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someTitle Inventory and Production Management in Supply Chains Fourth Edition Inventory and Production Management in Supply Chains Fourth Edition Edward A Silver University of Calgary (retired), Alber.

Inventory and Production Management in Supply Chains Fourth Edition Inventory and Production Management in Supply Chains Fourth Edition Edward A Silver University of Calgary (retired), Alberta, Canada David F Pyke University of San Diego, California, USA Douglas J Thomas Penn State University, Pennsylvania, USA CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway N W , Suite 300 Boca Raton, FL 33487-2742 © 2017 by Taylor & Francis Group, L L C CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed on acid-free paper Version Date: 20160830 International Standard Book Number-13:978-1-4665-5861-8 (Hardback) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material repro­ duced in this publication and apologize to copyright holders if permission to publish i n this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify i n any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, M A 01923, 978-750-8400 C C C is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the C C C , a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identifica­ tion and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Names: Silver, Edward A (Edward Allen), 1937- author | Pyke, D F (David F.) author | Silver, Edward A (Edward Allen), 1937- Decision systems for inventory management and production and planning | Silver, Edward A (Edward Allen), 1937- Inventory management and production planning and scheduling Title: Inventory and production management i n supply chains / Edward A Silver, David F Pyke, Douglas J Thomas Description: Fourth Edition | Boca Raton : Taylor & Francis, 2017 | Revised edition of Inventory management and production planning and scheduling | Includes index Identifiers: L C C N 2016022678 | ISBN 9781466558618 (hardback : alk paper) Subjects: L C S H : Inventory control—Decision making | Production planning—Decision making Classification: L C C HD40 S55 2017 | D D C 658.7/87-dc23 L C record available at https://lccn.loc.gov/2016022678 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Edward A Silver dedicates this work to Maxine, Michelle, Norman, and Heidi David F Pyke dedicates this work to Susan, James, Daniel, and Cory Ad majorem Dei gloriam Douglas J Thomas dedicates this work to Traci, Alison, Kate, and Maya Contents Preface xix Acknowledgments .xxiii Authors xxv SECTION I THE CONTEXT AND IMPORTANCE OF INVENTORY MANAGEMENT AND PRODUCTION PLANNING The Importance of Inventory Management and Production Planning and Scheduling 1.1 Why Aggregate Inventory Investment Fluctuates: The Business Cycle 1.2 Corporate Strategy and the Role of Top Management 1.3 The Relationship of Finance and Marketing to Inventory Management and Production Planning and Scheduling 10 1.3.1 Finance 10 1.3.2 Marketing 11 1.4 Operations Strategy .12 1.4.1 Mission 13 1.4.2 Objectives 13 1.4.3 Management Levers 15 1.4.4 General Comments 16 1.5 Measures of Effectiveness for Inventory Management and Production Planning and Scheduling Decisions 17 1.6 Summary 18 Problems 18 References 20 Frameworks for Inventory Management and Production Planning and Scheduling 23 2.1 The Diversity of Stock-Keeping Units 23 2.2 The Bounded Rationality of a Human Being .24 2.3 Decision Aids for Managing Diverse Individual Items 25 2.3.1 Conceptual Aids 25 2.3.2 Physical Aids .25 2.4 Frameworks for Inventory Management .26 2.4.1 Functional Classifications of Inventories 26 2.4.2 The A–B–C Classification as a Basis for Designing Individual Item Decision Models 28 vii viii Contents 2.5 A Framework for Production Planning and Scheduling 31 2.5.1 A Key Marketing Concept: The Product Life Cycle .31 2.5.2 Different Types of Production Processes 33 2.5.3 The Product-Process Matrix 37 2.6 Costs and Other Important Factors 40 2.6.1 Cost Factors 40 2.6.2 Other Key Variables 44 2.7 Three Types of Modeling Strategies 46 2.7.1 Detailed Modeling and Analytic Selection of the Values of a Limited Number of Decision Variables .47 2.7.2 Broader-Scope Modeling with Less Optimization .47 2.7.3 Minimization of Inventories with Little Modeling .47 2.8 The Art of Modeling .47 2.9 Explicit Measurement of Costs .49 2.10 Implicit Cost Measurement and Exchange Curves 52 2.11 The Phases of a Major Study of an Inventory Management or Production Planning and Scheduling System 53 2.11.1 Consideration 54 2.11.2 Analysis 55 2.11.3 Synthesis 57 2.11.4 Choosing among Alternatives 57 2.11.5 Control 58 2.11.6 Evaluation 58 2.11.7 General Comments 58 2.11.8 Transient Effects 59 2.11.9 Physical Stock Counts 59 2.12 Summary 61 Problems 61 Appendix 2A: The Lognormal Distribution 68 References 70 Forecasting Models and Techniques 73 3.1 3.2 3.3 3.4 3.5 The Components of Time-Series Analysis 75 The Three Steps Involved in Statistically Forecasting a Time Series 77 Some Aggregate Medium-Range Forecasting Methods 78 3.3.1 Regression Procedures 79 Individual-Item, Short-Term Forecasting: Models and Procedures .81 3.4.1 The Simple Moving Average 82 3.4.2 Simple Exponential Smoothing 84 3.4.3 Exponential Smoothing for a Trend Model .88 3.4.4 Winters Exponential Smoothing Procedure for a Seasonal Model 92 3.4.5 Selection of Smoothing Constants 101 Measuring the Performance of a Forecasting Process 104 3.5.1 Measures of Forecast Accuracy 105 3.5.2 Estimating the Standard Deviation of Forecast Errors over a Lead Time 109 3.5.3 Monitoring Bias 111 Contents ix 3.5.4 Corrective Actions in Statistical Forecasting 