybridMTS/MTO semiconductor production systems, the imbal-anced workload can be created in the shop floor if therelease of the products in the job pool is not controlled. Theimbalanced workload leads to unexpected bottlenecks thatshift dynamically in the shop. Therefore, the bottleneckposition cannot be exactly determined in such conditions.Thus, the application of only the close-looped controlmethods such as SA, which is based on TOC approach, isnot reasonable. Moreover, WLC can be more effective inreleasing the products from job pool in the semiconductormanufacturing which does not have a dominant productionflow direction. Thus, we use WLC method for releasing theproducts in which the workload of each workstation iscontrolled to prevent starvation or congestion of the shopfloor.

The main idea of WLC is to confine and balance WIP ona level as low as possible to achieve the high utilization rateand minimum cycle time of products. To achieve short andstable queues in all workstations, the workload balancingfunction has a highly important role. The WLC methodbalances the workload of the shop by imposing the loadlimit (LL) on the total workload of each workstation. Infact, workload balancing along with imposing LL leads tothe avoidance of the blocked workstation creation. LL is anorm which is defined for each workstation to control thetotal workload of that workstation. When the total workloadof a workstation exceeds its LL, this workstation is definedas the blocked workstation.

The TWL for each workstation is the sum of threeworkloads: direct workload, upstream workload, andreleasing workload. The direct workload of a typicalworkstation y is the sum of processing times for all presentproducts, both in the queue and in the machines of this

workstation. The upstream workload is related to theproducts queuing at upstream workstations which also needto be processed at workstation y. Finally, the releasingworkload is related to the workload of products which havebeen just released to the fab and need to be processed atworkstation y. Among these three workloads, only the firstone can be calculated precisely and the two others shouldbe estimated.

The total workload in workstation y at time t (TWLyt) iscalculated by imposing the workload conversion as follows:

TWLyt ¼Xi2SPy

PTi;y � Piyut ð1Þ

where SPy is the set of products placed either in the shopfloor or in the job pool that will pass through workstation y,PTi,y the processing time of product i in workstation y, andPiyut is the probability that product i, currently located inupstream workstation u, passes through workstation y in theplanning period. It is noteworthy that due to the existenceof reentrancy in the semiconductor manufacturing system,for workstations which a product passes more than one timeto complete its process route, e.g., photolithography, thedirect workload also can be the upstream workload forthese workstations. If product i in workstation u passes mworkstations before entering workstation y, the Piyut can becalculated from the following formula proposed by Ebadianet al. [8]:

Piyut ¼Ym

PCm

TWLmm 2 u; uþ 1; . . . ; y� 1; yf g: ð2Þ

In Eq. 2, PCm and TWLm are the planned capacity ofworkstation m and the total workload of workstation m,respectively. The ratio of PCm over TWLm is the workloadconversion coefficient for workstation m. If y=u, then thePiyut is set to one. The steps of determining the plannedcapacity (PC) and LL for each workstation has beenmentioned in Ebadian et al. [8].

Contrary to the previous equations like that of Bechte[3], the main advantage of Eq. 2 is that it takes into accountthe shop dynamics by considering the present workloadstate of the shop floor. In this formula, however, it ispossible that the ratio of PC to TWL for a workstationexceeds one while the workload conversion coefficient hasthe nature of probability and cannot be more than one. Inthis case, this formula can be misleading in showing theactual state of workload in the shop and can lead to thedelay at the release of products in the job pool. In fact,when this ratio is more than one, the total workload ofdownstream workstations increases virtually and therebythe probability that a workstation gets blocked increases. Tosolve this problem, we propose that this value should beequal to an upper limit parameter like M<1.


As discussed earlier, the proposed production controland scheduling model is comprised of two major modules:release module and dispatching module. The rest of thissection describes how the combination of these modulesleads to an efficient and stable production control andscheduling system in the hybrid MTS/MTO semiconductormanufacturing environment.

3.1 Release module

The major role of this module is to release products fromthe job pool into the fab at the right time and in appropriate

amount in order to achieve the production managementobjectives. Figure 1 illustrates the steps of the releasemodule in detail. Briefly, the steps of the release module are(1) prioritizing the products in the job pool and (2)examining the release conditions and release possibility.The release module performs these two steps concurrentlyand continuously in the course of time. At first, the releasemodule prioritizes the releasing products in the job pooland determines the sequence of them. Then, it examines allrelease conditions. If a release condition is actualized, itforms a set of products in the job pool that are eligible forrelease, called feasible set. Finally, it examines the release

No No

Yes

No

Finish

No

Have all products in the feasible set been

examined?

Yes Is with release of product a workstation becomes

blocked?

Release the product

Update the feasible set and fab workload

Don’t release

Examining the product with the next priority in feasible

set

Examining the release of the product with the highest priority in feasible set

Yes

Is the feasible set empty?

Forming the set of products in the job pool whose head

workstation is this starving workstation as the feasible set

Yes


Forming the all products in the job pool as the feasible set

No Is the total workload of potential bottleneck

workstation, photolithography, less than the predetermined

value?

Yes

Yes

No

Yes


Yes

Forming the set of urgent products in the job pool as the feasible set

Forming the set of urgent products in the job pool whose head workstation is

this non-urgent workstation as the feasible set

Is there any workstation that all its queuing

products are non-urgent?

Determining the priority and sequence of products in the job

pool

Yes

Is there any urgent product in the job

pool?

No Is any workstation in

the shop starving?

No

Fig. 1 Different steps of therelease module


possibility of each product in order of its priority in thefeasible set. The examining process continues until none ofthe products in the feasible set can be released.

The detailed description of the release module steps is inthe next sections.

3.1.1 Determining the sequence of MTO and MTS products

To determine the sequence of products in the job pool, atfirst, it is essential to determine the priority of all productsin the job pool.

