Optimal and heuristic solutions for the single and multiple batch flow shop lot streaming problems with equal sublots

Transcription

1 Optial and heuristic solutions for the single and ultiple batch flow shop lot streaing probles with equal sublots by Adar A. Kalir Dissertation subitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillent of the requireents for the degree of Doctor of Philosophy in Industrial and Systes Engineering Approved: Dr. Subhash C. Sarin Dr. Michael P. Deisenroth Dr. Hanif D. Sherali Dr. Philip Y. Huang Dr. Charles P. Koelling

2 Science is like the oke about the drunk who is looking under a lappost for a key that he has lost on the other side of the street, because that s where the light is. It has no other choice - Noa Chosky (4 June 993) ii

3 Optial and heuristic solutions for the single and ultiple batch flow shop lot streaing probles with equal sublots by Adar A. Kalir Dr. Subhash C. Sarin, Chairan Industrial and Systes Engineering ABSTRACT This research is concerned with the developent of efficient solutions to various probles that arise in the flow-shop environents which utilize lot-streaing. Lot streaing is a coonly used process of splitting production lots into sublots and, then, of scheduling the sublots in an overlapping fashion on the achines, so as to expedite the progress of orders in production and to iprove the overall perforance of the production syste. The different lot-streaing probles that arise in various flow-shop environents have been divided into two categories, single-lot probles and ultiple-lot probles. Further classification of the ultiple-lot probles into the lot streaing sequencing proble (LSSP) and the flow-shop lot-streaing (FSLS) proble is ade in this work. This classification is otivated by the occurrence of these probles in the industry. Several variants of these probles are addressed in this research. In agreeent with nuerous practical applications, we assue sublots of equal sizes. It turns out that this restriction paves the way to the relaxation of several typical liitations of current lot-streaing odels, such as assuption of negligible transfer and setup ties or consideration of only the akespan criterion. For the single-lot proble, a goal prograing (GP) approach is utilized to solve the proble for a unified cost obective function coprising of the akespan, the ean flow tie, the average work-in-process (WIP), and the setup and handling related costs. A very fast optial solution algorith is iii

4 proposed for finding the optial nuber of sublots (and, consequently, the sublot size) for this unified cost obective function in a general -achine flow shop. For the ore coplicated ultiple-lot proble, a near-optial heuristic for the solution of the LSSP is developed. This proposed heuristic procedure, referred to as the Bottleneck Minial Idleness (BMI) heuristic, identifies and eploys certain properties of the proble that are irregular in traditional flow-shop probles, particularly the fact that the sublot sizes einating fro the sae lot type and their processing ties (on the sae achines) are identical. The BMI heuristic attepts to axiize the tie buffer prior to the bottleneck achine, thereby iniizing potential bottleneck idleness, while also looking-ahead to sequence the lots with large reaining process tie earlier in the schedule. A detailed experiental study is perfored to show that the BMI heuristic outperfors the Fast Insertion Heuristic (the best known heuristic for flow-shop scheduling), when odified for Lot Streaing (FIHLS) and applied to the proble on hand. For the FSLS proble, several algoriths are developed. For the two-achine FSLS proble with an identical sublot-size for all the lots, an optial pseudo-polynoial solution algorith is proposed. For all practical purposes (i.e., even for very large lot sizes), this algorith is very fast. For the case in which the sublot-sizes are lot-based, optial and heuristic procedures are developed. The heuristic procedure is developed to reduce the coplexity of the optial solution algorith. It consists of a construction phase and an iproveent phase. In the construction phase, it attepts to find a near-optial sequence for the lots and then, in the iproveent phase, given the sequence, it attepts to optiize the lot-based sublot-sizes of each of the lots. Extensions of the solution procedures are proposed for the general -achine FSLS proble. A coprehensive siulation study of a flow shop syste under lot streaing is conducted to support the validity of the results and to deonstrate the effectiveness of the heuristic procedures. This study clearly indicates that, even in dynaic practical situations, the BMI rule, which is based on the proposed BMI heuristic, outperfors existing WIP rules, coonly used in industry, in scheduling a flow-shop that utilizes lot streaing. With respect iv

5 to the priary perforance easure cycle tie (or MFT) the BMI rule deonstrates a clear iproveent over other WIP rules. It is further shown that it also outperfors other WIP rules with respect to the output variability easure, another iportant easure in flow-shop systes. The effects of several other factors, naely syste randoness, syste loading, and bottleneckrelated (location and nuber), in a flow-shop under lot streaing, are also reported. v

6 ACKNOWLEDGEMENTS This is a drea coe true for which I first wish to thank y parents, without who this would not have been possible. Their unconditional love and constant support over the years is soething that I cannot thank the enough for. In the sae breath, I would like to thank y wife, Rina, for her ental support, patience and understanding and, for her willingness to postpone her own personal developent and career, to allow e to pursue y own. My deepest appreciation goes to y advisor, the Chairan of y coittee, Professor Subhash C. Sarin, for his valuable assistance, guidance, and encourageent in bringing this research work to a successful copletion. I regard hi as a personal friend and I highly coend hi for his character and acadeic achieveents. I a particularly grateful to y dissertation coittee eber, the Assistant Departent Head in the Departent of Industrial and Systes Engineering at Virginia Tech, Professor Michael P. Deisenroth, for his good advice, support, and, I dare say, friendship, throughout y graduate studies. I would like to sincerely thank y dissertation coittee eber, the Head of the Operations Research progra in the Departent of Industrial and Systes Engineering at Virginia Tech, Professor Hanif D. Sherali, for being a role odel in deonstrating what excellence in teaching and research truly eans. I highly coend hi for his acadeic capabilities and accoplishents. vi