115 3.5.5 Probability Distributions of Forecast Errors 117 3.6 Handling Anomalous Demand 117 3.7 Incorporation of Human Judgment 118 3.7.1 Factors Where Judgment Input Is Needed 118 3.7.2 Guidelines for the Input and Monitoring of Judgment 119 3.8 Dealing with Special Classes of Individual Items 120 3.8.1 Items with Limited History 120 3.8.2 Intermittent and Erratic Demand 122 3.8.3 Replacement or Service Parts 123 3.8.4 Terminal Demand 124 3.9 Assessing Forecasting Procedures: Tactics and Strategy 125 3.9.1 Statistical Accuracy of Forecasts 125 3.9.2 Some Issues of a More Strategic Nature 126 Problems 128 Appendix 3A: Derivations 135 References 137 SECTION II REPLENISHMENT SYSTEMS FOR MANAGING INDIVIDUAL ITEM INVENTORIES WITHIN A FIRM Order Quantities When Demand Is Approximately Level 145 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Assumptions Leading to the Basic EOQ 146 Derivation of the EOQ 147 4.2.1 Numerical Illustration 151 Sensitivity Analysis 152 Implementation Aids 154 4.4.1 Numerical Illustration 155 Quantity Discounts 155 4.5.1 Numerical Illustrations 158 4.5.2 Item A (An Illustration of Case a of Figure 4.5) 159 4.5.3 Item B (An Illustration of Case b of Figure 4.5) 159 4.5.4 Item C (An Illustration of Case c of Figure 4.5) 160 Accounting for inflation 160 4.6.1 Price Established Independent of Ordering Policy 161 4.6.2 Price Set as a Fixed Fractional Markup on Unit Variable Cost 163 Limits on order sizes 164 4.7.1 Maximum Time Supply or Capacity Restriction 164 4.7.2 Minimum Order Quantity 165 4.7.3 Discrete Units 165 Finite Replenishment Rate: The Economic Production Quantity 166 Incorporation of Other Factors 168 4.9.1 Nonzero Constant Lead Time That Is Known with Certainty 168 4.9.2 Nonzero Payment Period 169 4.9.3 Different Types of Carrying Charge 169 Just-in-Time, Optimized Production Technology 689 EDD Choose the job that has the earliest due date The previous two rules focus on the time a job spends in the shop, and they ignore any due date information This rule specifically focuses on due dates CR Critical ratio Compute the ratio (processing time remaining until completion)/(due date–current time), and choose the job with the highest ratio (provided it is positive) The ratio will be large for longer-remaining processing times, and for smaller amounts of time from the current time until the due date However, if a job is late, the ratio will be negative, or the denominator will be zero, and the job should be given the highest priority In the event that there is more than one late job, schedule the late jobs in SPT order There are dozens of priority sequencing rules that have been proposed in the literature for a multitude of objectives We shall focus on just a few to provide insights Valuable references for further information include Conway et al (1967), Baker (1974), Coffman Jr (1976), Graves (1981), French (1982), Lawler et al (1982), Lawler et al (1993), and Baker (1995) See Woolsey (1982) for an entertaining perspective on several of these rules in real shops Copyright © 2016 Taylor & Francis Group All rights reserved 16.3.3.1 Preliminary Comments and Notation We focus on the simplest case of n jobs with deterministic processing times to be scheduled on one machine This simple case will provide insights that are fundamental for more complex environment of a job shop with random processing times and dynamic arrivals However, it is also useful for factories that have a single bottleneck Recall that DBR and CONWIP, discussed earlier in this chapter, provide some insight into when jobs should be released into the shop As jobs arrive at the bottleneck, however, they need to be prioritized CONWIP explicitly allows for sequencing jobs based on sequence-dependent setup times, but if setup times are sequence independent, some sequencing rule is needed Two insights are immediately evident for the single machine case First, the optimal schedule for most objectives will have no inserted idle time Idle time simply delays jobs, leading to worse due date performance and longer flowtimes The exception is when there is a penalty for jobs being early Second, the optimal schedule most often will have no preemption Preemption delays the preempted job, and advances the preempting job But if the latter job should be advanced, it should have been scheduled prior to the preempted job in the first place We need some notation for the examples that follow Cj dj Ej Fj = completion time for job j = due date for job j = earliness for job j = max(0, −Lj ) = flowtime for job j = Cj − rj n F = total flowtime for all jobs to be scheduled = Fj j=1 Lj = lateness for job j = Cj − dj n = number of jobs to be scheduled pj = processing time for job j Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 690 Inventory and Production Management in Supply Chains Table 16.6 Data for Single Machine Illustrations Job Processing Time, pj (in Days) Due Date, dj (Day) 12 4 18 rj = ready time for job j, or the time at which job j is available for processing Tj = tardiness for job j = max(0, Lj ) Note that lateness can be negative One final piece of notation: [k] = i means that the kth job in the sequence is job i 16.3.3.2 Results and Insights We now give examples and results for several sequencing rules We shall use one numerical illustration, with data given in Table 16.6, for most of this subsection The current time is time zero, so that job is due days from now Copyright © 2016 Taylor & Francis Group All rights reserved 16.3.3.3 FCFS The FCFS schedule is quite easy to develop: simply take the jobs in the order in which they arrive The results are given in Table 16.7, where the