capacity coordination in hybrid make-to-stock/make-to-order production environments

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Capacity coordination in hybrid make-to-stock/make-to-order production environmentsH. Rafiei a & M. Rabbani aa Department of Industrial Engineering , College of Engineering, University of Tehran ,Tehran , IranPublished online: 14 Jun 2011.

To cite this article: H. Rafiei & M. Rabbani (2012) Capacity coordination in hybrid make-to-stock/make-to-order productionenvironments, International Journal of Production Research, 50:3, 773-789, DOI: 10.1080/00207543.2010.543174

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International Journal of Production ResearchVol. 50, No. 3, 1 February 2012, 773–789

Capacity coordination in hybrid make-to-stock/make-to-order production environments

H. Rafiei and M. Rabbani*

Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

(Received 5 July 2010; final version received 29 October 2010)

One of the most important decisions in hybrid make-to-stock/make-to-order (MTS/MTO) productionsystems is capacity coordination. This paper addresses capacity coordination of hybrid MTS/MTOproduction systems which deal with MTS, MTO and MTS/MTO products. The proposed model is developedto cope with order acceptance/rejection policy, order due-date setting, lot-sizing of MTS products anddetermining required capacity during the planning horizon. Additionally, a backward lot-sizing algorithm isdeveloped to tackle the lot-sizing problem. The proposed model presents a general framework to decide oncapacity coordination without too many limiting mathematical assumptions. The model combines qualitativeand quantitative modules to cope with the aforementioned problems. Finally, a real industrial case study isreported to provide validity and applicability of the proposed model. Having the model applied in the casestudy, considerable improvement was achieved.

Keywords: production planning; hybrid make-to-stock/make-to-order; capacity coordination; acceptance/rejection policy; due-date setting; lot-sizing

1. Introduction

One production system which has recently attracted academicians’ and practitioners’ attention is hybrid MTS/MTO. This system benefits from both pure MTS and pure MTO systems. A pure MTS production system ismanaged upon forecasts of future orders. Hence, deliverable items are processed in advance and stocked inwarehouses and then, customer orders are met with the finished products inventory. In this system, a production lineis designed for standard products and performance criteria are built upon higher fill rate, demand forecast, lot-sizing, average work-in-process, etc. (Soman et al. 2004). In contrast with the MTS systems, MTO ones deal withcustomer orders as the main issue. In other words, in an MTO production system, production is triggered when areal order is received from a customer. The criteria in MTO systems are average response time, average order delay,delivery lead-time, due dates, etc. (Soman et al. 2004). Inspired from both the above production systems, hybridMTS/MTO systems are applied to balance the two above-mentioned systems. In MTS/MTO systems, a commonsection of the line is dedicated to process MTS parts of different products and the remaining section of the lineattempts to differentiate end items upon incoming orders. To distinguish the three above-mentioned systems, theconcept of order penetration point (OPP) is utilised in Figure 1. This point specifies where the customer’s desiredspecifications influence the production value chain (Hoekstra and Romme 1992). As it is seen in Figure 1, thecustomer’s specifications are considered in different places along the production systems in MTS, MTO andMTS/MTO.

One approach which has been recently applied to the field of hybrid MTS/MTO production systems ishierarchical production planning (HPP). HPP was first introduced by Hax and Meal in the 1970s (Hax and Meal1975). By means of this approach, a decision is made through different decision-making levels with distinctattributes. For the first time, Soman et al. (2004) applied the HPP approach with three decision levels (strategic,tactical, and operational) in a system with both MTS and MTO products. In the first level, the hierarchy includesthree decisions. First, product families are formed, and then production systems of the product families and theirrelated OPP locations are decided (this level is called MTS/MTO decision). The second level, capacity coordination,is devoted to allocating capacity and MTS, MTO and hybrid orders. In this level, profitable MTO and hybrid ordersare accepted and their due dates are determined and non-profitable orders are rejected not to fill up capacity. Also,increasing capacity is decided to meet customer demands, as well as lot-sizes for MTS forecasted demands. In the

*Corresponding author. Email: [email protected]

ISSN 0020–7543 print/ISSN 1366–588X online

� 2012 Taylor & Francis

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last level, the sequence and the detailed production plan of the shop is determined in order to meet due dates and lot-

sizes which were obtained in the previous level (namely, the scheduling and controlling level). This paper addresses

capacity coordination (the second-level problem) for hybrid production systems with three kinds of products: pure

MTS, pure MTO, and hybrid MTS/MTO. To do so, the remainder of the paper is structured as follows. The next

section reviews the corresponding literature. Section 3 elaborates the proposed model comprising different steps for

different kinds of products. Validity and applicability of the proposed model is illustrated through a real industrial

case study in Section 4. Finally, Section 5 provides some concluding remarks, limitations of the proposed model and

future research directions.