7 I a also thankful to the reaining ebers of y dissertation coittee, Professor George Ioannou and Professor Philip Huang (of the Manageent Science progra) for their guidance and their interest in y research. A special thanks is also due to Dr. Charles P. Koelling who gracefully agreed to serve on y coittee at the last stages of the research. I take this opportunity to also thank y M.Sc advisor, Dr. Yohanan Arzi, a true colleague and a dear friend. Thanks is also due to Prof. Daniel Sipper, Prof. Avraha Shtub, and Prof. Oded Maion of the Departent of Industrial Engineering at Tel-Aviv University for their support. Last, but not least, I thank all y colleagues and friends that I have acquired throughout y years at Virginia Tech John Tester, Mark and Sue Eaglesha, Andre and Karla Raos, Alexandra and Arando Medina, Cole Sith, Dan Mullins, Vianni Perianayaga, and Michael Greco - to nae a few. I would also like to thank the Faculty and the Staff in the Departent of Industrial and Systes Engineering Dr. Willia Sullivan, Dr. Janis Terpenny, Dr. John Shewchuk, and Lovedia Cole, again, ust to nae a few. I a honored to have been a part of such a talented and dedicated staff during y years at Tech. I will cherish this period greatly for the rest of y life. vii

8 Table of Contents ABSTRACT...III ACKNOWLEDGEMENTS... VI CHAPTER : INTRODUCTION.... BACKGROUND AND MOTIVATION....2 STATEMENT OF THE PROBLEM RESEARCH OBJECTIVES CONTRIBUTIONS OF RESEARCH LOT STREAMING APPLICATIONS....6 ORGANIZATION OF RESEARCH... 4 CHAPTER 2: LITERATURE SURVEY HISTORICAL REVIEW EXISTING PPC METHODOLOGIES Just-in-tie (JIT) and Kanban Constant work-in-process (CONWIP) The Theory Of Constraints (TOC) and Optiized Production Technology (OPT) FLOW SHOP SEQUENCING AND SCHEDULING LOT STREAMING Terinology and definitions Single batch odels Multiple batch odels SUMMARY OF EXISTING RESEARCH AND DIRECTIONS FOR FUTURE RESEARCH PPC ethods and lot streaing Flow shop scheduling and lot streaing Justification for the use of equal sublots in lot streaing CHAPTER 3: SINGLE BATCH MODELS WITH EQUAL SUBLOTS SCOPE PRELIMINARY ANALYSIS OF OBJECTIVE FUNCTIONS AND POTENTIAL BENEFITS Makespan obective Mean flow tie (MFT) obective Average work-in-process (WIP) obective Suary of the benefits via lot streaing THE IMPACT OF TRANSFER ON THE OBJECTIVE FUNCTION Independent non-operator-based transfer Independent operator-based transfer Dependent (non-operator-based) transfer The ipact of transfer tie on a cost-based obective THE IMPACT OF SETUP ON THE MAKESPAN FUNCTION Analysis of the proble Optial solution algorith Coplexity of the algorith viii

9 3.4.4 Nuerical exaple Optial integer solutions THE IMPACT OF SETUP AND TRANSFER ON A COST-BASED OBJECTIVE THE IMPACT OF SETUP ON THE MEAN FLOW TIME (MFT) THE IMPACT OF SETUP ON THE AVERAGE WIP A UNIFIED COST-BASED MODEL USING A GOAL PROGRAMMING APPROACH Proble description and analysis Proposed solution algorith Coplexity of the algorith A coprehensive nuerical exaple SUMMARY OF RESULTS... CHAPTER 4: MULTIPLE BATCH MODELS WITH EQUAL SUBLOTS INTRODUCTION Classification of ultiple-batch lot streaing probles Notation and proble forulation PROBLEM COMPLEXITY POTENTIAL BENEFITS FROM LOT STREAMING IN A MULTIPLE-BATCH FLOW-SHOP The akespan obective The MFT obective The WIP obective Suary of benefits Case study THE LOT STREAMING SEQUENCING PROBLEM (LSSP) The two-achine case The general -achine case THE MODIFIED FIH HEURISTIC FOR LSSP The Fast Insertion Heuristic for LSSP (FIHLS) The coplexity of the FIHLS Optiality of the FIHLS heuristic Liitations and drawbacks of the FIHLS THE BOTTLENECK MINIMAL IDLENESS (BMI) HEURISTIC FOR THE LSSP Preliinaries Nuerical illustration Bottleneck-based analysis The BMI heuristic Nuerical exaples of the BMI heuristic Optiality of the BMI heuristic The ipact of setup on the perforance of the BMI heuristic Suary of the BMI heuristic for the LSSP THE FLOW SHOP LOT STREAMING (FSLS) PROBLEM Global sublot-size two-achine FSLS proble Lot-based sublot size two-achine FSLS proble Extensions to -achine flow-shops SUMMARY OF RESULTS CHAPTER 5: DYNAMIC LOT STREAMING WITH EQUAL SUBLOTS INTRODUCTION CONDITIONS FOR LOT STREAMING TO BE BENEFICIAL THE IMPACT OF WIP POLICIES PERFORMANCE MEASURES Cycle tie Cycle tie variability Output variability Average WIP WIP-Turns ix