jobs have been numbered in the order of their arrival and all are available at time zero (i.e., each rj = 0) To illustrate one job, consider job Its completion time is 13, which is its start time plus its day processing time Job begins in day because job completes on that day Its flowtime is 13 days because it is ready at time 0, and it completes on day 13 Because its due date is 6, it is late by days The makespan is 21 days Table 16.7 FCFS Schedule Job j pj dj Cj Fj Lj Ej Tj 7 −1 12 8 −4 13 13 7 4 15 15 11 11 18 21 21 3 Average 12.8 3.2 4.2 Maximum 21 11 11 Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Just-in-Time, Optimized Production Technology Table 16.8 SPT Schedule Job j pj dj Cj Fj Lj Ej Tj 12 1 −11 11 4 3 −1 8 2 18 14 14 −4 21 21 13 13 −0.2 3.2 Average Maximum 691 9.4 21 13 11 13 Also note that the completion times and the flowtimes are identical for each job Jobs spend, on average, 12.8 days in the shop, and on average they are tardy by 4.2 days Now let us see what happens when SPT is employed Copyright © 2016 Taylor & Francis Group All rights reserved 16.3.3.4 SPT In this case, we arrange jobs in increasing order of processing times, as shown in Table 16.8 Note that [2] = 4, or the second job in sequence is job The mean flowtime is lower than that for the FCFS case, as are the average tardiness and lateness The maximum lateness and tardiness are higher than in the FCFS case, however This latter result illustrates a common complaint with SPT schedules, that they can cause long jobs to be very late (Many students will recognize this problem The long job is that history paper that never seems to get done.) There has been a significant amount of research that proves that SPT schedules are optimal for a number of objectives We prove one case here, and then give the results for several others Total flowtime is minimized by SPT sequencing The proof uses a simple argument that appears in the appendix to this chapter Many proofs in simple sequencing problems follow a similar logic Begin with a sequence that is not ordered according to the rule in question Then interchange two jobs, so their ordering follows the rule If the performance measure always improves, the sequencing rule is optimal for that performance measure Similar proofs establish that SPT sequences are optimal for minimizing: (1) total flowtime, (2) mean flowtime, (3) mean waiting time, (4) mean lateness, and (5) total lateness 16.3.3.5 EDD It can be shown (by the same method illustrated in the appendix for SPT) that earliest due date sequencing minimizes maximum lateness and maximum tardiness It is intuitive that on these performance measures, EDD outperforms SPT, and other rules based only on processing times, because the latter ignore due date information We shall see, however, that our intuition is not always correct EDD sequences are extremely easy to develop so long as each job has a due date attached The EDD schedule for our numerical example is shown in Table 16.9 Note that, as expected, the average flowtime has now increased (compared with the SPT rule) Table 16.10 provides a summary of key performance measures for these three sequencing rules Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 692 Inventory and Production Management in Supply Chains Table 16.9 EDD Schedule Job j pj dj Cj Fj Lj Ej Tj 4 2 −2 7 1 14 14 6 12 15 15 3 18 21 21 3 Average 11.8 2.2 0.4 2.6 Maximum 21 6 Table 16.10 Summary of Results for Numerical Example Rule FCFS Average Average Average Maximum Average Maximum Number of Flowtime Lateness Earliness Earliness Tardiness Tardiness Tardy Jobs 12.8 3.2 1.0 4.2 11 SPT 9.4 −0.2 3.2 11 3.0 13 EDD 11.8 2.2 0.4 2.6 Copyright © 2016 Taylor & Francis Group All rights reserved 16.3.4 General Job Shop Scheduling It is clear from the previous section that many of the research results in scheduling are very specialized If one happens to manage a shop that has a single significant bottleneck, the single machine research can be helpful On the other hand, how should a manager approach a job shop that is more complex than the stylized cases we have been discussing? Real job shops have many complicating factors For instance, there may be multiple machines that can process jobs at a given work center There may be numerous different routings through the shop depending on the characteristics of the job Each job will have a set of precedence constraints that specify the order in which operations must be performed In addition, processing times may be probabilistic rather than deterministic Do the results for the simple cases apply to more complex and realistic settings? Complex job shops not lend themselves to analytical research, and, therefore, most of the research has been based on simulation experiments The problem with simulation is that it is difficult to know whether the results of the experiment apply in environments different from those tested For example, we might simulate a job shop composed of six highly utilized machines and find that using SPT at each machine provides good performance for, say, mean flowtime The question then is whether that result will generalize to shops of 10 machines, or to shops with some parallel machines, or to shops with lower utilization rates In this section, we provide some insights into the general job shop scheduling problem Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Just-in-Time, Optimized Production Technology 693 16.3.4.1 Dynamic, Probabilistic Job Shop In the dynamic probabilistic job shop, jobs arrive randomly over time, and processing times are probabilistic This is the most realistic job shop situation, and, of course, the most