2. Literature review

In the field of hybrid MTS/MTO production systems, the literature body has been dispersed to different issues of

this system since two decades ago. In comparison with MTS and MTO systems, there are a few research papers

presented in this field. The first academic research towards hybrid MTS/MTO dates back to the one by Williams

(1984). He studied a single-stage system with stochastic demands and interactions between demands and capacity

using queuing theory. Adan and Van der Wal (1998) studied effects of combining pure MTS and pure MTO

products in terms of lead-time. Arreola-Risa and DeCroix (1998) assessed the optimality condition of production

costs to choose an MTS or an MTO production system for manufacturing facilities with multiple products and

random demands. Other instances which similarly assessed shop-floor optimality conditions of manufacturing

systems include Federgruen and Katalan (1999), Mu (2001), and Tsubone et al. (2002). In a similar production

system, Gupta and Benjaafar (2004) called their considered system delayed differentiation (DD). They attempted

to answer ‘when is each system (MTS, MTO and DD) the best?’ In another research paper, Soman et al. (2006)

considered an economic lot scheduling problem in the case of MTS, MTO and MTS/MTO products. They modelled

a single-stage capacitated facility with the objective function of total cost (holding and setup) minimisation. Pricing

and lead-time negotiation were the topic of the study by Jiang and Geunes (2006). They considered a manufacturing

system devoted to MTS and MTO products. They defined MTS products as ones which met quick demands and

MTO products as ones related to the products whose customers waited to have the orders accomplished.

Rajagopalan (2002) proposed a non-linear integer program with service level constraints for an MTS/MTO

partitioning problem. He developed a heuristic procedure to solve this problem. Chang et al. (2003) also developed

a heuristic production activity control model to schedule and control wafer manufacturing in a hybrid wafer

fabrication environment (including MTS and MTO products). The main drawbacks of the analytical methods in the

above-mentioned research are fourfold. First, all models have too many assumptions. These assumptions were

posed to either simplify the models or make them compatible with some well-known models in theoretic aspects.

Second, the proposed models attempted to cope with different integrated decisions from different strategic, tactical

and operational levels. Third, the developed models had a considerable computational complexity. Therefore, they

are intractable in many cases. Fourth, the complexity of the models was not limited to solution methodologies. Their

implementation complexity made the models and their obtained results impractical. Hence, managers are not able to

comprehend and apply the models well.

System Fabrication Assembly Delivery

MTO

MTS/MTO

MTS

OPP

OPP

OPP

Figure 1. Different production systems; dotted and solid lines represent forecast-driven and customer-order-driven activities,respectively.

774 H. Rafiei and M. Rabbani

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The mentioned literature is mainly dedicated to mathematical models. In addition to this category, a new trendof qualitative research has been initiated to different issues in hybrid MTS/MTO systems since nearly a decade ago.Papers presented by Van Donk (2001) and Olhager (2003) were the first steps from this new point of view. VanDonk (2001) related the concept of production systems with the OPP by introducing eight criteria in two categories:process and stock, and product and market. Next, Olhager (2003) presented an extension of Van Donk’s proposedmodel by defining more criteria in three categories: market, product, and production. The turning point in this trendwas the HPP proposed by Soman et al. (2004). However, the drawbacks of the proposed HPP model are twofold.First, it is proposed for a system operating for MTS and MTO products and MTS/MTO products are neglected.Second, the proposed HPP is conceptual and the authors solely defined corresponding questions of every level.Therefore, lack of any decision-making models to answer defined questions has made the HPP structure lesspractical. To conquer this deficiency, Zaerpour et al. (2009) developed a fuzzy TOPSIS-AHP model to tackle thequestion of the first level (MTS/MTO partitioning). With respect to the second category of literature, someconclusions are provided. The reported research is mainly conceptual and they did not propose any decision-makingprocedure. Therefore, this research is only suitable for the introduction of hybrid production systems and is too farfrom implementation. Moreover, no attention has been devoted to shop-floor considerations.

Concluding from the literature, this paper is devoted to the second level of the HPP in hybrid MTS/MTOproduction systems. The related production systems process three kinds of products; pure MTS, pure MTO, andhybrid MTS/MTO products. The problem is tackled using both conceptual and analytical techniques. Therefore,the problem has become more tractable and more practical. Additionally, too many imposed assumptions are notconsidered to solve the problem. Generality of the developed model make it more practical and morecomprehendible to managers.

3. Proposed model

The proposed capacity coordination model is elaborated as shown in Figure 2. It is noted that input of the proposedmodel is threefold. First, product families are formed. Second, decisions are made on what production system everyproduct family follows and third, the OPP locations of the MTS/MTO product families are determined. Withrespect to Figure 2, MTO product families are separated from other product families, because MTS and MTS/MTO

MTS, MTO or

MTS/MTO?

MTO MTS, MTS/MTO

Prioritising MTO product families

Allocating initial capacity to MTO product families

Determining production values of MTS and MTS/MTO product families

Determining lot-size for MTS and MTS/MTO product families

Accepting/rejecting MTO and MTS/MTO orders

• Accepted MTO and MTS/MTO product families

• Lot-sizes of MTS and MTS/MTO product families

• Required capacity (overtime capacity)

Prioritising MTS/MTO product families

OPP for MTS/MTO product families

Figure 2. The proposed capacity coordination model.

