operations management of multiple machine automatic warehousing systems

international journal of

production economics

ELSEVIER Int. J. Production Economics 51 (1997) 83-98

Operations management of multiple machine automatic warehousing systems

Moshe Eben-Chaime*, Nava Pliskin

Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer Sheva, Israel

Abstract

Most operations management studies of automatic warehousing systems investigate single-machine systems in isolation

of the total system which includes other related functions. In this paper, we overcome these limitations and investigate an integrative model of a warehouse, containing several storage/retrieval (S/R) machines, which is integrated within a total system. Moreover, whereas performance was previously analyzed, mostly, in terms of throughput and travel times of the S/R machines, this paper considers additional performance measures such as response times, queue lengths, and utilization of the S/R machines. A simulation of the integrative model is used to study the effects of various operations management tactics on performance. The results demonstrate that economic gains are possible while hardly sacrificing performance. The gains result from decreasing the number of S/R machines - up to 20%, and reducing building space as a consequence of shorter queues.

Keywords: Automatic warehousing systems; Automatic storage/retrieval systems (AS/RS); Queue length; Response time

1. Introduction

In this paper, automatic warehousing systems

containing several storage/retrieval (S/R) machines are studied. An automatic warehousing system (AWS) consists of racks, S/R machines, input/out- put (I/O) station(s), and computerized control devi- ces. The S/R machines are cranes that travel and move objects between the racks and the I/O stations. These cranes usually operate under the control of a computerized system in one of two modes of operation. These operation modes are either based on a single command (SC) cycle, during

* Corresponding author. Tel.: 972-7-6472206; fax: 972-7-

6472958: e-mail: [email protected].

which a single storage or retrieval operation is performed, or on a dual command (DC) cycle, during which both a storage operation and a retrieval operation are performed between two con- secutive visits to I/O stations. It is also possible to employ a hybrid mode of operation under which DC cycles are performed whenever possible, SC cycles are performed otherwise, and the S/R machines become idle in the absence of requests for service.

This study focuses on the effect of operations management tactics on performance measures of automatic warehousing systems with multiple machines. Operations management is concerned with the sequencing of storage and retrieval requests, and the matching of both types of requests in DC cycles. Most operations management studies

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84 M. E&n-Chaime. N. PIiskinJInt. J Production Economics 51 (1997) 83.-98

analyzed AWS performance on the basis of the expected travel time of the S/R machines. Travel time is the major component of the service time in AWS. The other components, the pick and deposit (P/D) times, are constant and independent of operations management tactics.

Expected travel time of a single S/R machine formed the basis for the comparison of storage policies and assignment rules in the seminal works of Hausman et al. (1976), Graves et al. (1977) and Schwarz et al. (1978). Continuous approximations of the racks have been used for performance analysis of automatic storage/retrieval systems (AS/RS) in which the times to travel from one end of a rack to the other are equal in both dimensions. Analyti- cal expressions of the expected travel times have been developed for SC (Hausman et al., 1976) and DC (Graves et al., 1977) cycles under randomized storage and FIFO sequencing. Bozer and White (1984) have generalized these results for systems where the end-to-end travel times are not necessarily equal.

These results inspired the investigation of alternative sequencing policies by Han et al. (1987), who eveloped the “nearest-neighbor” (NN) heuristic rule (see next section) and assessed its efficiency via a simulation study. The results were later extended in simulation studies that covered applications of the standardization and approximation approach and the NN rule to carrousels (Han and McGinnis, 1986) and rotary racks (McGinnis et al., 1987). Note that service times under the NN rule are sequence-dependent and the assumption of FIFO sequencing, which facilitates analytical ap- proaches, does not hold. Thus, studies of the NN rule resorted to simulation because analytical ap- proaches are much harder, if not impossible. The NN rule has been applied in these studies for block sequencing, i.e., to sequence a block characterized by a fixed number of retrievals. Eben-Chaime (1992) showed that block sequencing can be hazardous in terms of other AWS performance measures such as response times, service time plus waiting time in the queues, and queue lengths. To overcome these effects, Eben-Chaime proposed a dynamic application of the NN rule for dispatch- ing an alternative which was shown to maintain response times and queue lengths at the levels of

FIFO sequencing, while significantly reducing machine travel times.