difficult to model Nevertheless, results from simpler contexts may provide insights In the dynamic job shop, each machine may have a queue of jobs awaiting processing at any point in time One primary decision is which job the machine operator should process next We shall see, for example, that in many cases, shop performance improves if each machine operator chooses the job in his or her queue that has the shortest processing time In other words, each operator uses SPT First, however, we discuss some ideas that provide intuition about shop performance in general We borrow the term factory physics from Hopp and Spearman (2011) for this discussion Then we address the dynamic probabilistic job shop scheduling problem 16.3.4.2 Factory Physics Copyright © 2016 Taylor & Francis Group All rights reserved Imagine a job shop that has just five machines, as illustrated in Figure 16.7 We begin with a very simple case For the moment, let us assume that many jobs arrive at the shop at the same time, and that all jobs follow the same routing through the shop In fact, let us assume that they proceed in order of machine letter, so that machine A is first, and so on For now, assume that there is no space that can hold inventory waiting for processing In Figure 16.7, the triangles that represent buffers (space for inventory) are always empty and can hold no jobs (Note that WIP includes the contents of these buffers—zero for now—and any jobs that are being processed.) Finally, assume that processing times are deterministic, and are hour for each job on each machine It is relatively easy to understand the dynamics of this shop Machine A is never starved for work because of the large number of jobs to be released to the shop Once each machine has a job to work on, each machine will process a job for exactly hour, and then pass it on to the next machine The average throughput (TH = the number of completed jobs per unit time) of the shop will be job per hour Now relax just one of the assumptions, that of deterministic processing times There is still no buffer space, there is still a large number of jobs waiting to be released to the shop, and the routings remain the same The processing times, however, now average hour, but may vary from 0.5 to 1.5 hours, according to a uniform distribution What will be the throughput of the shop? It seems Machine B Machine A Machine C Machine E Machine D Figure 16.7 A five machine job shop Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 694 Inventory and Production Management in Supply Chains Average throughput Copyright © 2016 Taylor & Francis Group All rights reserved clear that the average throughput should decrease, because of the variability in processing times Any time a machine works slower than hour, while the machine just upstream works faster, the upstream machine is blocked It has nowhere to put the job, and must wait for the slower machine to finish before it can get started on the next job Likewise, any time a machine works faster, while the machine just upstream works slower, the machine is starved It has no job to work on, even though it is available In this case, simulation results show that the average throughput is 0.78 jobs per hour, or a loss of 22% of the theoretical capacity of the shop The key insight is that variability decreases average throughput How, then, can one increase the throughput of this shop? Because much of the loss in throughput is due to blocking and starving, we could eliminate these effects by increasing the buffers from their current size of zero—in other words, increasing WIP Imagine now that we increase the provision for WIP, so that over time, the buffers, represented by triangles in the figure, fill up with jobs When a machine works faster than average, it can put its completed job in the input buffer of the next machine in line, and it can begin processing the next job in its own input buffer Blocking and starving will be eliminated if there is enough inventory in the buffers However, if there is room for only a small amount of inventory in each buffer, there may still be occasional blocking and starving The effect of increasing WIP on throughput is shown in Figure 16.8 Note that there is no throughput if there is no WIP (i.e., there is never a job in the shop), and that small amounts of WIP dramatically increase average throughput At some point, however, average throughput levels off In fact, the maximum throughput for this line is exactly job per hour If there were an infinite amount of inventory in front of each machine, so blocking and starving were completely eliminated, each machine would complete an average of job per hour In a shop with a bottleneck, the average throughput can never exceed the average throughput of the bottleneck The key insight is that WIP increases average throughput, but only to a point That point is the average throughput of the bottleneck WIP Figure 16.8 Relationship of WIP to average throughput Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Just-in-Time, Optimized Production Technology 695 Copyright © 2016 Taylor & Francis Group All rights reserved Many production managers have seen the benefits of WIP reduction (discussed in this chapter in the context of JIT) We can see, however, that inventory reduction, without reduction of variability, serves only to decrease throughput Well, then, why not increase WIP in every job shop? First of all, from the last point, we know that the throughput benefits disappear after WIP increases somewhat In addition, consider the time it takes a job, 1, to proceed through the shop, or the cycle time (CT) If there is no other job in the shop for