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product families are processed upon forecasts. In two separated product families they are prioritised, because themodel is proposed to accept the most desirable MTO families. On the other hand, production values of MTS andMTS/MTO product families are calculated to consider qualitative criteria in the next lot-sizing module. Afterprioritising MTO orders and calculating qualitative criteria for MTS and MTS/MTO products, capacity assignmentis decided. In this regard, MTO families are firstly considered, because their priorities are higher than those of MTSand MTS/MTO products (Zaerpour et al. 2009). Hence, an initial capacity is assigned to MTO families. To do so,expected value of required capacity to produce high-priority MTO orders is assigned, since high-priority MTOorders are the orders which should be accepted (Ebadian et al. 2009). Next, lot-sizes of the other two categories ofproducts are calculated, because their demands are forecasted. It is noted that forecasted demands (MTS and MTS/MTO products) are not first responded, as it is required to accept all incoming high-priority MTO orders. After lot-sizing, the available capacity equals the sum of initially assigned capacity and the remaining capacity from lot-sizing.On the other hand, MTS/MTO families afterwards are in their MTO-based production activities. Hence,acceptance/rejection is performed for MTO and MTS/MTO product families with respect to the available capacity.In this step, MTS/MTO priorities and OPPs are taken into account in order to decide on acceptance/rejection.Simultaneously, due-date setting is performed, because the due date plays a key role in accepting or rejecting orders.By means of the proposed model, capacity is balanced between MTS products and high-priority MTO and MTS/MTO orders. To do so, the required capacity is first devoted to high-priority orders and then lot-sizing is performedfor forecasted demands. Next, decisions on incoming orders are made upon the available capacity for these orders.

As declared in Section 2, the model is proposed for production systems with MTS, MTO and MTS/MTOproduct families without any sort of mathematical assumption on times for MTO and MTS/MTO arrivals togeneralise the obtained results. Moreover, the layout is assumed as a job-shop in which arriving orders have specificprocess routes. Also, there is no policy for holding inventories and raw materials are adequate to meet acceptedorders. Production systems and OPPs of the product families are decided in advance. Additionally, the proposedmodel is categorised in the tactical level of HPP in MTS/MTO. Therefore, it is a medium-term decision-makingmodel and the corresponding planning horizon varies from a month to a year with respect to the case (Gershwin1989, Soman et al. 2004).

3.1 Prioritising MTO product families

This step is proposed upon the criteria related to customer of MTO orders. Therefore, four criteria are adopted fromthe literature of MTO production systems. The criteria are customer’s profit contribution (Huiskonen et al. 2003),customer’s potential purchasing (Huiskonen et al. 2003), orders’ lot-sizes (Ebadian et al. 2009), and orders’ purchasingrange (Ebadian et al. 2009). Customer profit contribution reveals the gained revenue upon which customer’snegotiation power is analysed, while customer potential purchasing reflects the future of the manufacturer-customerrelationship. The third and the fourth criteria consider details of the customer’s order. To clarify these two criteria,two customers are supposed. The first one orders large lot-sizes from a few products and the other customer orderssmall lot-sizes with a high level of product variety. Obviously, the first customer is preferred for a manufacturer. Thevalues which are assigned to the criteria are low and high. Based upon different combinations of the criteria, Table 1demonstrates corresponding order priority of every combination (the values are presented according to the aboveorder).

As seen in Table 1, some combinations are not considered, because they are not logical. For example,combination (L, L,H,L) is not logical, because large lot-size, low contribution and low potential purchasing areconflicting.

3.2 Allocating initial capacity to MTO product families

Since high-priority MTO (HPMTO) product families must be delivered on-time (Ebadian et al. 2009), initialcapacity is allocated to this category of products. This procedure ensures that at least the required capacity ofHPMTO orders is allocated. To do so, expected required capacity of future incoming HPMTO orders is calculatedas follows:

Expected capacity of resource j for high-priority MTO products

¼X

Acceptance probability of order i� required capacity of order i in resource jð Þ,


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in which order i belongs to the HPMTO determined in Section 3.1 and resource j belongs to theprocess route of order i ( j 2 RðiÞ). Also, the acceptance probability is calculated using (1) (Easton and

Moodie 1999):

Pi ci, dið Þ ¼ 1þ �0 � exp �1di � TCAPi

TCAPiþ �2

ciCCAPi � TCAPi

� 1

� �� 1, ð1Þ

where:

ci is the contract price of order i;di is the promised lead-time per unit of order i;

TCAPi is the total estimated required time capacities per unit of order i;CCAPi is the average cost per unit of time capacity required for order i; and

�0, �1, �2 are parameters based upon historical data or experts’ viewpoints.

Therefore, the initial capacity of resource j which is allocated to the HPMTO orders is:

Xi2HPO

CAPRATij � 1þ �0 � exp �1di � TCAPi

TCAPiþ �2

ciCCAP � TCAPi

� 1

� �� 1, 8j 2 R ið Þ:

In the above expression, CAPRATij is the processing time of product family i in resource j.