(a) Prioritizing MTO products: the critical ratio (CR) rulepresented by Blackstone et al. [4] is used to calculatethe priority of MTO products:

CRi ¼ di � TnowCTi

: ð3Þ

The priority of MTO products increases as CR decreases.In Eq. 3, di is the due date of MTO product i, Tnow is thepresent time, and CTi is the predicted cycle time of MTOproduct i. If CRi≤1, the product i is urgent otherwise it isnonurgent. Since the determination of cycle time values isassociated with the fab workload, it cannot be determinedexactly. Hence, this value is estimated by historical data orestimated by successively running the presimulations.

(b) Prioritizing the MTS products: The priority of MTSproducts is determined by the following equation:

CRj ¼ WIPj;fabPWIPj;fab

ð4Þ

where the higher CR value is, the less priority is. In Eq. 4,WIPj,fab and PWIPj,fab represent the present amount of WIPof MTS product type j in the fab and the planned amount ofWIP of MTS product type j in the fab, respectively.

This prioritization rule is based on the CONWIP policywhich aims to keep the appropriate level of WIP of eachMTS product in the fab to meet the demand. As the demandfor a MTS product is met by the WIP in the fab, the amount

of WIP in the fab should be controlled exactly. Forexample, if the value of Eq. 4 is less than one, there isshortcoming of WIP in the fab. This leads to the decrease inthe utilization of resources and also service level infulfilling the demand. Thus, the release priority of therespective MTS product should be increased to prevent theWIP starvation in the fab. Also, if the value of this equationis more than one, there is WIP congestion in the fab. Thus,the capital-intensive resources in the fab are utilized byMTS products meaninglessly while these resources can beutilized by more important MTO products. Moreover, theWIP congestion may result in the lead time syndromephenomenon. Therefore, the release priority of this MTSproduct should be decreased to prevent the WIP congestionin the fab.

Figure 2 shows the prioritizing logic of MTS products inthe job pool for release. As shown in Fig. 2, the releasemodule determines the priority of MTS product j with threelayers with respect to its WIP state in the fab. In this regard,the release module dynamically monitors the amount ofWIP of product j and compares it with the planned one todetermine the priority. As it is shown later, the plannedvalue for amount of WIP in the fab for each MTS product iscalculated based on the demand rate of each MTS product.If CRj≤K≤1, the product j is urgent; otherwise, it isnonurgent. K is a constant parameter determined byproduction management which shows the importancedegree taken into account for producing MTS productsrather than MTO products. Notice that other products inFig. 2 represent all products except MTS product type j. Inother words, other products include all MTO and MTSproducts except MTS product type j.

By identifying urgent and nonurgent products for MTSand MTO products, the next activity is to sequence them inthe job pool. In this regard, we divide all existing productsinto four queues including: urgent MTO products in queue1, urgent MTS products in queue 2, nonurgent MTOproducts in queue 3, and nonurgent MTS products in queue4. The priority of queues is queue1 > queue2 > queue 3 >queue 4. Since MTO products are more profitable for the

Priority of MTS

Product j

PL WS Photolithography workstation

MTS product j

Other products

Release

Job pool

Releaser

Fab

Warehouse

Sale

Market demand of MTS product j

Exit

WIPj

fab

PL WS WS (1) PL WS WS (n)

WIPj

layer (3) WIPj

layer (2)WIPj

layer (1)

Fig. 2 Determination of priorityof MTS product j in the job poolfor release


company, we place urgent and nonurgent MTO productsprecedent urgent and nonurgent MTS products, respectively.In each queue, products are sequenced based on their CRvalues. In case of tie in MTS queues, the value of CRj,layer1

calculated from Eq. 5 determines the sequence:

CRj;layer1 ¼ WIPj;layer1PWIPj;layer1

: ð5Þ

Equation 5 determines the priority of MTS product jwith respect to the amount of its WIP in its first layer. Thepriority of a typical MTS product j increases with decreasein CRj,layer1 value. In Eq. 5, WIPj,layer1 and PWIPj,layer1represent the present amount of WIP of MTS product type jand the planned amount of WIP of MTS product type j inits first layer, respectively. WIPs of the next layers and thefulfillment of future demands highly depend on the amountof WIP in the first layer. In fact, the first layer for eachMTS product plays the role of WIP supplier for the nextlayers of that product. Therefore, the amount of WIP ofeach MTS product in its first layer should be controlled toprevent from WIP starvation and congestion in this layer. Ifthe value of Eq. 5 is less than one, it indicates that there isWIP shortage in the first layer which leads to the WIPshortage in the next layers and thereby inability to meet thefuture demands. Therefore, the release priority should beincreased to prevent the more WIP shortage in the firstlayer. On the other hand, if the value of Eq. 5 is more thanone, there is WIP congestion in the first layer. WIPcongestion means that the capital-intensive resources inthe fab are utilized by MTS products meaninglessly whilethese resources can be utilized by more important MTOproducts. Thus, the release priority should be decreased toprevent from more WIP congestion in the first layer.Therefore, in case that the values of Eq. 4 for two MTSproduct in a queue (queue 2 or 4) are the same, the productwith the less value of Eq. 5 has more priority for release. Incase of tie again in MTS products queues (queues 2 and 4)and in case of tie in MTO products queues (queues 1 and3), the shortest remaining processing time (SRPT) ruledetermines the sequence. SRPT rule leads to the workloadbalancing because a product with shorter total processingtime spends less time in the shop floor [8]. Furthermore, itactivates the release conditions sooner because the releaseconditions are activated whenever the workload of the fabbecomes under a certain level. As with SRPT rule, aproduct with shorter total processing time spends less timein the shop floor; therefore, the fab workload becomes lessthan a certain level sooner. If tie takes place in each queue(queues 1, 2, 3, and 4), the product with minimum sum ofprocessing times in the potential bottleneck, i.e., photoli-thography workstation, is released first. Otherwise, first-in-first-out (FIFO) determines the sequence. Figure 3 showsthe products sequencing in the job pool.

