A Simple Heuristic for Lot Sizing with Setup Times

This paper presents an easily understood and computationally efficient heuristic algorithm for the capacitated lot sizing problem (CLSP), the single machine lot-sizing problem, with nonstationary costs, demands, and setup times. The algorithm solves problems with setup time or setup cost. A variation of the algorithm can solve problems when limited amounts of costly overtime are allowed. Results of experimentation indicate that the most significant effects on solution quality are due to the level of setup costs relative to holding costs and the size of the problems as determined by the number of items. Also affecting solution quality are tightness of the capacity constraint and variability of demand in a problem. When the capacity constraint is extremely tightly binding, it sometimes has difficulty finding solutions that do not require overtime.     

Joint Lot Sizing and Scheduling of Multiple Items with Sequence-Dependent Setup Costs

The objective of this research is to investigate the effects of setup-cost estimating methods on the lot sizing and scheduling of multiple products in multiple periods. These initial setup cost estimators (ISCEs) are used to estimate sequence-independent initial setup costs from sequence-dependent setup costs. A search of the literature reveals that, although sequence-dependent setup costs are frequently found in practice and ISCEs are frequently used, there is a dearth of research concerning the effect of using ISCEs. After a review of the literature, a mixed integer formulation of the joint problem of lot sizing and scheduling is presented, followed by a discussion of the difficulty in solving the formulation. Next, the six ISCEs evaluated are presented. These ISCEs range from simple (select the minimum setup cost) to complex (use the branch-and-bound solution to a traveling salesman-type problem). Each ISCE is evaluated using a full factorial design with five independent variables: demand distribution (three levels), demand trend (three levels), setup to inventory level (six levels), setup distribution (three levels), and setup variability (two levels). Two hypotheses are researched. Do the more computationally complex ISCEs produce lower overall costs than do the simpler ISCEs? Does the reduction in total cost justify the additional computation cost? The results of this study demonstrate that it may be incorrect to use “conventional wisdom'’when selecting an ISCE.     

Efficient Heuristics for MRP Lot Sizing with Variable Production/Purchasing Costs*

Two heuristics based on branch and bound (B&B) are developed to solve closed-loop material requirements planning (MRP) lot-sizing problems that have general product structures and variable costs. A “look ahead method'’(LAM) heuristic allows for variable production/purchasing costs and uses a single-level B&B procedure to rapidly improve lower bound values; thus, LAM efficiently uses computer-storage capacity and allows solution of larger problems. The “total average modification'’(TAM) heuristic uses B&B, applied level by level, and modified setup and carrying costs to solve the variable production/purchasing costs MRP lot-sizing problem. LAM and TAM are tested on problems and compared to heuristics in the literature. TAM may be used to solve large MRP lot-sizing problems encountered in practice.     

A Simulation Study of Sequencing Rules in a Kanban-Controlled Flow Shop*

This paper addresses the problem of sequencing in decentralized kanban-controlled flow shops. The kanban production control system considered uses two card types and a constant withdrawal period. The flow shops are decentralized in the sense that sequencing decisions are made at the local workstation level rather than by a centralized scheduling system. Further, there are no material requirements planning (MRP)-generated due dates available to drive dispatching rules such as earliest due date, slack, and critical ratio. Local sequencing rules suitable for the decentralized kanban production-control environment are proposed and tested in a simulation experiment. These rules are designed so that they can be implemented with only the information available at the workstation level. Example sequencing problems are used to show why the shortest processing time rule minimizes neither average work-in-process inventory nor average finished-goods withdrawal kanban waiting time. Further, it is shown how work station supervisors can use the withdrawal period, in addition to the number of kanbans, to manage work-in-process inventories.     

Optimal Purchase and Transportation Cost Lot Sizing for a Single Item

A review of the literature indicates that the traditional approach for evaluating quantity discount offerings for purchased items has not adequately considered the effect that transportation costs may have on the optimal order quantity; despite the general fact that purchased materials must bear transportation charges. The transportation cost structure for less-than-truckload (LTL) shipments reflects sizable reductions in freight rates when the shipment size exceeds one of the nominal rate breakpoints. However, the shipper must also be aware of the opportunity to reduce total freight costs by artificially inflating the actual shipping weight to the next rate breakpoint, in order that a lower marginal tariff is achieved for the entire shipment. Such over-declared shipments result in an effective freight rate schedule that is characterized by constant fixed charge segments in addition to the nominal marginal rates. Over-declared shipments are economical when the shipment volume is less than the rate breakpoint, but greater than a cost indifference point between the two adjacent marginal rates. This paper presents a simple analytical procedure for finding the order quantity that minimizes total purchase costs which reflect both transportation economies and quantity discounts. After first solving for the series of indifference points that apply to a particular freight rate schedule, a total purchase cost expression is presented that properly accounts for the actual transportation cost structure. The optimal purchase order quantity will be one of the four following possibilities: (1) the valid economic order quantity (EOQ), QC; (2) a purchase price breakpoint in excess of QC; (3) a transportation rate breakpoint in excess of QC; and (4) a modified EOQ which provides an over-declared shipment in excess of QC. Finally, an algorithm which systematically explores these four possibilities is presented and illustrated with a numerical example.     