3.3 Determining production values of MTS and MTS/MTO product families

To consider all relevant criteria, production values of MTS and MTS/MTO product families are defined usingthree qualitative criteria. It is noted that this section is developed for MTS and MTS/MTO products, because

MTS/MTO products have the same behaviour as the MTS products before their OPPs. By means of this section,all qualitative criteria are considered in our decision-making structure and the proposed procedure converts these

qualitative criteria to quantitative ones. The criteria considered in production value are assessed using the

hierarchical structure shown in Figure 3 with three criteria: estimated contribution, reputation, and potentialfuture sale. At each level of the hierarchy, elements of that level are pairwisely compared using the scale presented

in Table 2. Then, a normalisation process is applied to normalise the obtained scores. Equation (2) shows thenormalisation process in which aij and wi represent comparison of element i over element j and the normal score

of element i, respectively. The proposed hierarchy is structured based upon the well-known analytic hierarchyprocess (AHP). Readers are referred to Saaty (1980) for elaborate explanations and procedures of AHP. The

output of this step is wi for every MTS and MTS/MTO product family, which is used in the mathematical model

Productfamily n

…

Production value

Estimated contribution Reputation Potential future sale

Productfamily 1

Productfamily n

Productfamily 1

Productfamily n

……Productfamily 1

Figure 3. Hierarchical structure to calculate production values of MTS and MTS/MTO product families.

Table 1. Prioritisation of MTOorders.

Value(L¼ low, H¼ high)

Orderpriority

(L, L, L, L) Low(L,H, L, L) Low(L, L, L,H) Low(L,H, L,H) Low(L,H,H,L) Medium(H,H, L,H) Medium(H,L,H,L) High(H, L, L,H) High(H, L,H,H) High(H,H,H,L) High(H,H,H,H) High


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as described in the next step.

A ¼

a11 a21 � � � an1

a12 a22 � � � an2

..

. ... ..

. ...

a1n a2n � � � ann

266664

377775)W ¼

Pnj¼1

a1jPn

i¼1aij

� �Pnj¼1

a1jPn

i¼1aij

� �

..

.

Pnj¼1

a1jPn

i¼1aij

� �

2666666666664

3777777777775: ð2Þ

3.4 Determining lot-sizes for MTS and MTS/MTO products

When the initial capacity is dedicated to the future incoming MTO orders, the remaining capacity is free to plan forMTS and MTS/MTO product families. Since setups are required for production of these products, it is crucial tocalculate lot-sizes of MTS and MTS/MTO product families. To do so, Equations (3)–(10) are proposed to minimise

total costs with manufacturing resources and warehousing capacity constraints. Also, it is noted that the regular-time capacity considered in this model is the remaining capacity; i.e., total available capacity minus the initiallyallocated capacity to MTO product families.

Nomenclature

Indices:

t¼ 1, . . . ,T time;k¼ 1, . . . ,K time;i¼ 1, . . . , I product;j¼ 1, . . . , J resource;

R(i) set of resources used for product family i (before OPP for MTS/MTO products).

Variables:

xitk lot-size of product family i with due date on k in regular time;yitk lot-size of product family i with due date on k in over time;sijt 1, if setup done for product family i on resource j in regular time t; 0, otherwise;tijt 1, if setup done for product family i on resource j in overtime t; 0, otherwise;

REGRESjt level of resource j used in regular time t;OTRESjt level of resource j used in overtime t.

Table 2. Scoring scale of pairwise comparisons (Saaty 1999).

Score Definition Explanation

1 Equal importance Two alternatives contribute equally to the objective2 Weak3 Moderate importance Experience and judgment favour slightly one alternative over another4 Moderate plus5 Strong importance Experience and judgment favour strongly one alternative over another6 Strong plus7 Very strong demonstrated

importanceAn alternative is favoured very strongly over another; its dominance

demonstrated in practice8 Very, very strong9 Extreme importance The evidence favouring one alternative over another is of the highest possible

order of affirmation


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Parameters:

Dik estimated demand of product family i with due date on k;RSTij setup time for product family i on resource j in regular time;OSTij setup time for product family i on resource j in overtime;RSCij setup cost for product family i on resource j in regular time;OSCij setup cost for product family i on resource j in overtime;HCi holding cost of product family i in one period;BCi backorder cost of product family i in one period;RCij production cost of product family i on resource j in regular time;

OTCij production cost of product family i on resource j in overtime;PVALi production value of product family i;CAP warehousing capacity;

REGCAPjt resource capacity j in regular time t;OTCAPjt overtime resource capacity j in overtime t;

CAPRATij consumption rate of product family i on resource j.