3.1.2 Releasing MTO and MTS products into the fab

After sequencing the products in the job pool, the next stepis to determine when and which products can be released.These decisions are taken by defining several releaseconditions. The proposed release conditions are based onthe real-time state of the fab workload. When the fabworkload is under a certain level, the release conditions areactivated and the possibility of releasing the products fromthe job pool is examined. These release conditions areexamined continuously in the course of time to react to theworkload variation in the shop floor. It is noted that foreach of these conditions, the release of the products takesplace only when none of the workstations in the fab getblocked because of this release. The release conditions areas follows:

& If a product in the job pool becomes urgent: In this case,the respective urgent product should be released inorder to achieve the on-time delivery for MTO productsand high production achievement ratio for MTSproducts. All of urgent products are placed in thefeasible set. If none of the workstations gets blockedwith release of the product with the highest priority inthe feasible set, this product is released. Otherwise, therelease of the second high-priority product in the fea-sible set is examined. If a product is released, the totalworkload of all workstations and the sequence ofproducts in the job pool are updated and this releaseprocess repeats for other products in the new feasibleset until all products in the feasible set are examinedand none of them are eligible to release. Due to theimportance of release of urgent products in reaching themanagement objectives, the release probability for theseproducts should be increased. To do so, we consider anallowance parameter, γ, which allows the workload fora workstation exceeds LL up to γLL to increase thechance for releasing the urgent products. In otherwords, in this release condition only when the totalworkload of a workstation exceeds the (1+γ)LL, thisworkstation gets blocked. γ is a positive parameter thatis determined by high-level production managementwith respect to the shop conditions such as existingproduction capacity and the amount of productioncapacity that can be added to production systemthrough overtime and outsourcing. Therefore, consider-

More priority

Urgent MTO

Urgent MTS

Non-urgent MTO

Non-urgent MTS

Fig. 3 Sequencing the products in the job pool for release


ing this parameter increases the probability of fastrelease of urgent products. Notice that this parameter isjust considered for this release condition.

& If all of the products in the queue of one workstation arenonurgent: This release condition is based on a pull-type approach to prevent from the starvation and theidleness of the head workstations, i.e., the workstationsrelated to first step of products. Here, the feasible setincludes the urgent products in the job pool that theirhead workstation is the respective workstation. Theprocedure of checking the release of products in thefeasible set is the same as the above release condition.

& If a workstation is starved: Here, the set of products inthe job pool that their head workstation in process routeis the corresponding workstation forms the feasible set.The procedure of examining the possibility of releasingthe products in the feasible set is the same as theprevious release conditions. This release condition isbased on the pull-type approach which results in higherutilization, reduction in waiting time in the job pool(pool time) or total lead time, and the smooth andbalanced workload in the fab.

& If the total workload of potential bottleneck work-stations is less than the predetermined value: Thisrelease condition is based on TOC approach. In fact,this exploits the benefits of two well-known releasepolicies which act based on TOC approach, SA, andCONLOAD. By controlling the bottleneck utilization,SA controls the throughput and utilization of themanufacturing system and CONLOAD provides thesmooth throughput, especially in varying product-mixenvironment. Also, Land and Gaalman [22] stated thatthe potential bottleneck workstations in job shopenvironments should have equal workload value oftheir load limit. This leads to the decrease in variancesof queue length in the workstations (higher stability)and also increase in utilization. Since the photolithog-raphy workstation is mainly considered as the potentialbottleneck in the semiconductor manufacturing systems,this release condition is applied for this workstation. Inthis release condition, all products in the job pool areplaced in the feasible set. The procedure of checking therelease of products in the feasible set is the same as theabove release conditions.

It should be noted that the first three aforementionedrelease conditions are based on the work of Ebadian et al.[8]. As the priority of a MTS product is related to theamount of its WIP in the fab, the release of any MTSproduct into the fab changes this priority. Thus, besides thechange in the workload of the fab, the priority of MTSproducts changes after each release attempt. As concludedfrom different release conditions, it is possible that the

lower priority products can be released into the fab insteadof higher priority products. As a result, there is always thepossibility of release of MTS products with lower priorityinstead of MTO products with higher priority in eachrelease condition. This fills the gap between the totalworkload and LL in each workstation and balances theworkload of fab. It also keeps the workload in a fairlyconstant level which decreases the idleness and creates amore reliable estimate of lead time and cycle time [22].

3.2 Dispatching module

The flow of the products in the fab is based on the applieddispatching rules in each workstation. To dispatch theproducts in each workstation, the priority of MTS and MTOproducts in the queue should be determined and whenever amachine becomes idle, the product with the highest priorityis dispatched to this idle machine. Therefore, the prioritiz-ing and sequencing the products in the queue of eachworkstation is the only decision that should be made in thedispatching module. Kingsman [21] and Land and Gaalman[22] stated that the dispatching rule is not as effective as therelease method for balancing the workload and keeping thequeue length short. In this paper, however, the proposeddispatching module tries to create a balanced productionline by imposing WIP balancing in each layer and betweentwo adjacent layers of MTS products. The different steps ofthe proposed dispatch module are depicted in Fig. 4.

3.2.1 Determining the sequence of MTO and MTS products

To determine the sequence of products in the queue of eachworkstation, it is essential to determine the priority of allproducts in that queue.