Others considered additional performance measures such as throughput and space consump- tion. The AWS throughput is the number of services completed, i.e., operations performed, per unit time. Dedicated storage was presumed to maximize throughput (White, 1980) while randomized storage was presumed to minimize storage space (Francis and White, 1974). However, Goetschalckx (1983) argued that the space reduction under randomized storage may result in a higher throughput than can be attained in dedicated storage. Bozer and White (1984) proposed to use the travel time expressions to establish throughput standards and Han et al. (1987) estimated throughput increases due to travel time reductions. Seidmann (1988) considered, in addition to travel times, response times and throughput, the utilization of the S/R machine in a warehouse that serves as a distribution center. The utilization of an S/R machine is the percent of time the machine is not idle, which is also termed the machine load.

One common denominator of most previous operations management studies is the focus on single- machine systems. However, because the S/R machines constitute a primary cost component in automatic warehouses, reducing their number can be instrumental to cost control. Han et al. (1987) have speculated, based on a study of a single- machine system considering performance only in terms of machine travel time, that “in a large, multi-aisle (AS/R) system, a 12% increase in throughput can lead to eliminating an aisle”. An- other common denominator of previous studies is that the storage function has been analyzed in isolation, ignoring its relationships with, and depend- encies on, other functions of the total system. While this might be acceptable for the distribution center studied by Seidmann (1988), the isolation premise does not hold for the more general case, where storage sub-systems interact with various other subsystems such as manufacturing. Recently, it was noted that “what makes AS/RS most justifiable is when you integrate it into an entire manufacturing system scheme” (Knill et al., 1993). Responding to this challenge, an integrative model for automatic warehousing systems containing a single S/R

M. Eben-Chaime, N. Pliskinllnt. .I Production Economics 51 (1997) 83-98 85

machine and operating within a total system has been developed already (Eben-Chaime and Pliskin, 1996).

Bozer and White (1990) developed design and performance models for end-of-aisle order picking systems with multiple S/R machines. However, each machine in their order picking systems operates independently with its dedicated order picker. Another limitation of their study is that they assumed FIFO sequencing and did not account for all the economic benefits, such as the potential reduction in the number of S/R machines and in the storage due to more efficient operations management. Other AWS design models, while considering the interaction between the warehouse and other system functions, are similarly limited because FIFO service is assumed in order to simplify the determination of the number of S/R machines (e.g., Zollinger, 1975; Karasawa et al., 1980; Bafna, 1981; Roll and Rosenblatt, 1981; Ashayeri et al., 1983: Perry, 1983; Azadivar, 1988; Rosenblatt et al., 1993).

This paper extends the integrative model of Eben-Chaime and Pliskin (1996) to multiple machines AS/RS and examines explicitly the trade-offs between a variety of AWS performance measures and relevant cost components, such as the total life-cycle cost of the S/R machines, which depends on the number of machines, and storage space cost. Believing that operational efficiency is of utmost importance, we prefer to study the integrative model under the NN rule, even at the expense of using simulation rather than analytic modeling. The motivation for this study is elaborated upon in the next section. The integrative multiple-machines AWS model and the simulation environment are presented in Section 3. In Section 4, general basic results under the DC and the hybrid operation modes are reported. Opportunities for cost reduction are discussed in Section 5, which is followed by concluding comments.

2. Motivation

The racks in AS/RS are paired back to back with aisles between the pairs. Each S/R machine can move horizontally and vertically at the same time

and can access the front (pick) face of the racks on both sides of the aisle. An S/R machine is either dedicated to a single aisle, or can move between aisles. Bozer and White (1984) offered to standar- dize (or normalize) the pick face of the racks and approximate them as continuous L x H rectangles, where L is the length and H is the height. Rack standardization implies that T =max(t,, tVj is the “standard time unit” and that b = min { t,,, tY} /T is the “shape factor” of the rack, where

th = Llsh, tv = HIS,,

with sh being the horizontal speed of the S/R machines and s, the vertical speed of the S/R machines.