10 5.5 THE DYNAMIC BMI HEURISTIC FACTORS IN THE EXPERIMENTAL STUDY WIP anageent rules Operating conditions: factors of randoness Operating conditions: syste loading and bottleneck effects Experiental design THE SIMULATION MODEL The Orders worksheet The Stations worksheet The Parts worksheet The Routes worksheet The siulated flow-shop The experients SIMULATION RESULTS ANALYSIS The ipact of WIP rules on syste perforance The ipact of randoness on syste perforance The ipact of syste loading on syste perforance Bottleneck effects on syste perforance SUMMARY OF RESULTS CHAPTER 6: SUMMARY AND CONCLUSIONS APPENDICES APPENDIX A: TERMS FOR THE STRICT CONVEXITY OF WIP ( n) APPENDIX B: BASIC PROGRAM FOR THE FIHLS HEURISTIC APPENDIX C: EXAMPLE OF FILE OUTPUT OF THE FIHLS HEURISTIC PROGRAM APPENDIX D: SUMMARY OF OUTPUT OF THE FIHLS APPENDIX E: A PROOF FOR THE DECREASING EFFECT OF THE NUMBER OF LOTS ON MAKESPAN REDUCTION APPENDIX F: A COMPARATIVE STUDY OF THE OPTIMALITY OF THE BMI AND FIHLS HEURISTICS APPENDIX G: FORMAT OF INPUT DATA OF THE SIMULATION MODEL APPENDIX H: SIMULATION MODEL RESULTS VITA x

11 List of Tables Table 2.. Suary of single batch odels 40 Table 3.. Upper bounds on the benefits via lot streaing 72 Table 3.2. Data for nuerical exaple Table 3.3. Data for exaple Table 3.4. Sensitivity analysis for exaple Table 4.. Benefits via lot streaing in a ultiple batch flow shop, under equal lot sizes, equal processing ties, and negligible transfer and setup ties 28 Table 4.2. Processing tie data for the case study 29 Table 4.3. Suary of results for the case study 29 Table 4.4. Data for nuerical exaple Table 4.5. Average akespan to lower bound ratios for different nubers of lots and different sublot sizes, when setup ties are ignored (i.e., 0%) 40 Table 4.6. Average akespan to lower bound ratios for different nubers of lots and different sublot sizes, for the case of 5% setup ties 40 Table 4.7. The ipact of setup tie on interingling in the FIHLS solution 43 Table 4.8. Data for nuerical exaple Table 4.9. The effect of sublot size on the optiality ratio of a zero bottleneck idleness schedule 52 Table 4.0. Estiated idle tie in LS-schedules for nuerical data Table 4.. Data for nuerical exaple Table 4.2. Data for nuerical exaple Table 4.3. Processing tie data for nuerical exaple Table 4.4. Values for classification of probles into groups according to level of doinance 7 Table 4.5. Optiality ratios for the BMI and FIHLS heuristics 73 Table 4.6. Data for nuerical exaple xi

12 Table 4.7. Setup tie data for nuerical exaple Table 4.8. Data for nuerical exaple Table 4.9. Solution suary for nuerical exaple Table Revised data for nuerical exaple Table 4.2. Solution suary for the revised nuerical exaple Table Data for nuerical exaple Table Coputations perfored in Step 2 for exaple Table 5.. Data for nuerical exaple Table 5.2. Lot-based WIP inventory levels over tie, exaple Table 5.3. Proble characteristics and the BMI heuristic: coparison for the static and the dynaic lot streaing probles 27 Table 5.4. Experiental design for siulation study 223 xii

13 List of Figures Fig... Scheatic SMT production line 2 Fig. 3.. Non-operator-based and operator-based transfer scenarios 73 Fig Attached setups in a three-achine flow shop 78 Fig Typical M ( n) functions as a function of the nuber of sublots 80 Fig The solution for the nuerical exaple via step 2 of the algorith 88 Fig The solution for the nuerical exaple via step 3 of the algorith 89 Fig The non-convex function WIP(n) 98 Fig The ters of the obective function as a function of nuber of sublots 0 Fig. 4.. Classification of ultiple-batch flow shop lot streaing probles 4 Fig The akespan ratios as a function of nuber of sublots and setup ties 42 Fig The effect of lot streaing on bottleneck idle tie 49 Fig A lexicographic rule-based sequence versus an arbitrary sequence 60 Fig The interingled BMI schedule for exaple Fig Makespan as a function of the sublot-size 88 Fig Phase schedule for exaple Fig. 4.8(a). Iproved schedule for exaple 4.9: first iteration 98 Fig. 4.8(b). Iproved schedule for exaple 4.9: second iteration 98 Fig. 4.8(c). Iproved schedule for exaple 4.9: third iteration 98 Fig. 4.8(d). Iproved schedule for exaple 4.9: fourth iteration 99 Fig. 4.8(e). Final schedule for exaple Fig Solution flowchart for the two-achine and -achine FSLS probles 20 Fig. 5.. FIFO and LIFO schedules, exaple Fig Average cycle tie for the deterinistic set of experients 230 Fig Average cycle tie for the stochastic set of experients 230 Fig Standard deviation of cycle tie for the deterinistic set of experients 23 xiii

14 Fig Standard deviation of cycle tie for the stochastic set of experients 23 Fig Standard deviation of output for the deterinistic set of experients 232 Fig Standard deviation of output for the stochastic set of experients 232 Fig Mean tie between departures for the deterinistic case (experient #3) 233 Fig Ipact of syste loading on the average cycle tie 236 Fig Ipact of syste loading on the cycle tie standard deviation 236 Fig. 5.. Ipact of bottleneck location(s) on the average cycle tie 238 Fig Ipact of bottleneck location(s) on the cycle tie standard deviation 238 xiv