(a) Prioritizing MTO products: The formula presented byChang et al. [6] is used here to determine the priorityof MTO products in the queue of a workstation asfollows:

PDPSi;y ¼ di � di � rið Þ �

PFSis¼yþ1

PTi;s

CTi

0BBB@

1CCCA ð6Þ

cri;y ¼ PDPSi;yPTi;y

: ð7Þ

To deliver a MTO product in its promised due date, it isessential to perform the process of each step in the righttime. In this regard, Eq. 6 is used to determine the due dateof MTO product i in step y with respect to its due date. In


Eq. 6, the PDPSi,y is the planned due date of MTO product iin step y, di is the due date of MTO product i, ri is therelease time of MTO product i, PTi,s is the processing timeof step s of MTO product i, CTi is the predicted cycle timeof MTO product i, and FSi is the final step (the last step) ofMTO product i in its process route. Equation 7 is criticalratio rule used for determining the priority of MTO producti. If cri,y≤1, this product is urgent; otherwise, it is anonurgent product.

(b) Prioritizing MTS products: The following formula isused to determine the priority of each MTS product inthe queue of the workstation of step y in all layersexcept the last layer and the last photolithography step:

crj;y ¼ WIPj;yPWIPj;y

� ��CWIPNSj;yPCWIPNSj;y

� �ð8Þ

where in Eq. 8, the WIPj,y represents the present amount ofWIP of MTS product type j in the workstation of step y inits process route, PWIPj,y is the planned amount of WIP ofMTS product type j in the workstation of step y in itsprocess route, CWIPNSj,y is the present cumulative amountof WIP of MTS product type j in the workstations of thenext steps of y until the first step in the next layer orworkstations of downstream steps in the layer, andPCWIPNSj,y is the planned cumulative amount of WIP ofMTS product type j in the workstations of the next stepsof y until the first step in the next layer or workstations of

downstream steps in the layer. For photolithography steps,CWIPNSj,y and PCWIPNSj,y are the existing WIP of MTSproduct j in the next layer and the planned amount of WIPof MTS product j in the next layer, respectively. Therelation between the priorities and cr values is straight. Thisprioritizing policy is based on the pull-type approach whichaims at balancing and keeping the appropriate amount ofWIP in each layer.

The numerator tries to prevent from the congestion andstarvation of WIP in a workstation. The denominator triesto prevent from the congestion and starvation of WIP indownstream workstations in the layer. For example, if thedenominator is less than one, there is the WIP shortage orstarvation in the downstream workstations in the respectivelayer. Thus, the priority of product should be increased toprevent from more WIP starvation. Also, if the denominatoris more than one, there is WIP congestion in thedownstream workstations in the respective layer. Therefore,the priority of product should be decreased to prevent frommore WIP congestion. Therefore, this prioritizing policybalances the amount of WIP in each layer. Also, inphotolithography workstations, except for the workstationof the last photolithography step, the denominator of Eq. 8monitors the amount of WIP in the next layer. Thus, thisprioritizing policy for these workstations tries to preventfrom starvation and congestion of MTS products in the nextlayer. Therefore, the proposed prioritizing policy balancesthe amount of WIP between two adjacent layers and keeps

Place it in the queue 3 (non-urgent)

Place it in the queue 1 (urgent)

Place it in the queue 2 (urgent)

Place it in the queue 4 (non-urgent)

Dividing the products in the queue of

workstation into MTS and MTO

MTO

MTS Is the product MTO or MTS?

Is its cr >1?

Yes

No Is its cr >1?

Yes No

Determining the sequence of queue 3




Dispatching the product with the highest

priority based on queue1>2>3>4.

Fig. 4 Different steps of thedispatch module


the appropriate amount of WIP in each layer. In otherwords, the balance in amount of WIP between layers isactualized by dispatching policy in the photolithographysteps.

In general, the priority of MTS products is determinedwith respect to the dynamic changes of WIP in the fab tokeep and balance the amount of WIP in each layer. Figure 5shows the prioritizing process for a typical MTS product jin the workstation of step y in a layer except for the lastlayer and the last photolithography step. When a machine inthis workstation becomes idle, the dispatching moduledetermines the priority of product j with respect to thevalues of WIP in the workstation and in downstreamworkstations in the layer.

For the last layer workstations and workstation of thelast photolithography step, as the daily demand or demandrate is met by the WIP in this layer, the finished goodsinventory (FGI) in the warehouse and the daily demandshould be involved in prioritizing process. In this regard,the following formula is presented:

crj;y ¼ WIPj;yPWIPj;y

� ��CWIPNSj;y þ FGIjPCWIPNSj;y þ DDj

� �: ð9Þ

In Eq. 9, definitions of WIPj,y, PWIPj,y, CWIPNSj,y, andPCWIPNSj,y are the same as those of Eq. 8. The FGIj is thecurrent finished goods inventory of MTS product type j andthe DDj is the daily demand of MTS product type j. Larger crvalue represents higher priority. Like previous prioritizingrule, this policy is also pull type which balances the amountof WIP in the last layer and finished goods inventory in thewarehouse. Similar to Eq. 8, the numerator hinders thecongestion and starvation of WIP in the workstation andthe denominator controls the amount of WIP in the last layer.Also, the denominator balances the amount of WIP in thislayer and the finished goods inventory in the warehouse. Forexample, if the denominator is less than one, there is WIPshortage in downstream steps in the last layer and/or shortagein FGI in the warehouse. Thus, the priority and flow ofproduct should be increased to augment the FGI. Also, ifthe denominator is more than one, there is WIP congestion inthe downstream steps in the last layer and/or much FGI in thewarehouse; therefore, there is sufficient WIP in the last layer

and/or FGI in the warehouse to meet the demand. Therefore,the priority and flow of product should be decreased. In fact,this prioritizing policy attempts to keep the amount of WIP inthe last layer and FGI in an appropriate level. As in the lastphotolithography step, Eq. 9 considers the sum of WIP in thelast layer and FGI, this prioritizing policy tries to preventfrom starvation and congestion in this layer and warehouse.Also, the prioritizing rule in this step tries to balance betweenthe FGI and WIP state in the last layer and in the previouslayer.