The pick face of a normalized rack is considered as a 1 x b (or b x 1) rectangle. A rack of a unit shape factor, b = 1, is called a “squared in time” rack. This approach allows analysis in terms of the parameters b and T, disregarding physical attributes, size and structure of the rack and speeds of the S/R machines. In particular, Bozer and White (1984) developed the following analytic expressions which closely approximate the expected travel time of SC and DC cycles, assuming that the I/O point is located at a corner of the rack, and verified their quality by comparing them to simulation results:

E(SC) = 1 + b2/3, (1)

E(DC) = 4 + b2/2 - b3/30. (2)

These are normalized times and actual times are obtained by multiplying by T.

The relative merit of the DC mode can be quantified by comparing these terms. The travel time per operation in a DC cycle is half the figure in (2), since two operations are performed during that cycle, while E(SC) in (1) is associated with the single operation executed during that cycle. Thus,

f E(DC)/E(SC) = +($ + b2/2 - b3/30)/(i + b2/3)

< (4 + b2/2)/2(1 + b2/3)

= (8 + 3b2)/(12 + 4b2) < 2.

86 M. Ehen-Chaime, N. P&kin/M. J. Production Economics 51 (1997) 83-98

In other words, at least 25% reduction in the expected travel time per operation is obtained under the DC mode. Actual reductions are even larger, for example, in a squared-in-time rack, the ratio is 0.911.33 =0.675 or 32.5% reduction.

Further reductions have been obtained by Han et al. (1987), who developed the NN rule to sequence and match retrievals with empty slots for storage operations in DC cycles. Given a set R of retrieval points and an initial set S of empty slots, the NN heuristic operates as follows.

While R is not empty, 1. Select a pair r E R and s E S, with minimum

travel distance/time between Y and s.

much longer waiting times in longer queues and may, in extreme cases, result in system instability and even collapse. Work is not preserved under the pure DC mode as well, because when only DC cycles are performed, S/R machines may stand idle in the presence of service requests, if all pending requests are of the same type. Before designating the DC as the preferred mode of operation, the possible damages of this idleness should be evalu- ated and compared with the benefits due to the short travel times. This issue is addressed below in search for an answer to the question of whether the DC mode is the preferred mode of operation for multiple-machines AWS.

2. Perform a DC cycle, storing in s and retrieving from r.

3. Delete s from S and remove Y from R to S. 3. The model and the simulation The results of a simulation study where blocks of

retrievals were sequenced according to the NN rule indicate that, depending on the number of retrievals in the block - the number of items in R, and the number of empty slots in S, reductions of up to 20% in the expected travel time of DC cycles are achievable. Combined with the result above, the mean travel time per operation under the DC mode is more than 40% shorter than that under the SC mode. As mentioned earlier, travel time constitutes a major component of the service time and, hence, shorter travel time implies faster service and higher throughput.

The following terminology is used herein after for the sake of brevity: warehouse - an automated storage facility; system - a total system in which the warehouse is installed; item - a stored element such as a part, sub-assembly, or final product; unit load (UL) - a storage container of items, such as a bin, drawer, or pallet, which is the target of a storage or a retrieval operation.

Throughput, however, is not the only concern and service level is not solely measured by the service time. An AWS is a queuing system (e.g., Bozer and White, 1990) where response time is a very important issue, especially in a manufacturing environment where a whole line may stand idle waiting for items from the warehouse. Han et al. (1987) applied the NN rule to sequence blocks of fixed size - fixed number of items in R, i.e., block sequencing. This implies that the S/R machines, the servers of the queuing system, may stand idle in the presence of more than one but less than the desired number of customers, i.e., retrieval requests. Thus, in queuing theory terms, block sequencing is a non-work-preserving strategy (e.g., Cooper, 1981). The hazardous effects of block sequencing have been demonstrated by Eben-Chaime (1992) who showed that lack of work preservation causes

The integrative model of a warehouse within a system is illustrated in Fig. 1. The warehouse consists of racks, S/R machines, storage and retrieval queues, and a list of empty slot addresses. The system and the warehouse operate in the following manner: retrieval requests, generated by various system functions, trigger the start of UL processing by the warehouse. A retrieved UL is transferred by an S/R machine to the location where items stored in it are processed by system function(s). Upon completion of item processing, the UL is returned to the warehouse and re-stored, and UL processing is completed. The arrows in Fig. 1 clarify the cause-and-effect relationships between both service types.