minXi

Xj

RCij �Xk

Xt

xitk

!þ OTCij �

Xk

Xt

yitk

!þ RSCij �

Xt

sijt

!þ OSCij �

Xt

tijt

!" #

þXk

Xt5k

k� tð Þ �HCi � xitk þ yitkð Þ þXi

BCi �Xk

max 0,Dik �Xt5k

xitk þ yitkð Þ

( )�Xi

PVALi �Xk

Xt

xitk

ð3Þ

Xi

CAPRATij �Xk

xitk þ yitkð Þ þXi

RSTij � sijt þOSTij � tijt� �

� REGRESjt þOTRESjt 8j 2 R ið Þ, t ð4Þ

xitk �M � sijt 8j 2 R ið Þ, i, t, k ð5Þ

yitk �M � tijt 8j 2 R ið Þ, i, t, k ð6Þ

REGRESjt � REGCAPjt 8j 2 R ið Þ, t ð7Þ

OTRESjt � OTCAPjt 8j 2 R ið Þ, t ð8Þ

Xi

Xt5k

xitk þ yitkð Þ � CAP 8k ð9Þ

xitk, yitk,REGRESjt,OTRESjt � 0, sijt, tijt 2 0, 1f g 8i, j, t: ð10Þ

Objective function (3) minimises total production, setup, holding and backlog costs. The last term of theobjective function seeks to maximise the production value of all product families which are processed in regulartime. Constraint (4) model how resource j is allocated to production and setups in period t. Constraints (5) and (6)correspond to the setups in regular time and overtime, respectively. Available regular-time and overtime resourcecapacities are taken into account in (7) and (8), respectively. The warehousing capacity is also considered using (9).Finally, Constraint (10) defines required variables.

3.4.1 Backward lot-sizing algorithm

The zero-one setup variables (sijt and tijt) make the proposed lot-sizing model intractable. Therefore, a backwardheuristic is proposed to determine lot-sizes of MTS and MTS/MTO product families. The proposed heuristic worksbackward from the forecasted due dates of product families in order to minimise holding cost, while overtime


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utilisation prevents any demands from being backlogged. In other words, the lot-sizing model is developed todistribute production of the forecasted demands during the planning horizon. The most notable characteristic of theproposed heuristic is its ease of use. Near-optimal lot-sizes are determined in a reasonable amount of time usingsimple computer software, such as Microsoft Excel� spreadsheets. Figure 4 demonstrates the pseudo-code of thebackward lot-sizing algorithm.

3.5 Accepting/rejecting MTO and MTS/MTO orders

After lot-sizing of the MTS and the MTS/MTO product families, profitable MTO orders are distinguished to beaccepted and the ones which do not yield our desired level of profitability will be rejected. In addition to MTOorders, MTS/MTO orders are considered as well, because MTS/MTO orders are finished with respect to theincoming orders from customers. Therefore, acceptance and rejection of MTS/MTO orders are also brought up.Figure 5 shows the proposed procedure for accepting or rejecting incoming orders. It is noted that priorities andOPP locations of MTS/MTO product families are utilised in this step. Similar to MTO products, priorities of hybridones are calculated using the procedure explained in Section 3.1.

3.5.1 Non-negotiable orders

First, the orders are divided into MTO and MTS/MTO to assess whether the available unfinished inventories at theOPP of MTS/MTO products are adequate to meet the hybrid orders. If orders cannot be accomplished using theOPP inventories, the order is rejected. If the inventory is adequate, the MTS/MTO orders enter the procedure to beconsidered for acceptance or rejection. It is assumed that the inventory of raw materials is enough to meet MTOorders, but the unfinished inventory of MTS/MTO orders is the result of the lot-sizing problem solved inSection 3.4.

3.5.1.1 Calculating latest starting time. Delivery lead-time consists of several stages including processing times,transfer times, queue times, etc. (Kingsman 2000). Hence, the lead-time is estimated by the manufacturing expertsof the firm. To consider lead-times, latest starting time (LST) of any order is calculated using (11). Equation (11) is

Set the latest due dates as the current planning period

While all demands are not responded

Line 1.While t > 0

Calculate maximum lot-size of hybrid product family regarding only available

capacity

Select a product family mix with the maximum number of products included

Determine lot-size of product i in planning period t with respect to the above product

family mix

Update

Available capacity of resource j in planning period t

Non-responded demand of product family i

t = t − 1

End while

If all demands are not responded

Go to line 1 using available overtime capacity

Repeat the procedure for MTS product families

End while

Figure 4. Pseudo-code of backward lot-sizing algorithm.


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inspired from the backward method of Kingsman and Hendry (2002). Orders’ LSTs are calculated to check whether

completing an order is feasible with respect to the available time of the planning period until the due date of

the order:

LSTi ¼ DDi �DLTi, ð11Þ

in which:

LSTi is the latest stating time of order i;DDi is the due date of order i; and

DLTi is the delivery lead-time of order i.

Having LSTs of the orders calculated, it is possible to check whether the orders can be accomplished with respect

to the available time from the present time to the due dates of the orders. If the LST of an order is less than the

present time (the time period in which planning is performed), it cannot be accomplished until its due date. Hence,it is rejected; otherwise, its required capacity is checked in the next step.

3.5.1.2 Checking rough-cut capacity. To check feasibility of delivering incoming orders upon the available capacity,a rough-cut capacity check is performed. To do so, (12), (13), and (14) are utilised to check the feasibility of high-

priority, medium-priority, and low-priority orders, respectively. Those orders that meet the following constraints areaccepted:

Pi � REQCAPij �Xk�¼t

REGCAPj� 8j 2 R ið Þ ð12Þ


REGCAPj�

" #1� �jt� �

8j 2 R ið Þ ð13Þ

(a)

Yes

MTS/MTO

Is the incoming order feasible

upon unfinished inventory at

OPP?