Figure 6 shows the prioritizing process of the MTSproduct j in the workstation of step y in its last layer and inthe workstation of the last photolithography step. When amachine in this workstation becomes idle, the dispatchingmodule determines the priority of product j with respect tothe values of WIP in the respective workstation andworkstations of downstream steps and FGIj in the ware-house. It should be noted that in both of Eqs. 8 and 9 if cr≥1, the product is urgent; otherwise, it is nonurgent.

After prioritizing the products in the queue of aworkstation, the sequence of these products should bedetermined. Like release module, we divide the products inthe queue of the workstation into four queues of 1, 2, 3, and4. Queues 1, 2, 3, and 4 include urgent MTO, urgent MTS,nonurgent MTO, and nonurgent MTS products, respective-ly. The priority of queues in dispatching module is queue1 > queue 2 > queue 3 > queue 4. In each queue, theproducts are sequenced based on the aforementioned Eqs. 8and 9. In case of tie, SRPT rule determines the product withhigher priority. As stated by Blackstone et al. [4], SRPT leadsto high throughput, workload leveling, and on-time delivery.If tie takes place again, the product with less cumulativeprocessing time in the remaining potential bottleneck step,photolithography step, gets higher priority. Based on the TOCconcept, this rule increases the throughput, on-time delivery,and workload balancing in the bottleneck workstation andconsequently in the fab. Otherwise, FIFO determines thesequence.

To determine the values of PWIPj,y, PCWIPNSj,y,PWIPj,layer1, and PWIPj,fab, the flow time and demand rateshould be known. It is assumed that average flow time of eachproduct can be estimated from historical data or presimula-tions runs. Also, as mentioned in the inventory literature, the

WIPj in the WS (y) Priority

of MTS product j

MTS product j

Other products


PL WSWS (y+1) WS (y)

Dispatcher (y)

Cumulative WIPj in the next steps of WS (y)

(CWIPNSj,y)

Fig. 5 Determination of priorityof MTS product j in worksta-tions except the workstation ofthe last photolithography stepand workstations of the lastlayer


demand rate is mostly assumed to be normal as in Silverand Peterson [38] and Hax and Candea [15]. In this paper,we assume that the demand in each day is constant andobeys from the normal probability distribution function.

As shown in Fig. 7, since the daily demand for MTSproducts is based on the normal distribution function withmean μ and standard deviation σ, N(μ,σ), the demand forthe time interval of h follows a normal distribution functionof (hμ,√h σ). Thus, the planned cumulative amount of WIPin the workstations in which the flow time of that product isless than h is:

PCWIPj;h ¼ h� mj þ Ka �ffiffiffih

p� s j ð10Þ

where Kα represents the 100(1−α)% point of normaldistribution function. In fact, production management plansto meet the demand in 100(1−α)% times. Higher value ofKα increases the planned WIP, throughput, and thefulfillment of the demands for MTS products. Giving thevalues of h1 and h2 in Eq. 10, the absolute difference ofthe two resulted values for PCWIPj,h indicates the cumu-lative amount of WIP of product type j in the workstationsin which the flow time is between h1 and h2. For example,if h1 is the flow time of product j in an operation in a layerand h2 is the flow time in the first operation of the nextlayer, this difference shows the PCWIPNSj,y. Moreover, ifh2 is the flow time of the next step, this subtraction resultsin PWIPj,y. Also, if h1 represents the predicted cycle time ofproduct type j and h2=0, the difference calculates PWIPj,fab.If h1 is the flow time of product j in the first step in layer t

and h2 is the flow time in the first step in the next layer, thissubtraction shows PWIPj, layer t.

4 The simulation experiments

In this section, the validity and practicability of the pro-posed production control and scheduling model is demon-strated through a number of simulation experiments. Toevaluate the performance of the proposed release anddispatching modules, we conduct some numerical experi-ments using simulation studies. In this regard, a smallvirtual fab with 14 workstations is simulated by EnterpriseDynamics 7.0 studio simulation software (see “Appendix”).In this virtual fab, workstation 6 is considered as thephotolithography workstation. Among these 14 worksta-tions, ninth and 11th workstations are batch processing. Forbatch workstations, we use the minimum batch size 6 fordispatching. This small fab produces three MTS products(I, J, K) and eight types of MTO products (A–H). At t=0,all machines are assumed to be idle and finished goodsinventory is zero.

For product mix, two scenarios are considered. In thefirst scenario, I, J, and K have the daily demand withnormal probability distribution with mean and standarddeviation following uniform distribution of [10, 14] and[2, 4], respectively. MTO products enter the job pool withPoisson rate of λ=5 orders per day. In the second scenario,the daily demand for MTS products have normal probabil-ity distribution with mean and standard deviation following

Dispatcher (y)

Finished goods inventory (FGIj)

MTS product j

Other products


WS (n) WS (y)

Priority of MTS

product j

PL WS WS (y+1) Exit

Market demand

Daily demand (DDj)

Warehouse

WIPj in WS (y) Cumulative WIPj in the

next steps of WS (y) (CWIPNSj,y)

Fig. 6 Determination of priorityof MTS product j in worksta-tions of the last layer and in theworkstation of the lastphotolithography step

Fig. 7 Calculation of plannedamount of WIP of MTS productj in the area that the flow time isthe less than h


uniform distribution of [20, 24] and [4, 8], respectively.MTO products enter the job pool with Poisson rate of λ=5.5 orders per day. The planning period for simulation is150 days with the first 60 days as the warm up and eachcase replicates 30 times to test the hypothesis statistics.