15 Chapter : Introduction. Background and Motivation With the approach of the twenty first century, there has been a great deal of discussion aong researchers, as well as practitioners, regarding the Factory of the Future (FOF). Many technologies needed for the FOF are already well developed. Others are under active iproveent. Still others are quite hazy and need significant developent to be considered viable contributors. For exaple, MRP-II won t schedule the factory of the future (Mather, 986). Factories present various probles, any of which have been addressed by researchers with a significant aount of success. To effectively deal with these probles, probles have coonly been divided into three hierarchical categories (Anthony, 965): Strategic planning Tactical planning, and Operations control Strategic planning deals with the process of selecting the obectives by which to easure the overall perforance of the factory, and the optial level of the resources required to attain these obectives. The tactical planning level addresses probles pertaining to the effective utilization of the resources in view of the desired obectives. Finally, the operations control level is concerned with the detailed operational and scheduling decisions. The research work described herein falls into the last category. The iportance of this work eerges fro the root causes as to why MRP won t schedule the factory of the future, as indicated by Mather. Material Requireents Planning (MRP) and Manufacturing Resources Planning (MRP-II) were the first structured ethods to be developed for Production Planning and Control (PPC). Even today, these ethods are widely

16 used in the industry. MRP-based ethods provide a tiely plan for the acquisition of raw aterials and their processing, based on the Bill Of Materials (BOM), and the procureent and production Lead Ties (LT s) of the end products. MRP-II-based ethods further accoodate the liited capacity of the available resources, ensuring that the MRP tiely plans would also be feasible. However, both MRP and MRP-II systes do not allow overlapping of the operations on a batch for processing by sequential achines. The production batch in these systes is an integral entity which cannot be further broken down. This represents a aor liitation of MRP-based systes, fro a practical standpoint. The overlapping of operations for processing by the achines has also been the priary reason for the success of two other PPC ethods during the 80 s, which rapidly replaced MRPbased systes in the any industries. These two ethods are the well-known Just-In-Tie (JIT) and Optiized Production Technology (OPT). In contrast to MRP ethods, these JIT and OPT ethods strongly support the overlapping of operations in production. JIT calls for the eliination of unproductive setup ties and for the production of very sall (sub-)lot sizes, preferably of size one. OPT is less restrictive than JIT and calls for the splitting of lots into transfer batches the OPT ter for sublots - before and after the bottleneck achine(s). Both JIT and OPT, although differing in their analysis of production systes, have reached siilar conclusions. They have concluded that significant iproveents can be attained by breaking down production batches into saller transfer batches. Soewhat surprisingly, the critical probles, pertaining to the splitting of the production batches into transfer batches and the sequencing (or streaing) of these transfer batches throughout the production syste have reained open. Neither JIT nor OPT have addressed these probles explicitly (Jacobs, 984). This research is otivated by the need to develop practical solutions for these open probles. JIT and OPT have both, independently, articulated that better syste perforance would be attained by streaing sall portions of work through the syste. But they have both fallen short, as far as ipleentation goes, in certain practical situations. JIT does not address cases in which the setup ties cannot be reduced to insignificant levels relative to the processing ties. Furtherore, it does not provide a straightforward answer as to what a sufficiently sall setup tie for JIT to work as expected is. OPT does not provide the eans for deterining the optial transfer batch sizes and/or the sequence in which these transfer batches should be 2

17 processed. OPT erely utilizes transfer batches to save tie on the bottleneck resource(s). The utilization of transfer batches, in OPT, is liited to the neighborhood of the bottleneck, and does not extend throughout the syste. As we shall see in the literature survey of lot streaing, optiizing the sizes of transfer batches and streaing the throughout the syste, as opposed to ust near the bottleneck, can further enhance the gains. In addition to the above liitation, OPT also falls short in coping with systes in which several resources experience the sae workload (i.e., parallel siultaneous bottlenecks.) OPT postulates that such cases are rare in reality and are not desirable. However, efforts of assebly line balancing, group technology, and other techniques do lead to flow-shop configurations with alost perfect balance and, therefore, such cases should not be overlooked. To further otivate the need for this research, consider the following siple proble. A single batch of 00 ites is to be produced using a three-achine flow line. The routing is {M, M2, M3} with unit processing ties of {2,, 3} respectively. Assue that, at tie zero, all the achines are available, and that, setup and transfer ties are negligible. In traditional batch production, the entire batch is processed before it is transferred fro one achine to the next. This results in a akespan of 00(2++3)=600 tie units. Now suppose that there are no liitations on the transfer of products between the achines. In that case, it would be ore efficient to transfer the first ite, upon copletion on the first achine, to the next achine, instead of letting it await the copletion of the reainder of the batch on that achine. By transferring the parts one by one, as soon as the processing is copleted on the, the akespan can be reduced to: (2++3)+99(3)= 303 tie units, a reduction of alost 50%! This result deonstrates the potential benefits that can be gained fro the utilization of lot-streaing. However, this result relies heavily on the assuption that the transfer tie is negligible. Otherwise, the akespan ay increase significantly. For exaple, let TT be the transfer tie of any transfer batch size fro one achine to the next. Assue that the transfer tie is independent of the transfer batch size and that the achine is not operational during transfers (e.g., when the operator of the achine is also used to transfer the ites.) Then, the akespan under no splitting becoes: M = ( TT) 3