job 1’s entire cycle time, it never has to wait in queue Every machine is available when it arrives, and on average, the CT will be hours, or hour for each of the machines However, when there are other jobs in the shop, that is, there is WIP, the job may have to wait in queue for some time before processing, and the CT will increase Imagine that we observe a job going through the shop, and that there is just one other job in the shop at that time The probability of our job having to wait for the other job is quite low Hence, WIP inventory must increase more for there to be a significant effect on cycle time The relationship is shown in Figure 16.9 Notice how the cycle time increases very slowly as WIP first increases Then, it increases more rapidly, and finally levels off to increase at a linear rate The straight line portion of the curve has slope equal to the average processing time at the bottleneck One more unit of WIP simply means that jobs must wait at the bottleneck for one more job to be processed The key insight is that cycle time increases with WIP These insights apply to any complex job shop as well as to the simple case we have been using to develop intuition In fact, we have used these insights in a consulting engagement to help managers examine whether they should inject more WIP into the shop Perhaps the shop is operating with too little WIP, so that a small increase would generate a large increase in throughput with little cost in cycle time In other words, the shop is operating on the steep part of the WIP–TH curve and on the shallow part of the WIP–CT curve On the other hand, if the shop is really further up on the curves, increases in WIP will generate little gain in throughput, at the expense of a large increase in CT A fundamental law from queueing theory, due to Little (1961), captures some of these relationships WIP = TH (CT ) (16.1) If there are 100 jobs in WIP on average, and the average throughput of the shop is 20 jobs per day, it is intuitive that the average time a job spends in the shop will be days This relationship, known as Little’s law, holds for any factory, not just job shops It can be extremely valuable for predicting delivery times, if the manager has a sense for average WIP and average throughput.* But it should be used in conjunction with the insights from Figures 16.8 and 16.9 when determining how much WIP to hold on average One final insight is illustrated in Figure 16.10 Recall that utilization is the proportion of available time that a machine is occupied As utilization increases, average cycle time increases, at first gradually, and then very rapidly This relationship is evident from the insights we have discussed To increase utilization, machines must be starved less often, and this is accomplished by increasing WIP When utilization approaches 1.0, the machine is busy constantly, and cycle times get longer and longer If there is variability in job arrivals or in processing times, the problem is magnified because machine (idle) time, lost due to variability, can never be recaptured Throughout this book, we have emphasized “changing the givens,” and this is no exception If managers can reduce the variability of the machine, by training or process improvements, or if they can reduce * For other insights on predicting delivery times, see the papers by Enns listed in the references at the end of this chapter, and Cheng (1985) Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Inventory and Production Management in Supply Chains Average cycle time 696 WIP Figure 16.9 Relationship of WIP to average cycle time High variability Average cycle time Copyright © 2016 Taylor & Francis Group All rights reserved Low variability Utilization 1.0 Figure 16.10 Variability and utilization the variability of job arrivals, by demand management, the entire curve shifts downward So, we present these graphs and relationships as valuable tools for understanding the physics of factories, but we stress the importance of process improvements that shift the tradeoff curves in a favorable direction Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Just-in-Time, Optimized Production Technology 697 We note that the discussion in this subsection did not address sequencing In the next subsection, we provide insights on sequencing in dynamic probabilistic job shops Copyright © 2016 Taylor & Francis Group All rights reserved 16.3.4.3 Results for Dynamic, Probabilistic Job Shop Scheduling Most of this chapter has assumed deterministic processing times When we allowed for probabilistic processing times, we only presented general insights Now we present some specific insights and tools for more complex probabilistic job shops Because much of queueing theory is unable to accommodate priority sequencing rules, researchers have relied on simulation to gain insight into sequencing in complex job shops The discussion that follows is based on a vast amount of research that is summarized in Panwalkar and Iskander (1977), who provide a survey of over 100 dispatching rules; Conway (1965a,b), Conway et al (1967), Blackstone et al (1982), Chapter of Hax and Candea (1984), Lawler et al (1993), MacCarthy and Liu (1993), and Chapter 12 of Baker (1995) We begin with some general comments on sequencing rules in this environment Local rules require information only about the queue at the current machine SPT is a local rule because to use it only requires knowledge of the processing times of each job in the current queue Global rules require information about conditions elsewhere in the shop as well Work in next queue (WINQ) is an example This rule assigns the highest priority