The total processing time for each product is shown inTable 1. The due date for each MTO order is calculated by:

di;k ¼ Ei;k þ TPTi � R a; bð Þ ð11Þwhere di,k is the due date of kth product type i, Ei,k is thearrival time of kth product type i into the job pool, TPTi istotal processing time of product type i, and R(a, b) is theuniform random distribution number between a and b thatactually roles as the actual to theoretical cycle time in thesemiconductor plants [29]. In this simulation study, a and bare 2.5 and 5, respectively. Moreover, the values of Kα, K, M,and γ are 3, 0.8, 0.95, and 0.05, respectively. Table 2 showsthe considered performance measures. As shown in Table 2,separate performance measures are considered and comparedfor MTO and MTS products.

Based on Table 2 for MTS products, the followingperformance measures are considered:

1. Cycle time: The cycle time of a product is the elapsedtime between the product being released into the faband its departure from the fab. The mean and standarddeviation of the cycle time indicate the workloadbalancing in the shop floor. In fact, since the workloadand the queue length of each workstation is undercontrol, the cycle time for each product should be short

and reliable. On the other hand, the less standarddeviation of cycle time means that the change of valueof the fab workload is small. Moreover, the lessstandard deviation of cycle time indicates that thevalues of the prediction of flow time and meeting thedemands can be more reliable.

2. Production achievement ratio: The production achieve-ment ratio is defined as the minimum of {1, throughput/DD} in which DD is the daily demand [23]. This showsthe ability of the company to meet the demands. Highermean of production achievement ratio leads to the highersale revenue and the customer satisfaction. Also, lessstandard deviation of production achievement ratio is anindicator of higher reliance of customers on the companyfor future purchases.

3. Throughput rate: Higher throughput rate indicates higherproduction volume or utilization and also more ability ofproduction system in utilizing the production resources.High value of mean throughput rate shows the decrease inproduction costs. On the other hand, the mean andstandard deviation of throughput rate can be applied bythe top management for evaluating the ability of theproduction system in using the production resources forfuture production planning and decreasing the costs.

4. Finished goods inventory: Finished goods inventory is anindicator for appraising the holding inventory costs as avery important performance measure in MTS systems.

5. WIP in the fab: The amount of WIP in the fab indicatesthe workload balancing in the shop floor. In fact, thisindicator measures the ability of the proposed produc-tion control and scheduling for controlling the amountof WIP in the shop floor in an optimum level.

6. Inventory turns: In semiconductor industries, there areseveral stages from procurement of wafers to deliver thefinished goods to customer that can be regarded as asupply chain. Since the production stage of semiconduc-tor products takes more time than other stages in supplychain, this stage plays an important role in supply chainmanagement. Thus, the strength of this production stagemay be considered as the strength of supply chain. One ofthe important measures to evaluate the strength ofproduction unit in the supply chain is inventory turns.Inventory turns for a typical product is defined as theannual sales of the respective product divided by theaverage quantity on hand [17]. For example, a productwhich is sold 60 units in a year with an averageinventory of ten units has an inventory turns (turnover

Table 2 The performance measures

Product type

MTO MTS

Mean and standard deviationof cycle time

Mean and standard deviation ofcycle time

Mean and standard deviationof total lead time

Mean and standard deviation ofproduction achievement ratio

Mean and standard deviationof on-time delivery

Mean and standard deviation ofthroughput rate

Mean and standard deviation ofthe finished goods inventory

Mean and standard deviation ofWIP in the fab

Mean and standard deviation ofinventory turns

Product type MTO MTS

A B C D E F G H I J K

TPT 122 142 99 112 87 132 128 151 48 75 83

Table 1 Total processing time(hours) of each product


ratio) of 60/10=6. The higher value of this measureshows the efficient performance of the production unit inthe whole supply chain.

For MTO products, the major performance measures areas follows:

1. Cycle time: Definition of this measure is similar to thatof MTS but the only difference is that for MTOproducts; the less standard deviation of cycle time meansthat the determination of due date and price can be morenegotiable. In other words, the less standard deviation ofcycle time increases the bargaining ability for determin-ing the due date and price of each MTO product.

2. Total lead time: The total lead time is the interval timebetween the arrival of a MTO product into job pool andits departure from the shop floor. It is one of the key

factors for fast growth and high income and profits forthe enterprises in the competitive market [25]. Thisperformance measure shows the balanced workload andfast workload flow in the shop floor that is an importantfactor to control the production in the shop floor.Besides the workload balancing, this measure is anindication of pool time [22]. Less total lead time andpool time indicates the ability of production control andscheduling model for quick releasing and dispatchingthe MTO products.

3. On-time delivery: On-time delivery is the most impor-tant measure in evaluating the customers’ satisfaction.Also, it shows the holding costs or tardiness penalties.Therefore, this performance measure by itself can showthe other important performance measures such astardiness.