18 whereas the akespan under lot-splitting becoes: M = ( TT) Clearly, for TT 5. tie units, it becoes undesirable to split the batch into unit-sized transfer batches. So, suppose TT = 2. Does this iply that splitting is undesirable? The answer is negative. It ay still be desirable to split the batch but, preferably, to larger transfer batches, in order to balance the additional transfer tie involved. For exaple, equal transfer batches, of 0 ites each, result in the following akespan: [ ( )] [ ( )] M = = 370 This akespan is still significantly better than the one attained under no splitting. As we shall deonstrate in the literature review of single batch odels, by letting the transfer batches be of unequal sizes, the akespan ay be iproved even further. This is due to the following two reasons. First, and ore obvious, the transfer tie can be reduced if we allow unequal transfer batches. In the above exaple, there is no need to transfer sub-batches of 0 ites fro the second achine to the third every tie that these sub-batches are copleted on the second achine. These sub-batches need only be transferred after the copletion of every three subbatches since, only by that tie, the third achine copletes the processing of the previous subbatch. The second reason for which unequal transfer batches ay be ore desirable is that, by doing so, the achines can be ore efficiently utilized. As evident by the exaple, the proble of the deterination of optial transfer batch sizes is a proble worthy of study. Several versions of this proble are addressed in this research. Although JIT and OPT have not provided specific answers to this proble, they have given rise to any essential probles, in the area of lot streaing, that have not been addressed before and have finally started drawing the deserved attention. Certainly, lot streaing as a research area is not new. Its first appearance in the literature dates back ore than thirty years ago, when Reiter (966) first coined the ter. Although his work, at the tie, was very liited, because of the liited coputer capabilities and the absence of PPC tools, it was still an identification of a possible avenue to iproving efficiency in production systes. As iplied in the discussion thus far, lot streaing is the process of splitting production lots into sublots, and then scheduling these sublots in an overlapping fashion 4

19 on the achines (or ore generally, the resources), in order to accelerate the progress of orders in production (Baker and Jia, 993), and to iprove the overall perforance of the production syste. Research in the area of lot streaing was not conducted in the 70 s. There were inor exceptions in this regard that will be entioned in the literature survey. It was not until the late 80 s and the early 90 s, after extensive research into JIT and OPT had been carried out, that the area of lot streaing was re-discovered. Soe progress has definitely been ade during the past few years. Analytical and siulation-based works have contributed to a better understanding of the ipact of lot streaing in various anufacturing environents. Truscott (986) entions several potential benefits of lot streaing: Reduction of production lead ties (thus, better due-date perforance) Reduction of WIP inventory, and associated WIP costs Reduction of interi storage and space requireents ; and Reduction of aterial handling syste (MHS) capacity requireents Siulation studies and industry-based reports, published in recent years, have confired that the above benefits can indeed be achieved via lot streaing in various batch production environents. Following are soe exaples: Job shops (Dauzere and Lasserre, 997 ; Sunt et. al., 996) Flow shops and serial production systes (Wu and Egbelu, 994) Flexible assebly systes (FAS) (Sohlenius et. al., 989) Group Technology (GT) cells (Vebu and Srinivasan, 995) Cellular Manufacturing Systes (CMS) (Logendran and Raakrishna, 995) Still, as far as research is concerned, any of the lot streaing probles reain poorly understood (Vickson, 995). The next Section describes two such probles. These two probles are the focus of this research. 5

20 .2 Stateent of the Proble The proble that is addressed in this research can be stated as follows. Given a batch, or a set of batches, to be processed in a flow shop, deterine sublots of equal size and the associated sequence in which to process the sublots, so as to iniize akespan and other perforance criteria. This proble can be divided into two cases. One pertains to the deterination of the sequence of the sublots, given that the sublot size had been pre-deterined. The second pertains to the deterination of the sequence of the sublots as well as their size. The forer case will be referred to as the Lot Streaing Sequencing Proble (LSSP) while the latter will be referred to as the Flow Shop Lot Streaing (FSLS) proble. In both, the sublots ay or ay not interingle while streaed throughout the syste. These two different probles correspond to two different practical applications, which will be described in ore detail in Section.4. The following characteristics apply to both cases: There are N lots to be processed on an -achine flow shop. The lots can be split into sublots (of unknown size) during production. The sequence in which a achine processes the lots (or sublots) is unknown (but all the lots follow the sae achine ordering.) The achines require setup before the start of sublots processing. The lots are of different sizes. The sublots of each lot are of equal size. The above characteristics constitute an extreely difficult-to-solve sequencing proble, with the additional coplication resulting fro the unknown sublot sizes in the FSLS proble. As will be discussed in the Literature Review (Chapter 2), the traditional -achine flow shop sequencing proble (i.e., without lot streaing) is known to be NP-hard. Thus, under lot streaing, if the sublots are considered independently, a large-scale coplicated flow shop sequencing proble results, which is notoriously NP-hard. The assuptions that are ade in the odels developed in this research coply with the traditional assuptions of regular flow-shop sequencing probles. These assuptions are as follows: 6