to the job that will join the queue (after this operation is completed) with the smallest workload, where workload is the sum of processing times waiting in that queue Static rules have priorities that not change over time EDD is a static rule because the due date does not change as the job progresses through the shop SPT, on the other hand, is static at a particular machine, but a job’s priority can change as the job moves through the shop Dynamic rules generate priorities that can change over time Minimum slack time (MST) is a dynamic rule Jobs are given priority based on slack time, which is the difference between the job’s due date and the earliest possible completion time The earliest possible completion time is the sum of the processing times of all remaining operations of this job, and it changes as operations are completed Sequencing rules are generally divided into two groups: rules for relieving shop congestion and rules for meeting due dates We discuss each in turn Shop congestion is exhibited by high levels of WIP, or by long flowtimes A number of simulation experiments have found that SPT is the best rule for many performance measures related to shop congestion, including mean flowtime, mean lateness, and WIP level SPT, however, may cause long jobs to experience excessive delays because short jobs keep arriving and moving to the front of the queue Therefore, the variance of job flowtimes may be quite high with SPT One possible solution would be to use truncated SPT (or TSPT) TSPT imposes a time limit on jobs in the queue Any jobs exceeding the limit are sequenced according to FCFS If no jobs in queue exceed the limit, use SPT TSPT, therefore, moves jobs to the front of the queue if they have been waiting too long As expected, flowtime variance decreases if we use TSPT in place of SPT, but WIP and average flowtimes increase Another solution is to use relief SPT (RSPT) which employs FCFS until the queue length hits a value Q Then we switch the rule to SPT The results are roughly the same as with TSPT: flowtime variance decreases at the expense of higher average flowtime and WIP Our intuition might suggest that performance will improve if global rules are used in place of the local rules described in the last paragraph Two possibilities are WINQ, which was mentioned above, and expected work in next queue (XWINQ) XWINQ is identical to WINQ except that it accounts for jobs that are expected to arrive to the subsequent queue In fact, neither rule outperforms SPT when the performance measure is the mean number of jobs in queue It seems that SPT is consistently the best, or near best, rule for relieving shop congestion Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 698 Inventory and Production Management in Supply Chains There are many possible rules designed to meet due dates (assuming due dates are preassigned) These include EDD and CR, which were introduced above A number of other rules have been proposed by researchers, including Copyright © 2016 Taylor & Francis Group All rights reserved MST Minimum slack time Slack time is the difference between the time until the due date and the remaining processing time Choose the job with the minimum slack time ODD Operation due date For this rule, we create operation due dates that serve as intermediate deadlines prior to the real due date Operation due dates may be spaced evenly between the job arrival and the final due date, by dividing the time interval by the number of operations to be performed However, several other ways to set ODDs have been investigated One is to use a proportion of the job’s total work Research has shown that this method performs better than dividing the time interval by the number of operations In either case, the operation due dates are used to assign priority to jobs exactly as EDD does It is worth noting that the operation due dates outperform job-based due dates (like EDD) in certain experiments See Kanet and Hayya (1982) and Baker (1984) S/OPN Slack time per operation The job with the smallest ratio between slack time (as described above) and the number of operations remaining is given highest priority A/OPN Allowance per operation The remaining allowance is the time between the current date and the due date The job with the smallest ratio between remaining allowance and the number of remaining operations is given the highest priority MOD Modified operation due date A modified operation’s due date is the larger of its original operation due date and its earliest possible finish time COVERT COVERT stands for “C over T,” where C represents the delay cost for the job, and T represents the processing time for this operation Jobs are sequenced according to the ratio of delay cost to processing time Simulation experiments have shown that S/OPN performs best when the performance measure is the fraction of jobs tardy or the variance of job lateness SPT, however, actually is very close on fraction of jobs tardy, and is even better than S/OPN for mean job lateness and mean flowtime Some of these results are surprising because SPT ignores due date information SPT even outperforms EDD on average job lateness! For variance of job lateness, however, EDD performs better than SPT COVERT has been shown to outperform other rules on mean job tardiness But, in general, the studies show mixed results for mean job tardiness For the performance measure of mean tardiness, computed only for the set of tardy jobs, CR and similar rules have been shown to perform best In addition to the surveys mentioned above, see Conway (1965b), and Carroll (1965) for some of these results To summarize, research would indicate