A retrieval (storage) of a UL does not necessarily imply that items are retrieved (stored). A UL, for instance, may be retrieved in order to add to its contents, i.e., store item(s). Similarly, ULs are often re-stored after some items are removed, i.e., retrieved from them. Thus, the steady-state operation of AWS can be described as a collection of cycles,

M. Eben-Chaime, N. Pliskinllnt. J. Production Economics 51 (1997) 83-98 87

retrieval Warehouse (UL processing)

racks L list of empty slots

Fig. 1. The integrative model for automatic warehousing systems.

each of which consists of retrieval followed by storage of a UL. In between, other functions of the system engage in such processing of the item(s) in the UL as adding, withdrawing, counting, and maintaining. Hence, storage requests are not generated independently but as a result of prior retrievals. Further, warehouse activities are triggered by other system functions that generate UL retrieval requests. These observations imply that there are two separate queue types, queues for retrieval requests and queues for ULs to store, and that more than a single queue of each type may exist. There are two noteworthy differences between the two queue types. First, the queues of retrieval requests are lists stored in the computer memory while ULs are physically waiting to be stored in the storage queues. Therefore, response times are of greater importance with respect to the retrieval queues, and queue lengths are more important with respect to the storage queues. Second, an exact location of a UL is specified for each retrieval, while under the assumption of randomized storage, ULs can be stored in any empty slot in the warehouse. The addresses of the empty slots are stored in another list in the computer memory.

The advantage of the integrative model is in providing a general modeling framework for AWS

while giving the user the freedom to configure the specific AWS under study. The user may character- ize the item-processing scheme and may specify the type of AWS and the storage policy (random, dedicated or class-based, or combinations of the three). Any number of dedicated or mobile S/R machines, with any travel velocities, are possible. Racks of any size can be designated. Any location can be assumed for the I/O stations. The queues may be separated for each aisle or subset of aisles. Queue size can be limited or not. Once the specific AWS is configured, the user may experiment with the operations management tactics, i.e., designate the operation mode and the sequencing policy. For example, it is possible to configure the end-of aisle order picking systems of Bozer and White (1990) by specifying: randomized storage, squared-in-time AS/RS with I/O stations at the lower-left corners of the racks, dedicated S/R machines and separate queues of size 1, which operates under the DC mode and FIFO sequencing. Our simulations below are also of randomized storage, squared-in- time AS/RS with I/O stations at the lower-left corner the racks and dedicated S/R machines. However, the queues in our work are not limited and there is a single common storage queue. Also, operations management tactics and the number of

88 M. Eben-Chaime, N. Pliskiniint. J. Production Economics 51 (1997) 83-M

S/R machines are the subjects of our study and, therefore, are altered. The NN rule is dynamically applied for operations sequencing in all cases below.

The integrative model has been simulated on an 80486 platform using both Turbo-Pascal 6.0TM and ParadoxTM in a complementary manner for pro- gramming. Turbo-Pascal provided methodological flexibility and powerful mathematical processing, while Paradox provided a user friendly interface and sophisticated database management. For the sake of generality, the continuous approximation and rack standardization of Bozer and White (1984) is adopted in the simulation. Specifically, all times and rates in the simulation studies are specified in terms of standard time units, 7’.

The results discussed in the following sections are based on simulations of 100000 service cycles. Preliminary runs showed that this number elimin- ates the need for a warm-up period because warm- up effects are negligible. The discussion is focused on the behavior patterns rather than point values. Therefore, consistency is more meaningful than statistical analyses which were not used.