21 The achines are available for continuous processing. Preeption is not allowed, i.e., once the processing of a sublot has begun it cannot be stopped. The setup ties and the unit processing ties are deterinistic and known in advance. The lots considered for sequencing are available at the beginning of the planning period (this assuption is relaxed in Chapter 5.) The achines cannot process ore than one sublot at any tie. This research akes a first attept to deal with the general proble of sequencing ultiple lots in a ultiple-achine flow-shop under lot-streaing with non-negligible setup ties and unknown sublot sizes. In accordance with the two applications, consideration is restricted to the case of equal sublots. Justifications for this restriction are provided in the literature review. In soe cases, as will be discussed later, this restriction akes the proble even ore coplicated. To further ustify the need for the proposed research, it is noted that the single ost iportant proble facing production anagers, on a daily basis, is how to effectively carry out daily production. Daily production is typically derived fro the Master Production Schedule (MPS) that specifies lot sizes and due dates for a tie period of several days work, norally a onth. The MPS does not specify the sequence in which the lots should be produced and/or the transfer batches that should be utilized. These iportant decisions, which ay significantly ipact the perforance of the entire production syste and, in fact, of the entire facility, are unfortunately ade, on a daily basis, by production anagers who do not possess the proper tools for aking the best decisions. As explained in the previous Section, JIT and OPT have not provided sufficient and broad eans to cope with these decisions. JIT suggests solutions only for particular cases in which the transfer and the setup ties are negligible. OPT suggests solutions by focusing on the bottleneck, but does not explain explicitly how to deterine the transfer batch sizes and their sequence. This research is geared towards developing and providing effective, and yet practical, solutions for the flow-shop lot-streaing probles, to enable production anagers to ake 7

22 better decisions when faced with these types of probles. Although the sae probles arise in alost every batch production syste, this research is particularly concerned with general flowshop systes. Flow-shop systes are coonly used in the industry for the production of a single product or a faily of siilar products that are in high deand. In a flow shop syste, achines are organized in serial and the lots flow fro one achine to the next in the sae order. Production lines, assebly lines, and flow lines all fall into the category of flow-shop systes..3 Research Obectives The priary obective of this research is to study the effects of lot streaing in single and ultiple batch flow-shop systes and to provide optial and heuristic solutions for a variety of lot-streaing probles that arise in these systes. Fro a practical standpoint, this research is geared toward developing and providing effective solutions for these probles to enable production anagers to ake better decisions when faced with the. In view of the above, the following obectives are pursued: To analyze and evaluate the extent of the potential benefits of lot streaing with respect to various obective functions To study the effects of the proble paraeters on the potential benefits of lot streaing with respect to various obective functions To solve the single-batch lot-streaing proble under various scenarios of non-negligible transfer and setup ties, and for various obective functions To develop an efficient optiu seeking algorith for the single-batch lot-streaing proble with respect to a unified obective function To effectively extend the results developed for the single-batch lot-streaing proble to the ultiple-batch lot-streaing proble To suggest efficient heuristics for the solution of the ultiple-batch lot-streaing proble with respect to the akespan criterion To study the effects of lot streaing in a dynaic flow shop with respect to tie-invariant obective functions (e.g., ean flow tie, output variability, etc.) 8

23 .4 Contributions of Research This research akes a first attept to deal with the general proble of sequencing ultiple lots in a ultiple-achine flow shop that utilizes lot-streaing, with the consideration of non-negligible sublot-attached setup ties. Meaningful results and useful insights are provided for this proble. In particular, the proposed research akes the following contributions to the literature for the single-lot ultiple-achine flow-shop proble: Analysis of the extent of the potential benefits via the use of lot streaing with respect to the three coonly used perforance easures. These easures are:. Makespan (i.e., the total copletion tie of all the lots.) 2. Mean Flow Tie (MFT). 3. Average WIP level. Closed-for forulae for the optial (equal) sublot size with respect to both operational and econoical obective functions, under various fors of non-negligible transfer ties. An optial solution algorith of coplexity O( ) coputations and O( 2 ) coparisons for the obective of iniizing the akespan, for the case of non-negligible sublot-attached setup ties, and its odifications for ipleentation for the iniization of production cost as well. An optial solution algorith to obtain the optial sublots, and a quick approxiation schee, for the ost general case of an obective function that considers the weighted su of the akespan, the ean flow tie, the average work-in-process, the setup, and the aterial handling associated costs. For the ultiple-lot ultiple-achine flow-shop, the contributions of this research are as follows: Analysis of the extent of potential benefits via the use of lot streaing in a ultiple-lot, ultiple-achine flow shop with respect to the sae three easures listed above. A near-optial heuristic procedure for the lot streaing sequencing proble (LSSP) under both cases of interingling and no sublot interingling. 9

24 A fairly fast optial solution algorith for the two-achine flow shop lot streaing (FSLS) proble with identical sublot size. An optial solution algorith for the two-achine FSLS proble with lot-specific sublot sizes, and a heuristic that offers a faster solution for practical large scale probles in which the optial solution algorith ay require too uch tie due to its coplexity. Extensions of the optial and heuristic solution procedures developed for two-achine FSLS probles, that are expected to produce near-optial solutions for general -achine FSLS probles. A study of the effects of the proble paraeters on the quality of the solution and the perforance of the proposed procedures. These paraeters are:. The nuber of achines in the flow shop 2. The nuber of lots considered for sequencing 3. The percentage of setup ties 4. The sublot size A coprehensive siulation study that deonstrates the effectiveness of the proposed procedures in practical dynaic situations with respect to two priary easures:. Cycle tie (or MFT) 2. Output variability A study of the effects of the following factors in a dynaic lot streaing environent:. Syste randoness 2. Syste loading 3. Bottleneck-related factors (location and ultiple bottlenecks) 0