Table 3 Statistical analysis of performance measures for MTS products (scenario 1)

Performance measure Models Mean Duncan test (mean) Standard deviation Duncan test (SD)

Cycle time (hour) Proposed model 119.3 A 9.5 A

Chang et al. [6] 139.6 CD 20.4 B

Wu et al. [44] 122 A 13.9 AB

SA*-SRPT 151.5 D 34.1 C

SA*-CR 155.5 DE 22.1 BC

Production achievement ratio (%) Proposed model 96.2 A 3.7 A

Chang et al. [6] 68.4 C 17.4 C

Wu et al. [44] 75.3 B 12.2 B

SA*-SRPT 61.9 D 24.7 D

SA*-CR 87.3 AB 14.2 B

Throughput rate (lot/week) Proposed model 136 A 8.9 A

Chang et al. [6] 85.6 DE 25.2 C

Wu et al. [44] 99.1 C 14.6 B

SA*-SRPT 83 E 30.5 D

SA*-CRq 125.8 B 26.9 C

Finished goods inventory (lot) Proposed model 5.3 DE 1.1 A

Chang et al. [6] 2.4 B 1.5 AB

Wu et al. [44] 4.2 CD 4 E

SA*-SRPT 1.6 A 1.5 AB

SA*-CR 4.2 CD 1.8 B

WIP in the fab (lot) Proposed model 41.5 A 6.1 A

Chang et al. [6] 73.1 E 17.2 C

Wu et al. [44] 44.6 AB 12.4 B

SA*-SRPT 75.2 E 31.7 E

SA*-CR 41.8 A 28.6 D

Inventory turns Proposed model 7.5 A 0.6 A

Chang et al. [6] 3.3 D 2.1 E

Wu et al. [44] 6.2 B 0.8 AB

SA*-SRPT 2.1 DE 0.7 A

SA*-CR 5.3 BC 1.4 CD


To validate the proposed model, the results of applyingfour well-known production control and scheduling meth-ods in the literature are compared with the results of theproposed model. These production control and schedulingmethods are the models proposed by Chang et al. [6], Wu etal. [44], SA*-SRPT, and SA*-CR. The four benchmarksoutperform other production control and scheduling meth-ods either closed-loop or open-loop in terms of the relatedperformance measures [44]. It should be noted that SA* is amodified version of SA release model proposed by Wu etal. [44]. The results of comparison of various methods areillustrated in Tables 3 and 4 for scenario 1 and in Tables 5and 6 for scenario 2. The Duncan’s multiple range test isapplied to rank these models. The models are graded intofive levels, namely, A, B, C, D, and E in descending order.

The results of Tables 3, 4, 5, and 6 show that theproposed production control and scheduling model gener-ally outperforms the alternative excellent methods in termsof performance measures. Tables 3 and 5 listing theperformance of MTS products in two scenarios indicatethat the proposed model generally is superior to othermethods in terms of mean and standard deviation of cycletime, production achievement ratio, throughput rate, WIP inthe fab, inventory turns, and standard deviation of finishedgoods inventory. However, the proposed model has nosuperiority in terms of mean of finished goods inventory toother methods. The reason is that other methods place theMTS products in the second rank after MTO products torelease; thus, most of the production capacity is dedicatedto producing the MTO products. As a result, FGI in thesemethods is averagely less than the proposed model. Whilethe objective of the proposed model for production of MTS

products is to meet the demand. Thus, the productionachievement ratio and mean FGI are higher than othermethods. Also, since the proposed model releases MTSproducts based on pull-type approach and tries to keep WIPlevel in the fab in a constant level, the standard deviation ofthe finished goods inventory in the proposed model is lessthan almost all benchmarking methods.

Tables 4 and 6 show the results of comparison of theproposed production control and scheduling model forMTO products with other models. The results of theseTables indicate the superiority of the proposed model onother models in terms of mean and standard deviation ofcycle time, total lead time, and on-time delivery. Also, bycomparing the results of two scenarios, it can be concludedthat although the number of acceptance of MTO productsand the demand of MTS products in scenario 2 are morethan those of scenario 1, the proposed model shows morereliability than other models in terms of changing in theproduct mix. As mentioned before, this reliability of theproposed production control and scheduling model originatesfrom applying the WLC approach in controlling theworkload of each workstation and release conditions whichare based on the workload leveling and smoothing principle.On the other hand, the proposed model considers a job poolthat absorbs the external dynamics. Thus, the dynamics isdamped through job pool even by changing product mix.

5 Conclusions

Semiconductor manufacturing systems have been alwaysconsidered as one of the most complex production systems

Table 4 Statistical analysis of performance measures for MTO products (scenario 1)



Chang et al. [6] 233 B 26.4 BC

Wu et al. [44] 224.8 B 23.2 B

SA*-SRPT 289.2 E 41.1 D

SA*-CR 240.7 BC 33.1 CD

Total lead time (hour) Proposed model 359.7 A 10.1 A

Chang et al. [6] 396.9 B 29.3 D

Wu et al. [44] 390.4 B 28.9 C

SA*-SRPT 478.7 E 54.9 E

SA*-CR 424.1 CD 50.2 E

On-time delivery (%) Proposed model 89.5 A 2.4 A

Chang et al. [6] 81.3 AB 12.3 BC

Wu et al. [44] 89.4 A 14.6 C

SA*-SRPT 58.1 DE 18.6 CD

SA*-CR 79.7 B 17.9 C


to plan and control. This is due to the specific character-istics of these systems such as the existence of reentrancycharacteristic, long process route of each product, productvariety, uncertainty, constant device miniaturization, chang-ing technologies, and also the existence of both MTS andMTO products. With respect to the importance of thesemiconductors in electronic industries, the academics andpractitioners have been attempting to improve the planning,control, and scheduling of such systems. In this regard, wedeveloped a new production control and scheduling modelfor this system to meet the management objectives of MTOand MTS products.

The proposed model includes two major modules:release and dispatching modules. The release module aimsat releasing products from the job pool at the right time andin appropriate amount. The dispatching module deals withthe sequencing the products in each workstation to reach

short and reliable delivery date for MTO products and WIPbalancing for MTS products in each layer to achieve highthroughput rate and production achievement ratio.

The proposed model handles the existing dynamics andirregularities in the hybrid MTS/MTO semiconductor man-ufacturing system by:

& Forming the job pool which controls and absorbs theexternal dynamics such as changes in demands of MTSproducts and stochastic arrival of MTO products

& Releasing the products from the job pool into fab withrespect to fab workload. Once the fab workload is undera certain level, the release conditions are activated andthe possibility of the release of products in the job poolis examined. Also, release prioritizing of MTS productsis performed based on the dynamic transaction with theamount of WIP in the fab.