4. Simulation results

4.1. Throughput, utilization and queues

To gain insight regarding the behavior of the system, we first examined the relationships between the number of S/R machines, their utilization, and the throughput of the system. Recall that the throughput of an AS/RS is the number, per unit time, of service requests performed, which equals the number of requests that arrive at the system. According to the integrative model, each retrieval request is followed by a storage request. Conse- quently, the total arrival rate, and hence the throughput, is twice the arrival rate of retrieval requests. Throughput rates as a function of the number of S/R machines and their utilization are plotted in Fig. 2 for the DC mode, note that the patterns are identical (the patterns, not the values) in all cases that have been studied. As can be expected, the throughput is an increasing function of both the number of S/R machines in the warehouse and their utilization. Of course, similar throughput rates can be achieved with fewer

% 5b% ‘d/. 66% 69% 7b% 7cjz 6bi: 64X 3’?W Sk 1 average machlne utllleation

-n- 2 machlnes . . ., 4 machines d& 6 machines --W-, LO machines

Fig. 2. Throughput vs. utilization for 2, 4, 8, and 10 S/R machines.

M. Eben-Chaime. N. Pliskinllnt. J. Production Economics 51 (1997) 83-98 89

56% 5& S6z 6+X 7b% 7+X 6bz S&X 96X 95X 11 aoersge machlne utillratlon

--D- 2 mpchlnes --+-~ 4 machlnes -b+ B machlneo --)- 10 machlnen

a. DC mode

56z 5$X 6bz 65% 76% 75% & & 9dx 9&L 1 average machine utlllratlon

__E)_. 2 m*eh,nes . . . ..I..... 4 machlnen -K- 6 mnchlnes --)- 10 machlnes

b. hybrid mode

Fig. 3. Waiting time in retrieval queues vs. utilization for 2, 4, 8, and 10 S/R machines.

machines by increasing their utilization and at The behavior of the retrieval queues is also the expense of inferior service levels as discussed similar for both the DC mode of operation and next. the hybrid mode (see Fig. 3, parts (a) and (b),

M. Eben-Chaime, N. PliskinJInt. J. Production Economics SI (1997) 83-98

2’ 48~ 56% 55% 60% 69% 76% 79% 60% 65% 9bz 9sz 1

average machine utilization

P. DC mode

a 0.8- E

2O.T c

; 0.6-

&0.5- E P d 0.4-

0.3 -

b. hybrid mode

Fig. 4. Waiting time in storage queues vs. utilization for 2, 4, 8, and 10 S/R machines

respectively). The pattern is quite expectable: waiting times are much shorter under the hybrid mode, ing times (and hence queue lengths) increase as the especially at high utilization! system is more heavily loaded, i.e., utilization of the The picture is entirely different with respect to S/R machines is higher. Note, however, that wait- the storage queues (see Fig. 4). First, waiting time,

M. Eben-Chaime, N. Pliskinllnt. J. Production Economics 51 (1997) 83-98

2 2.5 3 3.3 4 4.3 average throughput rate

-E- hybrid mode + DC mode

a. Waiting Time in Retrieval Queues

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-B- hybrld mode -M- DC mode

b. Storage Queue Length

91

Fig. 5. Queue performance vs. throughput (7 machines).

92 M. Ehen-Chaime, N. Pliskinjlnt. J Production Economics 51 (1997) 83-98

and hence queue lengths, decrease as the utilization increases under the DC mode, while the opposite trend govern the storage queues under the hybrid mode. Second, the number of S/R machines seems to have no effect on the storage queues under the DC mode, while under the hybrid mode the waiting time in these queues decreases.

Recall the throughput increase due to increase of the number of machines (Fig. 2). Thus, same average utilization in Figs. 3 and 4 implies higher throughput rates for larger number of machines. It seems, however, that under the DC mode each machine operates independently. Under the hybrid

mode, on the other hand, there seem to be mutual cooperation and assistance between machines, which result in the shorter waiting times in both queues and the declining trend in Fig. 4(b). This may be the result of yet another difference between the two modes. Under the DC mode, the number of empty slots in the racks on both sides of each aisle remains constant, since during each cycle, one slot is filled up and another one is emptied. Under the hybrid mode, the number of empty slots varies because SC cycles are also performed, but when an

aisle is saturated ULs can be stored in other aisles. The differences between the two modes motivate us to further compare their performance in the next section.