MTO or MTS/MTO?

B

MTOMTO or

MTS/MTO? MTS/MTO

Is the incoming order feasible

upon unfinished inventory at

OPP?

Yes

MTO

No

Reject

YesIs the

coming order negotiable?

No

A

Figure 5. Proposed module toward MTO and MTS/MTO acceptance/rejection.


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REGCAPj�

" #1� �jt � �jt� �

8j 2 R ið Þ: ð14Þ

In the above inequalities, REQCAPij represents required capacity for order i on resource j. �jt and �jt areallocated percentages of the available resource j to high-priority and medium-priority orders coming later than

period t, respectively. These parameters are calculated using formulae presented by Bodily and Weatherford (1995).�jt is the largest value for which PrðXHPO � �jtÞ � �PHPO= �PMPO, in which XHPO is the total estimated required

capacity of high-priority orders coming later than t and �P is the average profit of the orders per unit of resources(subscript MPO relates to medium-priority orders). Similarly, �jt is the largest value for which

A

Lateststarting time

< present time?

Yes

No

(b)

No

Rough-cut capacity check

Profitable increase?

Capacity increaseevaluation

No

Enough capacity?

Accept

Yes

Yes

Reject

Figure 5. Continued.


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PrðXMPO � �jtÞ � �PMPO= �PLPO (subscript LPO relates to low-priority orders). To calculate the mentionedprobabilities, probability distributions of orders are used from historical data. In the case of poor historical data,experts’ judgments are utilised instead of a probability distribution. Moreover, it is noted that acceptanceprobability (Pi) is 1 for accepted orders and is calculated using Equation (1) for the orders which are not yetaccepted. After the rough-cut capacity check, if the order does not violate the corresponding inequality, the

No

YesLatest

starting time < present

time?

Set new due date as early as possible

B(c)

Reject

No

Is the order accepted by the

customer with new characteristics

(price, due date)?

Negotiation on new due date

Negotiation on new due date and new price

Negotiation on new price

No


No




Enough capacity?

Enough capacity?


No


No

Yes

Yes

Yes

Yes

Yes

Accept

Figure 5. Continued.


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available capacity is adequate to accomplish the order and the order is accepted; otherwise, it is evaluated whethercapacity increase is profitable to accept the incoming orders.

3.5.1.3 Evaluating capacity increase. As mentioned before, profitability of increasing capacity is evaluated in thisstep. Hence, the contribution of the order needing capacity increase is compared with the cost of capacity increase. Ifthe contribution is greater than the cost, it is profitable to increase capacity and accept the order; otherwise, theorder is rejected.

3.5.2 Negotiable orders

Similar to the case of non-negotiable orders, unfinished inventories in the OPPs of MTS/MTO product families areexamined if adequate to meet MTS/MTO incoming orders. If the order can be accomplished with respect to theavailable unfinished inventory, the order will enter the proposed procedure in Figure 5(c); otherwise, it will berejected. Steps of the proposed procedure are mostly similar to the ones of that of non-negotiable orders. In thissection, the differences are solely explained. First of all, the feasibility of the orders is assessed based upon theavailable time. If the time is not adequate, it is necessary to set a new due date for the order to have adequate time tobe accomplished. It is crucial to set the new due date as early as possible, because the due date is the most importantspecification of an order to the customer (Kingsman and Hendry 2002). Then, the available capacity is assessed asto whether the orders can be fulfilled. Therefore, the rough-cut capacity check is utilised (readers are referred toSection 3.5.1.2). If an order meets the criteria of Equations (12), (13), and (14) for high-priority, medium-priority,and low priority orders, respectively, it is accepted; otherwise, the capacity increase is evaluated using the procedurein Section 3.5.1.3. Finally, four kinds of orders result. The first category relates to the orders for which availabletime and (available or increased) capacity are adequate. This category of orders is directly accepted. The secondcategory includes the orders for which available time is adequate and increasing capacity is not profitable. Hence, itis required to negotiate on the price of this category of products to cover the cost of the increased capacity. In thethird category of products, the available time is not adequate and the (available or increased) capacity is adequate.This category requires negotiation on due date to cover the required time for production. The fourth category oforders is related to the orders for which neither lead-time nor capacity (available or increased capacity) is adequate.Hence, negotiation is required on their due dates and prices. The explained four categories are shown in Figure 5(c).Regarding different categories of products in Figure 5(c), three sorts of negotiation are performed for the orders ofthe second, the third and the fourth category. If new specifications of the negotiated orders (price and/or due date)are accepted by the customer, the order with the new specification is accepted; otherwise, it is rejected.