Table 5 Statistical analysis of performance measures for MTS products (scenario 2)



Chang et al. [6] 184.3 CD 32.6 CD

Wu et al. [44] 137.9 A 21.6 BC

SA*-SRPT 206.8 D 59.7 E

SA*-CR 245.9 E 37.5 D

Production achievement ratio (%) Proposed model 87.5 A 5.3 A

Chang et al. [6] 65.3 D 23.5 CD

Wu et al. [44] 67.2 CD 21.3 C

SA*-SRPT 56.1 E 30.1 DE

SA*-CR 79.3 B 21.5 C

Throughput rate (Lot/week) Proposed model 144.7 A 13.8 A

Chang et al. [6] 79.4 E 27.2 C

Wu et al. [44] 94.8 CD 21.6 B

SA*-SRPT 83 E 45.2 E

SA*-CR 127.1 BC 32.1 CD

Finished goods inventory (lot) Proposed model 7.6 E 1.7 AB

Chang et al. [6] 2.8 B 1.1 A

Wu et al. [44] 4.5 C 2.3 C

SA*-SRPT 1.4 A 1.7 AB

SA*-CR 4.1 D 2.2 C

WIP in the fab (lot) Proposed model 55.2 A 9.1 A

Chang et al. [6] 80.2 E 21.5 C

Wu et al. [44] 57.3 AB 15.8 BC

SA*-SRPT 72.9 E 43.8 E

SA*-CR 54.8 A 38.5 E

Inventory turns Proposed model 6.9 A 1.5 A

Chang et al. [6] 3.4 DE 2.7 D

Wu et al. [44] 6.4 AB 2.4 CD

SA*-SRPT 2.1 E 1.9 AB

SA*-CR 5.5 C 3.4 E


& Prioritizing the MTS products for dispatching in thelayers except for the last layer and except the lastphotolithography workstation based on the dynamicchanges of WIP in the fab. Moreover, prioritizing theMTS products for dispatching in the last layer andthe last photolithography workstation is carried outby a dynamic relation with the change of WIP statein the last layer, demand rate, and finished goodsinventory.

& Controlling the dynamic changes of fab workload byapplying a new workload conversion coefficient

The simulation study conducted in this research showsthe efficiency and applicability of the proposed model as a

dynamic production control and scheduling method. Thesimulation experiments include two scenarios and fourwell-known benchmarking production control and sched-uling methods. The obtained results reveal that the pro-posed model outperforms the four benchmarking models interms of performance measures for both MTO and MTSproducts.

In summary, the main advantages of the proposedproduction control and scheduling model compared to theprevious models are as follows:

& The proposed production control and scheduling modelworks in a dynamic manner and controls the productionof both MTS and MTO products strictly.

Table 6 Statistical analysis of performance measures for MTO products (scenario 2)



Chang et al. [6] 246.1 C 33.4 C

Wu et al. [44] 233.1 B 33.1 C

SA*-SRPT 322.7 E 55.8 E

SA*-CR 267.9 D 42.1 D

Total lead time (hour) Proposed model 374.9 A 16.2 A

Chang et al. [6] 420.1 BC 38.4 CD

Wu et al. [44] 414.2 B 41.9 CD

SA*-SRPT 522.8 E 61.9 E

SA*-CR 465.2 D 55.2 DE

On-time delivery (%) Proposed model 87.9 A 5.3 A

Chang et al. [6] 75.4 BC 11.3 B

Wu et al. [44] 82.9 AB 9.6 B

SA*-SRPT 52.1 E 34.5 E

SA*-CR 78.3 B 29.6 DE

Fig. 8 Model layout of thesimulation experiment


& The proposed model applies TOC reasonably along withWLC approach in the complex semiconductor manufac-turing system.

& The proposed model is superior to the previous models interms of inventory turns as a critical performance measurein supply chain management.

& The proposed model applies a new adjusted dynamicworkload conversion coefficient.

& The proposed model applies the WLC method in con-trolling the workload of the hybrid MTS/MTO produc-tion environment.

The main direction for future research is to develop ahierarchical production planning and control (HPP) forhybrid MTS/MTO production systems such as semicon-ductor manufacturers. Since most of the production systemsare actually working in a hybrid MTS/MTO environment,the production control and planning of such systems isrecently receiving a lot of attention. By combining theproposed model as one level of the HPP with other decisionmaking levels, a comprehensive HPP structure could bedeveloped for hybrid MTS/MTO environments. This issueis on our research line. Besides the existence of pure MTSand MTO products, in some manufacturing systems, thereare some MTS products that are produced not only for saleto customers but also for using in production of some MTOproducts, i.e., MTS/MTO products. Developing the pro-duction control and scheduling model for these environ-ments can be considered as another future research.

Acknowledgments This study was supported by the University ofTehran under the research grant no. 8109002/1/02. The authors aregrateful for this financial support.

Appendix: the simulation model

In this section, a brief description of the simulation modelcoded in Enterprise Dynamics 7.0 is presented. As depicted inFigs. 8 and 9, each new accepted MTO product is first placedat the job pool by source atom. The MTS products, whichalways are produced with arrival list atom, are also placed inthe job pool. There are three warehouses for storing themanufactured MTS products. Then, they move to sink withrespect to the daily demand of MTS products. Sink plays therole of the customers’ demand. Summary record and datarecord atom are used to collect the statistics of performancemeasure. The release conditions and examination of thepossibility of release are checked by release atom.

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a developed production control and scheduling model in the semiconductor manufacturing systems with...

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