that for most performance measures, except variance of job lateness and mean job tardiness, managers should direct each machine operator to sequence jobs in queue according to the SPT rule There may be other exceptions, however, and it is best to simulate the specific job shop environment to be scheduled In a complex shop with the financial resources to employ a more elaborate scheduling system, it would be wise to consider APS systems, which we briefly introduced earlier in this chapter and in Chapter 15 These systems use advanced search techniques such as genetic algorithms, tabu search, and simulated annealing, among others See the review by Blazewicz et al (1996) for an excellent introduction to some of this literature, and Fleischmann and Meyr (2003) for a more detailed discussion In very general terms, these techniques begin with a trial solution (an SPT sequence at the Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Just-in-Time, Optimized Production Technology 699 bottleneck, for instance), and then make some adjustment The adjustment might be a pairwise interchange of two jobs in the sequence at a given machine If the new sequence looks promising, retain that sequence and continue making interchanges, eventually including interchanges at all machines in the shop Stop when the improvements are small For large shops with multiple machines and jobs in progress, this process clearly involves a huge number of calculations, which is why sophisticated search algorithms are necessary Fortunately, researchers have made significant progress on these algorithms, not to mention the dramatic increases in computing speed For further information, see the references at the end of Section 16.3.2 For other research on job shop scheduling, see Ragatz and Mabert (1984), Scudder and Hoffman (1987), Wein (1988), Vepsalainen and Morton (1988), Enns (1994), Brah (1996), and Randhawa and Zeng (1996) Hopp and Spearman (2011) provide details on the application of CONWIP in job shops Treleven (1989) and Gargeya and Deane (1996) examine job shops that are constrained by multiple resources, including machines, labor, and tools 16.4 Summary Copyright © 2016 Taylor & Francis Group All rights reserved In this chapter, we have discussed two powerful systems, JIT and OPT, that have made intellectual and practical contributions to operations management in the past several decades JIT has had a significant impact on practicing managers, having been implemented in numerous plants One of its primary contributions is the paradigm shift from the static view of reorder point systems or MRP to one of continuous improvement OPT has had less of an impact as a production scheduling system, but it has made an important contribution by encouraging managers to focus improvement efforts on bottlenecks We then reviewed a multitude of sequencing rules that apply to simple job shops We used the rules and insights developed for the simple cases to establish effective procedures for more complex job shops We discovered that the SPT rule is remarkably robust, providing the best, or near best, results for a number of different performance measures in a number of different environments Managers should be wary of using this single rule in every environment, however, because other rules outperform it in some cases Simulating the shop is a useful exercise to find the best strategy for each particular case As always, managers should try to change the givens by controlling due dates, employing lot streaming, and eliminating bottlenecks Problems 16.1 For a local manufacturer, discuss the production process and describe why MRP, JIT, or OPT would be most suitable 16.2 Describe the difference between a process batch and a transfer batch 16.3 What could be the primary contribution of JIT for a manufacturer using MRP? 16.4 What could be the primary contribution of OPT for a manufacturer using MRP? 16.5 Which is better, MRP, JIT, or OPT? 16.6 Describe the difference between push and pull systems for production Why is MRP often called a push system, while JIT is called a pull system? 16.7 Design a simple production line using a real or hypothetical product and simple materials Develop Kanbans for this line, and with your group, operate until it runs smoothly 16.8 Describe drum-buffer-rope scheduling and apply it to a production line of a local organization Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 700 Inventory and Production Management in Supply Chains 16.9 For the following data, assume that there are 80 hours of time available on the bottleneck machine Find the number of each product to produce using the conventional approach based on contribution margin Then find the optimal numbers using the OPT principles Product A B Price ($/unit) 600 400 Cost of materials ($/unit) 250 200 50 30 350 200 Market demand per week (units) Time on the bottleneck machine (hours/unit) Copyright © 2016 Taylor & Francis Group All rights reserved Contribution margin per unit ($/unit) 16.10 Why is short-term scheduling not as appropriate for continuous process industries? Give an example of how some of the methods discussed in this chapter nevertheless might be helpful 16.11 Why is short-term scheduling not as appropriate for Kanban systems? Give an example of how some of the techniques discussed in this chapter nevertheless might be helpful 16.12 Briefly discuss how a local firm uses, or might use, Gantt charts and finite scheduling 16.13 Briefly discuss how a local firm uses, or might use, sequencing rules such as SPT or EDD 16.14 What insights from single machine deterministic problems are useful for more complex job shops? What warnings would you give a manager who is planning to use these insights? 