4.2. Performance comparison under the DC and hybrid modes

So far, various parameters have been presented as functions of the utilization of the S/R machines under the same mode of operation, and modes have been compared with regard to behavior patterns, Next, service levels are compared for the two operation modes. The primary measures for quality of service of AWS are throughput rates and response times. Another important parameter is the space required for the ULs that are waiting in the storage queues, i.e., the lengths of these queues. Compari- sons of the relationships among these parameters under the DC mode and the hybrid mode are displayed in Fig. 5, for an AS/RS with seven machines. Average waiting time in the retrieval queues, which constitutes the major component of

50% ! 1 I I 1 I 2 2.5 3 3.5 4 4.5


-B- hybrid mode -X- DC mode

Fig. 6. Utilization vs. throughput (7 machines).

M. Eben-Chaime. N. Pliskinllnt. J Production Economics 51 (1997) 83-W 93

the response time, and average storage queue length are displayed as functions of the throughput in Figs 5(a) and (b).

It is obvious from Fig. 5 that while the waiting- time curves for the retrieval queues are similar under the two modes, the queue-length curves for the storage queues are not. The latter de- pict a decreasing function of the throughput, under the DC mode, and an increasing function, under the hybrid mode. Furthermore, the rate of increase in the length of the storage queue under the hybrid mode is rather slow and, for the most part, the queue is much shorter than under the DC mode. An explanation of these seemingly contradicting behaviors, shorter storage queue lengths despite the longer travel time, can be found in Fig. 6, where average utilization of the seven S/R machines is plotted as a function of the average throughput. Definitely, the utilization under the hybrid mode is higher than under the DC mode for all throughput values. The higher utilization of the S/R machines under the hybrid mode allows both compensation for the longer travel time and reduction in the length of storage queues by more rapidly storing the returned ULs. Thus, except for very high throughput levels the hybrid mode outperforms the DC mode.

Note also that because the simulation failed at utilization higher than 97%, the curves for the DC mode in Figs. 5 and 6 are shorter than the curves for the hybrid mode. In contrast, the hybrid mode performed well at close to 100% utilization providing 4.8 services in a standard time unit. The loss of system stability under the DC mode has also been observed at high throughput/utilization values in the case of a single machine (Eben-Chaime and Pliskin, 1996).

5. Discussion

The results presented in the previous section suggest that to provide the same service level, a smaller number of machines may be required under the hybrid mode than under the DC mode. To verify this conclusion, numerous simulations have been executed using varying numbers of S/R

machines. Three examples are presented in Figs. 7-9. In each example, the waiting time in the retrieval queues (part (a) of each of the 3 figures) and the length of the storage queues (part (b) of these figures) are plotted against the throughput rates. Unlike Fig. 5 where the two modes of operation were compared for the same number of machines (seven), Figs. 7-9 compare the DC mode, using a certain number of machines, and the hybrid mode, using fewer machines.

In Fig. 7, performance using six machines under the DC mode is compared with that of using five machines under the hybrid mode. For a throughput rate of about 2.8 service (storage and/or retrieval) requests per unit time, the waiting time in the retrieval queues is 2 time units for six machines (DC) and 4.5 time units for five machines (hybrid). On the other hand, the length of the storage queues is about 8.5 and 2.5, respectively. For lower throughput rates, the differences in the waiting time in the retrieval queues are smaller while the corresponding reductions in the storage queue length are much larger.

As can be seen in Fig. 8, similar results were obtained for seven S/R machines under the DC mode and six machines under the hybrid mode. For example, for a throughput rate of about 3.3, the waiting time of retrieval requests is 2 units for seven machines (DC) and somewhat less than 4 units for six machines (hybrid), while the length of the storage queues are 10 and 2, respectively. Again, the relative gap between respective waiting times declines for lower throughput rates while the relative gap between respective storage queue lengths grows larger.

The presentation is completed with the comparison in Fig. 9 of 10 machines, under the DC mode, with eight machines, under the hybrid mode. The point to look at is at throughput rate of about 4.8. The waiting time in the retrieval queues increases from about 2.5 time units for 10 machines (DC) to about 6.5 units for eight machines (hybrid). At the same time, the storage queue length is reduced from more than 13 to less than 4. As in the previous examples, the waiting times become closer and the storage queue lengths become further apart for lower throughput rates.