4. Case study

In this section, the applicability and validity of the proposed model is assessed using a real industrial case study. Thereported case study corresponds to a wood-industry manufacturing company in Iran, which is one of the leadingones in the Iranian and Western Asian market. The company is called Company X in this section. The authors ofthis paper have been requested to diagnose the issues which have recently arisen in the company. The companysuffered long lead-times which resulted in many cases whose promised due dates were not met. Also, some otherproblems such as high holding and backlog costs convinced managers of the company to treat the problems.Therefore, the authors decided to restructure the production planning procedures of the company. The procedurewas already performed using staff’s experience, while different characteristics of the products required differentcriteria and consequently, different decision-making procedures. To do so, it was decided to concentrate on thecapacity coordination issues of Company X, because the main reported problems were relevant to this level ofdecision-making (high holding cost, high overtime cost, delivering orders with delay, unfinished inventory shortage,etc.). Hence, the proposed model in Section 3 was developed and applied to the firm. As a brief description, productsof the firm include nine product families from which three families are MTS, three families are MTO and the lastthree families are MTS/MTO. These products are processed through different process routes using 19 workstations.Table 3 contains data about processing times of the product families in the workstations. The numbers inparentheses correspond to setup times (setup times in regular time are the same as setup times in overtime).Moreover, production cost per unit of regular time, production cost per unit of overtime and setup cost per unit oftime (both regular time and overtime) are 15, 20 and 25, respectively.


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Table

3.Data

aboutprocessingtimes

ofproduct

families(setuptimes

are

inparentheses).

Product

family

Workstation

12

34

56

78

910

11

12

13

14

15

16

17

18

19

112(2)

10(2)

14(2)

11(2)

14(2)

12(2)

16(2)

13(2)

10(2)

13(2)

210(2)

16(2)

20(3)

14(1)

16(2)

12(2)

15(2)

314(2)

15(2)

18(1)

20(3)

16(2)

18(2)

12(2)

423(8)

24(8)

19(9)

18(5)

32(11)

29(12)

20(6)

18(7)

33(6)

25(10)

526(8)

18(5)

30(8)

28(10)

28(11)

22(9)

30(12)

18(4)

20(8)

20(11)

16(5)

24(5)

618(4)

24(7)

18(8)

20(8)

30(11)

16(4)

712(2)

15(2)

12(2)

18(3)

18(7)

26(4)

30(11)

26(6)

28(6)

22(8)

814(2)

16(2)

12(2)

16(2)

18(2)

20(3)

28(7)

24(6)

20(9)

912(2)

14(2)

16(2)

16(2)

18(2)

18(9)

20(8)

24(10)

22(6)

20(7)


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Based upon the data from Company X, data of the product families is presented in Table 4. In this table,

contract prices are approximately 130% of the total cost (sum of processing and setup costs), while holding and

backlog costs are 10% and 30% of MTS prices, 30% and 10% of MTO prices and 20% and 20% of MTS/MTO

prices, respectively. Also, it is noted that the planning horizon is one month which includes 4 weeks � 5 days � 7

hours � 60 minutes ¼ 8400 minutes regular time and 4 weeks � 4 days � 2 hours � 60 minutes ¼ 1900 minutes as

overtime (overtime is allowed on Monday, Tuesday, Wednesday and Thursday). Moreover, an order of product

family 6 with quantity of 60 is accepted in advance and the warehouse’s capacity is adequate.In Table 4, lead-times of the product families are estimated by experts of the company. Holding costs are

considerably different; because customised products have higher cost of storage (readers are referred to Cakravastia

and Takahashi (2004) to study the relationship between product types and their holding costs). On the contrary,

backlog costs are higher for MTS products. If a backlog occurs for an MTS product, the product will be supplied by

competitors in the market. From another point of view, these costs are considered to avoid MTS products from

being backlogged and two other types from being held.With respect to the orders prioritisation and products production values, experts’ judgments and comparisons

were collected and analyses were performed. Table 5 presents results of this procedure.In order to calculate initial capacity for HPMTO orders, parameters �0, �1 and �2 were set at 0.1, 0.5, and 0.75

based upon the historical data from the customer (for an elaborate description, readers are referred to Easton and

Moodie (1999)). CAPRATEij was assumed as the sum of total processing and setup times of product family i in

resource j. Also, CCAPi was equal to the average of production cost in regular time, production cost in overtime and

setup cost; i.e., CCAPi¼ (15þ20þ25)/3¼ 20. Using this data, acceptance probabilities of product families 4, 5, 6, 7,

8, and 9 were calculated as 0.85, 0.92, 0.88, 0.93, 0.93, and 0.93, respectively. Afterwards, lot-sizes of MTS and

MTS/MTO product families were calculated using the proposed backward lot-sizing algorithm as shown in Table 6.

Table 4. Data of the product families.

Productfamily

Productionstrategy

Deliverylead-time

Holdingcost

Backlogcost

Contractprice

1 MTS 5 355 1065 35502 MTS 8 250 750 25003 MTS 6 269 807 26904 MTO 16 2214 738 73805 MTO 14 2574 858 85806 MTO 17 1155 385 38507 MTS/MTO (7a) 14 (5b) 1180 1180 59008 MTS/MTO (11) 17 (9) 888 888 44409 MTS/MTO (8) 15 (6) 1056 1056 5280

Note: anumbers in parentheses correspond to the workstations in which OPPs are located;bnumbers in parentheses correspond to estimated lead-time before OPP.