25 .5 Lot Streaing Applications In this Section, two applications are described. These applications correspond to the two lot streaing probles discussed earlier, naely the Lot-Streaing Sequencing Proble (LSSP) and the Flow-Shop Lot-Streaing (FSLS) proble. The first application is the Surface Mount Technology (SMT) production line. SMT production lines are widely used today for anufacturing Printed Circuit Boards (PCBs). A typical SMT production line consists of the following achines in serial: Screening achine Pick and Place (P&P) achines, the nuber ay vary fro one up to as any as eight in serial Visual (or autoated) inspection station Reflow oven Unprocessed PCBs of a given lot are loaded onto a buffer at the beginning of the line. They are then transferred one by one via a conveyor fro one achine to the next along the SMT line. The conveyor also serves as a sall interediate buffer between the achines. Fig.. depicts a scheatic SMT line. Each P&P achine along the line perfors, basically, the sae task. Coponents are sequentially picked by the header fro the back of the achine, where coponent-feeders have been pre-installed, and are then placed in the correct locations on the PCB. Assebly Line Balancing (ALB) of the P&P achines, which are alost always the bottleneck in the process, is clearly essential to iniize the idle tie and the cycle tie of the line. However, the proble of balancing SMT lines is a coplicated one, and even if solved optially, additional technological constraints ay prevent the feasibility of a perfect balance. Moreover, the sae proble arises for different types of PCBs and thus, the ibalance varies fro one PCB to the other.

26 Input Buffer Output Buffer Screening Machine Orientation of flow Reflow Oven P&P Machine P&P Machine P&P Machine Inspection Fig... Scheatic SMT production line. The proble characteristics are as follows: The lots are streaed one-by-one (i.e., unit-sized sublots are utilized.) The lots are not interingled. The transfer tie is negligible copared to the processing tie. The setup of the P&P achines (i.e., the loading of the coponent feeders) is only required for the entire lot, and can be done in parallel to the processing of the current lot. Therefore, it can be considered negligible as well, as long as the total processing tie of the current lot is larger than the setup tie of the next lot. The SMT sequencing proble can succinctly be stated as follows: Deterine a sequence for the lots (no interingling), given that they are streaed one by one, in order to iniize the akespan (i.e., the total copletion tie of all the lots listed for the next shift.) Hence, it is an exaple for the Lot Streaing Sequencing Proble (LSSP). The second application considers a special case of the production of wafers in Sei- Conductor (SC) anufacturing. In general, the production process of wafers is perfored via a re-entrant flow shop syste, in which the sublots re-enter the sae achines several ties throughout their production. As a first attept at this proble, we only consider the special case 2

27 of sei-conductor processes involving uni-directional flow patterns (i.e., no re-entrance.) Under this assuption, the flow shop experiences ixed sublots (i.e., lots are allowed to interingle) of equal sizes. The sublots are transferred between the achines using a device called cassette. Each cassette contains a fixed aount of wafers. The wafers within a single cassette are processed and oved together throughout the shop. Soe achines process the wafers in the cassette one-by-one (still, the transfer is only done after all the wafers within the cassette have been processed) while other process the altogether. In both cases, setup of the achine is required before the start of processing. Thus, the characteristics of this proble can be suarized as follows: The lots are streaed in equal-sized sublots, using cassettes. Sublots of different lot types can interingle. Setup is required prior to the processing of every sublot. The transfer tie is negligible copared to the processing tie. The key questions constituting this proble are as follows: (a) How should the sublots be sequenced, and (b) What should the sublot size be, in order to optiize a given obective function. Due to the significantly longer processing ties of the lots in SC anufacturing, criteria such as iniizing the average WIP and the ean flow tie are considered at least as iportant as the akespan iniization criterion. 3

28 .6 Organization of Research This work contains six chapters. Introduction to the proble, the research obective, and two possible applications of the work have been presented in Chapter. In Chapter 2, a review of the literature on lot streaing and other related areas is provided. Chapter 3 presents detailed analysis and results, obtained for the single-batch lot streaing proble. Optial and heuristic solutions for the ultiple-batch lot streaing proble are developed and presented in Chapter 4. Both Chapter 3 and Chapter 4 address the static version of the proble. In contrast, Chapter 5 presents siulation-based analysis of the dynaic lot streaing proble. A suary of the research and concluding rearks are ade in Chapter 6. 4

29 Chapter 2: Literature Survey The obective of this chapter is to provide a review of the published literature on lot streaing as well as other strongly related areas. These areas include production planning and control (PPC) ethodologies which support the splitting of lots (JIT, CONWIP, and OPT) and flow-shop sequencing and scheduling. The review of the literature begins with a historical overview of the progress ade in the area of lot streaing during the past thirty years. This is followed by a review of the PPC ethodologies that support the possibility of lot-splitting. Ephasis is given to the concept in which lot streaing is perfored via each of the ethods. Then, a review of the existing heuristics for the regular flow-shop sequencing proble is presented and, lastly, an up-to-date detailed coverage of the research on lot streaing is provided. The literature review of the latter is suarized in two Sections. The first Section deals with single batch odels while the second deals with the ore general case of ultiple batch odels. 2. Historical Review The ter lot streaing first appeared in the literature ore than thirty years ago, when Reiter (966) coined the ter lot streaing in his article A Syste for Managing Job-Shop Production. Although his work at that tie was very liited, a breakthrough was achieved regarding the identification of a possible avenue to iprove the efficiency of production systes. Soehow, possibly due to the coplication involved in it, developers of the MRP syste, in the early 70 s, had chosen to ignore the possibility of splitting lots. In MRP-based systes for production planning and control, lots are considered the sallest integral entities to flow throughout the production syste. Generally speaking, research in the field of lot streaing was neglected in the 70 s. However, there were soe exceptions. Szendrovits (975) analyzed a 5