94 M. Eben-Chaime, N. Pliskinllnt. J. Production Economics 51 (1997) 83-98

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AL Eben-Chaime. N. Pliskinllnt. J. Production Economics 51 (1997) 83-98

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-B- hybrid mode --+t DC mode

16-


1 4 _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 _ . . __...............,.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

c 0 10 _ _..........._..._........................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

B s 8 _ .__........._..............................................,........................................................... . . . . . . . . . . . . . . . . b

!j 6 _ .._........._._..............................................................................................................,...................................

*

4 _ . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 _ . . . . . . . . _......_........,...................................... . . . . . . . . . . . . . . .

o! I I I I 8 I

2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 .rerage throughput rate

-8- hybrid mode * DC mode



95

A-f Eben-Chaime, N. PliskinJInt. J. Production Economics 51 (1997) 83-98

40

35 _ ,............._........,....................................

30 - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 25 - ..f...........................‘......”.’.. ...... “..‘..“...

a

i 2Q - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

cl g 15 _ . . . .._.......................................................

d

10 _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x 0 I , I I I I I 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 F


a hybrid mode + DC mode


6

3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 average throu#hput rate

-E- hybrid mode * DC mode



M. Ehen-Chaime, N. PliskinJInt. J. Production Economics 51 (1997) 83-98 97

Evidently, similar patterns appear in all three examples and in other cases not shown. The service level, in terms of response (waiting) time to retrieval requests, declines when fewer machines are used. However, this should be balanced against the space required for the ULs that are waiting to be stored, i.e., the length of the storage queue. In each of the three examples, there is a wide range of throughput rates where the storage queues are much longer under the DC mode, with more machines, than under the hybrid mode with fewer machines. For the same range of throughput rates, the differences in the waiting times in the retrieval queues are not so big and the times themselves are fairly short.

6. Conclusion

This paper extends the scope of previous studies in two major ways. First, we studied performance of AWS within a total system from various angles. Second, we looked at AWS with multiple machines rather than a single machine. Based on this study it is possible to provide a negative answer to the question of whether the DC mode, due to its shorter travel times, is the preferred operation mode for multiple-machine AWS. Evidently, due to system instability and the longer storage queues associated with the DC mode, the slower hybrid mode is the preferred alternative. When one adds this finding to the results reported by Eben-Chaime (1992), it can be generally concluded that if work is not preserved in order to shorten service time, service time reduction is not always the best strategy.

The practical implication of this conclusion is, in addition to direct service improvements, the oppor- tunity to maintain a desired service level while reducing the number of S/R machines. The simulations revealed that, under the hybrid mode, for low to moderate throughput levels, reductions in the number of S/R machines.and in the waiting space for ULs to store can be obtained, at the expense of a minor loss in the level of service in terms of response time. For high throughput rates, the same number of S/R machines is needed under both modes, but the space required for the storage queues can still be reduced by using the hybrid

mode as indicated in Fig. 5(b). These finding have significant economic ramifications because the in- vestment in the S/R machine constitutes a domi- nant component of the total cost of the warehousing system. Using six machines rather than seven, or eight rather than 10, leads to 15520% saving in machine life-cycle cost. Since building space is required to hold the physical ULs that are waiting in the storage queues, further savings can be achieved under the hybrid mode because of the shorter storage queues.

The integrative warehousing model and the simulation approach presented in this paper can be incorporated into system design schemes, e.g., the search scheme of Bafna (1981), the optimization and simulation scheme of Roll and Rosenblatt (1981), etc., to enhance their applicability. The integrative model and the simulation approach can also be employed to further study the effects of storage policies and assignment rules. Moreover, the proposed approach forms a basis for studying all these issues in an integrative manner to enable better warehouse design in terms of economic efficiency.

Acknowledgements

Special thanks are due to our students D. Sosna and S. Shafir who developed the simulation system and provided the results in both numerical and graphical form.

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