Table 6. Lot-sizes of the product families within each planningperiod.

Productfamily

Forecasteddemand

Planning period

1 2 3 4 5 6 7 8 9

1 30 7 3 3 9 82 40 5 9 18 83 10 1 1 87 50 4 23 238 35 3 16 169 55 17 19 19

Table 5. Production values and priorities of productfamilies 1–9.

Product family Production value Order priority

1 0.1782 0.0593 0.2294 High5 Medium6 High7 0.201 High8 0.217 Low9 0.116 Medium


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After determining lot-sizes, required overtime capacities were calculated as 8, 8, and 104 minutes for resource 1 inperiod 4, resource 5 in period 6, and resource 8 in period 6, respectively.

Finally, it was decided to accept or reject the incoming orders during the planning horizon. During 20 days of theplanning horizon, eight orders were received from different customers in different periods. The proposed procedurefor accepting or rejecting the orders was performed for each order and the suitable decisions were made. The relateddecisions are briefly presented in Table 7.

To validate the strengths of the proposed model, a comparison is presented between before and afterimplementation of the proposed model in the case study. Table 8 summarises results of this comparison.

As seen in Table 8, although the number of accepted orders was reduced after implementation, the acceptedorders were completely delivered on time. Hence, the most problematic issue of Company X was resolved. Withrespect to the ratio of OPP semi-finished shortage to total MTS/MTO accepted orders, it is also proved that theproposed model is suitably designed and implemented. This result is achieved, because unfinished inventories atOPPs are taken into account in the proposed acceptance/rejection procedure. Additionally, appropriate distributinglot-sizes among accepted orders resulted in less required overtime capacity. Finally, the number of setups might bethe negative aspect, however, setups are considered in the proposed lot-sizing model.

5. Conclusion and future research directions

This paper addressed the second level of HPP in a hybrid MTS/MTO production system with three kinds ofproducts: MTS, MTO and MTS/MTO. This level of the HPP consists of order acceptance/rejection policy, orderdue-date setting, lot-sizing of MTS products, and determining required capacity during the planning horizon of thelevel. To do so, a five-step model was proposed. Compared with previous, dispersed models proposed in this field,the current model attempted to decide on several important decisions in hybrid production systems in the tacticallevel of HPP. The proposed model does not rely on too many mathematical assumptions. Therefore, it is moreapplicable to various cases. Another advantage of this model is its ease of use which makes it more comprehendiblefor managers. Also, to cope with intractability of the proposed lot-sizing sub-model, a backward lot-sizing heuristicwas developed, which can be easily implemented without any high level programming skills. However, the proposed

Table 7. Summary of acceptance/rejection decisions.

Orderno.

Productfamily Quantity

Receivingperiod Negotiable Decision

1 7 15 1 Yes Accept2 6 60 3 No Accept3 4 40 3 No Accept4 5 35 5 Yes Accept5 9 60 6 Yes Reject6 9 40 7 Yes Accept7 7 30 8 No Accept8 8 30 10 Yes Accept

Table 8. Comparison between before and after application of the proposed capacity coordination model.

Measure Before application After application

No. of received MTO and MTS/MTO orders 9 8No. of accepted MTO and MTS/MTO orders 9 7MTO and MTS/MTO orders delivered on due date 4 7Ratio of backordered to total accepted MTO and MTS/MTO orders 0.24 (¼ 75/315) 0 (¼ 0/250)Ratio of OPP semi-finished shortage to total MTS/MTO accepted orders 0.25 (¼ 45/180) 0 (¼ 0/115)Setups done for MTS and MTS/MTO products 8 13No. of planning periods with overtime 8 2


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model has some inevitable limitations. First, the model was developed for no-buffer production systems which

restrict its applicability into some distinct industries. Second, shop-floor layout was assumed as job shop. Third, asconcluded in Section 4, the number of setups was increased after implementation of the model. However, setupswere considered in the proposed lot-sizing sub-model and their frequencies are optimised with respect to otherparameters of the model. Finally, a real industrial case study was reported to demonstrate applicability and validity

of the proposed capacity coordination model. This was achieved by presenting a brief description of implementationand comparing before and after implementation of the model.

To continue the research direction of this paper, four suggestions are provided. First, it can be so practical todevelop decision-making frameworks in other levels of the MTS/MTO HPP structure in such a way that inputs andoutputs of those frameworks conform to those of the proposed model in this paper. The second suggestion is toconsider other assumptions in the proposed lot-sizing model to make it suitable for some other cases. These

additional assumptions include outsourcing possibility for MTS products, shelf life of perishable products etc.Third, taking into account supplier issues (such as capacity, lead-time and flexibility) can complete the proposedmodel in this paper, because suppliers play a key role in activities of any firms. Lastly, developing other heuristicsand meta-heuristics to tackle complexity of the lot-sizing model is suggested.

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capacity coordination in hybrid make-to-stock/make-to-order production environments

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