16.15 Give an intuitive explanation of why SPT performs so well for (a) mean flowtime and (b) mean lateness 16.16 Explain how short-term scheduling tools work together with MRP Explain how shortterm scheduling tools work together with ERP 16.17 Find and diagram the process flows for a local flow shop 16.18 Find and diagram the process flows for a local job shop 16.19 The choice of sequencing rule should be consistent with the operations strategy of the firm What strategies are consistent with SPT? With EDD? With FCFS? With SWPT? With S/OPN? With MOD? 16.20 Draw a Gantt chart for the following data, assuming that jobs are sequenced in order of job number Machine Job A B 4 16.21 Draw a Gantt chart for the following data, assuming that jobs are sequenced in order of job number Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Just-in-Time, Optimized Production Technology 701 Machine Job A B 30 45 20 15 60 25 80 10 50 50 20 70 16.22 Use the following data to forward load the three machines Copyright © 2016 Taylor & Francis Group All rights reserved Machine Job Priority A B C First Second 3 Third 16.23 Use the data in the previous example to backward load the three machines, assuming the three jobs have due dates of 20, 12, and 21, respectively 16.24 Assuming a priority sequence of 1, 2, 3, 4, schedule the following jobs on a Gantt chart The numbers in parentheses indicate the order in which operations are to be done So job requires hours on A, followed by hours on B Job begins on machine C for hours, and then proceeds to machine B for hours, and so on Machine Job A B 3(1) 4(2) 4(3) 3(2) 2(1) 1(1) 3(2) 1(2) 2(3) 2(1) C 16.25 Assuming the data in the previous example, improve the makespan by changing the schedule 16.26 Backward load for the following data: Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 702 Inventory and Production Management in Supply Chains Machine Job Due Date A B C 2(1) 3(2) 4(3) 4(2) 1(3) 3(1) 2(2) 4 3(3) 3(2) 4(1) 5(1) 3(2) 6(1) 16.27 For the following data (assuming jobs are numbered in the order of their arrival), find the mean flowtime, mean lateness, mean tardiness, and maximum tardiness a Using FCFS b Using SPT c Using EDD d Using CR e Using SWPT, assuming weights of 3, 4, 6, 10, 1, respectively Copyright © 2016 Taylor & Francis Group All rights reserved Job Processing Time, pj (Days) Due Date, dj (Day) 10 11 16 15 22 16.28 For the following data (assuming jobs are numbered in the order of their arrival), find the mean flowtime, mean lateness, mean tardiness, and maximum tardiness a Using FCFS b Using SPT c Using EDD d Using CR e Using SWPT, assuming weights of 2, 2, 3, 5, 1, 6, 1, respectively Job Processing Time, pj (Days) Due Date, dj (Day) 19 10 Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 Just-in-Time, Optimized Production Technology Job Processing Time, pj (Days) Due Date, dj (Day) 22 12 30 15 50 703 16.29 A job shop manager has been asked what the average lead times in her shop have been Unfortunately, no one has been tracking these values She has, however, been able to determine that approximately 14 jobs are completed per week, and that there are currently 65 jobs in the shop What should she quote as the average lead time? Should she tell marketing that the next job can be delivered in this time? 16.30 The president of a small job shop is frustrated by the amount of money he is spending on WIP inventory, and by the low revenues the shop has been earning The sales manager tells the president that if she could quote lead times of week, sales could increase significantly The average job generates $2,000 in revenue, and the shop has been earning about $16,000 per week A count of WIP reveals that the average number of jobs in WIP is about 20 What should you tell the president? Appendix 16A: Proof that SPT Minimizes Total Flowtime Total flowtime is minimized by SPT sequencing The proof uses the following simple argument The flowtime of the kth job in sequence is k F[k] = p[i] (16A.1) Copyright © 2016 Taylor & Francis Group All rights reserved i=1 So the flowtime for job 3, for instance, is + + = 8, or p[1] + p[2] + p[3] = p2 + p4 + p3 The total flowtime, then, is n n k F[k] = k=1 p[i] (16A.2) k=1 i=1 In our example, the total flowtime is n k p[i] = p[1] + (p[1] + p[2] ) + (p[1] + p[2] + p[3] ) + (p[1] + p[2] + p[3] + p[4] ) k=1 i=1 + (p[1] + p[2] + p[3] + p[4] + p[5] ) = 5p[1] + 4p[2] + 3p[3] + 2p[4] + p[5] = + (1 + 2) + (1 + + 5) + (1 + + + 6) + (1 + + + + 7) = 47 and the mean flowtime is 47/5 = 9.4 Now consider a sequence that is not SPT, and call this sequence S Because it is not SPT, there must be two jobs, i and j, with i before j such that pi > pj Now interchange jobs i and j in the sequence and call the new sequence S See Figure 16A.1 All Silver, Edward A., et al Inventory and Production Management in Supply Chains, Taylor & Francis Group, 2016 ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/rmit/detail.action?docID=4771754 Created from rmit on 2021-03-01 20:28:26 ... for inventory management and production and planning | Silver, Edward A (Edward Allen), 1937- Inventory management and production planning and scheduling Title: Inventory and production management. .. as supply chain management The supply chain lever, of course, pertains to supply chain management, but so inventory management (as we shall see in Chapters 11 and 12), production planning and. .. a production environment will be developed 10 Inventory and Production Management in Supply Chains 1.3 The Relationship of Finance and Marketing to Inventory Management and Production Planning