30 single batch ultiple achine akespan proble, with equal sublots of known size, and under the assuption of continuous processing, i.e., no idleness between any two consecutive sublots on any achine. Goyal (976) continued the work of Szendrovits, and developed a schee for obtaining the optial sublot sizes (which were assued to be known in Szendrovits odel.) As the 80 s brought two new and revolutionary approaches, naely JIT and OPT, which strongly supported the streaing of saller portions of lots throughout the production syste, research into lot streaing was re-discovered. Insights gained into JIT and OPT have enhanced the need of quantitative ethods to deterine optial sublots (or transfer batches, as they are referred to in OPT.) Vollann (986) even categorized OPT as siply being an enhanceent of MRP, as it provides the possibility of splitting lots, although, in addition to transfer batches, OPT supports other features pertaining to the scheduling and the utilization of bottlenecks, that MRP-II packages do not. According to a broad interpretation of the OPT principles, these transfer batches need not necessarily be of equal size, but no further details regarding their deterination are available in the public doain (Trietsch, 989). Judging by the output of the OPT software, it sees that equal sizes of sublots are used in OPT (Jacobs, 984). Meanwhile, after gaining an enorous deal of insights into JIT, a ore generalized and powerful concept - CONWIP (CONstant Work-In-Process) - had eerged in 990, as an alternative to JIT. According to CONWIP, it ay be better to have soe level of WIP throughout the production syste, as long as this level is strictly preserved. In the late 80 s and the early 90 s, after extensive research had been carried out to cover alost all aspects of JIT and OPT, it becae apparent that the concept of lot streaing, a aor issue related to both of the, was neglected. Fro this point on, research has drawn its attention directly to the question of lot streaing in various production systes. The early analytical works of Truscott (986), Trietsch (987), and Baker (988) were ainly concerned with the ipact of a single lot, split into sublots, on syste perforance, where the production syste under exaination was typically liited to a two-achine flow shop. Subsequently, two research directions have evolved. The first pertains to the analysis of ore coplex systes, such as systes with ultiple batches or ob shop systes (El-Nadawi (994) ; Doutriaux and Sarin (996)). The second pertains to the generation of insights using siulation-based studies (Wagner and Ragats (994) ; Hancock (99)). These works have shed soe light on our understanding of the ipact of lot streaing in various anufacturing environents. 6

31 2.2 Existing PPC Methodologies In this Section, three production planning and control (PPC) ethodologies are briefly described. These are the well-known ust-in-tie (JIT), constant work-in-process (CONWIP), and optiized production technology (OPT). For each, the obectives, principles, and production control ethods are discussed. Ephasis is given to the concepts of lot-streaing in these ethodologies Just-in-tie (JIT) and Kanban The JIT philosophy originated in the plants owned by Toyota, a giant Japanese autoobile anufacturer. JIT is a straightforward philosophy and its logic is easy to follow. Nevertheless, it is not straightforward that it guarantees achieving the ultiate goal, which is profit axiization. Unlike the theory of constraints (TOC), which will be discussed next, JIT is not a direct derivative of the above goal. JIT evolved in Toyota due to the need to eliinate waste. Toyota defined waste as anything other than the iniu aount of equipent, aterials, parts, and working tie absolutely essential to production (Hay, 988). Thus, JIT is concerned with the entire production syste and not erely with aterial scrap, rework, or line fallout. Via JIT, waste is anything that is not necessary for the anufacturing process or is in excess. For exaple, labor hours spent reworking products because of poor quality as well as buffer inventories required to store defective parts awaiting repair are considered waste (Hernandez, 989). By absolute iniu resources, it is also eant that one supplier is preferred as long as that supplier has enough capacity, that there should be no safety stock held in storage, and that, there should be no excess lead ties for raw aterials, and no work that does not add value to the product. There are three ain obectives for JIT (Suzaki, 987). These obectives are hoogeneous in the sense that they can be applied to a diversity of organizations within industries that differ greatly fro one another (Cheng and Podolsky, 996). These three obectives are : 7

32 To increase the organization s copetitiveness, over the long run, by systeatically optiizing the anufacturing processes. To increase the degree of efficiency, within the production process, by achieving greater levels of productivity while iniizing the associated costs of production. To reduce production costs by reducing the level of wasted aterials, tie, and effort involved in the production process. To accoplish its ain obectives, JIT calls for the following conditions to be et: Eliination of unproductive processing tie, ainly setup tie. Eliination of process variability, i.e., (alost) deterinistic processing ties and reliable resources (via preventive aintenance and total production aintenance.) Eliination of non-value added work, which leads to siplified anufacturing processes. Eliination of aterial waste via perfect quality and quality control Eliination of stock and inventories by using sall procureent lead ties through constant reliable vendors. Thus, any necessary ipleentation of JIT should first address the above issues to deterine whether or not they are achievable. The JIT philosophy postulates that if the above conditions are satisfied, custoer deands can be et within a very short tie frae, alost ust-in-tie, and with great certainty. This, in turn, ensures custoer satisfaction, and is achieved with inial production costs (inial WIP associated costs, inial production costs, and inial setup costs.) The PPC ethod which supports the JIT philosophy is known as Kanban. The word Kanban eans "signal" in English. Kanban, siilar to MRP-based systes, is basically used to establish the scheduling of operations, the quantity of the product to be produced, and the direction of production flow (Cheng and Podolsky, 996). In Kanban, the transfer unit between each two successive achines is usually referred to as a container. Each container is designated for one specific part type. Production on a achine does not start unless the following three conditions are satisfied: 8