A Note on the Effect of Sudden Obsolescence on the Optimal Lot Size

In most management situations, the decision to hold inventory involves some element of obsolescence risk The traditional approach to this problem, in both theory and practice, is to incorporate obsolescence costs in the inventory holding cost. This note explores this issue and demonstrates that the traditional approach is appropriate for items subject to sudden obsolescence; that is, for items with demand lifetimes that are exponentially distributed.     

An Investigation of Scheduling Policies in a Dual-Constrained Manufacturing Cell*

In previous group scheduling studies, labor has essentially been ignored by assuming that enough labor is assigned to each machine in the cell. In reality, however, management usually does not have the resources to employ a laborer at each machine in the cell (i.e., machines need to share labor). Both labor scheduling and group scheduling heuristics need to be administered to manage the cell effectively. This study develops and examines scheduling procedures for a dual-constrained (i.e., machine and labor) manufacturing cell. Eleven decision rules are developed and tested under 16 different experimental conditions. The experimental factors used are interarrival time distribution, cell load, setup-to-run-time ratio, and transfer-to-run-time ratio. Results show that interarrival time distribution and cell load have the greatest impact on the performance of the cell. This suggests that effective production planning aimed at reducing job arrival variation and leveling the cell load can substantially improve cell performance. Among the experimental factors, setup and transfer-to-run-time ratio factors had the strongest influence on the rankings of the decision rules. These rankings were fairly robust across all experimental conditions and performance measures. The results also indicated that the inclusion of labor as a contraint in the cell had a significant impact on the performance of several group scheduling heuristics. Finally, it was shown that the best performing decision rules consider both transfer time and subfamily setup times.     

The Impact of Learning and Labor Attrition on Worker Flexibility in Dual Resource Constrained Job Shops

This study investigates the impact of worker learning, worker flexibility, and labor attrition on the system performance of a dual resource constrained (DRC) job-shop. The effects of learning and labor attrition have not been previously addressed in DRC literature. Results from the study, consistent with previous literature, show that the greatest benefits are achieved when inter-departmental worker flexibility is incrementally introduced into the system. In addition, the learning environment, which depends on the initial processing time of jobs and the learning rates of workers, is shown to impact the acquisition of flexibility. The study also shows that the impact of labor attrition on system performance under certain shop conditions may be significant.     

Application of the Net Present Value Criterion in Random and Flow Shop Scheduling*

While the majority of the literature on shop scheduling has emphasized time-based performance criteria such as mean flow time, lateness, and tardiness, the primary goal of management should be the maximization of shop profitability. In this research the net present value (NPV) criterion is introduced to measure shop profitability. This measure combines aspects of job flow time and inventory holding costs into a single measure. A simulation model of a job shop is used to examine the performance of a variety of time- and value-based scheduling rules. These rules are evaluated with respect to the NPV criterion in both random and flow shop environments. The results suggest that priority rules that utilize monetary information about jobs yield a higher NPV than many time-based rules in most situations, with little sacrifice in job tardiness. A well-researched time-based rule, critical ratio, also provides excellent performance when the shop is heavily loaded.     

Simulation Tests of FCFS and SPT Sequencing in Kanban Systems

One of the basic tenets of scheduling theory is that the SPT sequencing rule maximizes average production rates and minimizes average in-process inventories. This paper shows that on single-card kanban-controlled lines FCFS often has greater average production rates than SPT. Further, the performance of SPT declines relative to FCFS for larger queue capacities and less frequent material handling. Results for the single-card system are also compared to those of Berkley and Kiran [1]. In that article it was shown that for two-card systems with periodic material handling, SPT has larger average inventories than FCFS. This paper shows that these surprising results can be attributed to Berkley and Kiran's material-handling mechanism.     

Scheduling with Sequencing Flexibility*

This study examines the effects of sequencing flexibility on the performance of rules used to schedule operations in manufacturing systems. The findings show that taking advantage of even low levels of sequencing flexibility in the set of operations required to do a job results in substantial improvement in the performance of scheduling rules with respect to mean flowtime. Differences in the mean flowtime measure for various rules also diminish significantly with increasing sequencing flexibility. Performance improvements additionally result for such due-date related performance measures as mean tardiness and the proportion of jobs tardy. At high levels of sequencing flexibility, some nonparametric scheduling rules outperform the shortest processing time rule in terms of the mean flowtime criterion. Rules based on job due dates also outperform rules based on operation milestones in terms of tardiness related criteria at high levels of sequencing flexibility. The implications of these findings for the design of manufacturing systems and product design are noted.     

Planning and Control in Multi-Cell Manufacturing

This research compares Material Requirements Planning (MRP), Kanban, and Period Batch Control (PBC) as alternative approaches to the planning and control of multi-cell manufacturing involving flow cells and assembly. Since previous research on performance of these systems in cellular manufacturing has been primarily conceptual, the experiments reported here provide new insights into their comparative performance. The results show that the production environment is a major factor in system choice. Three operating factors—Master Production Schedule (MPS) volume variation, MPS mix variation, and setup time/lot size—clearly affect system choice. All systems performed well under Justin-Time (JIT) conditions; there was no advantage to Kanban. Under the mixed conditions of high MPS variation, but small setup time/lot sizes, PBC produced superior performance compared to Kanban and MRP. Under non-JIT conditions, MRP was seen as clearly more effective. Finally, the results indicate that when conditions permit very small lot sizes relative to requirements, Kanban may perform best, even when MPS variation is high.     

Economic Production Lot Sizing with Periodic Costs and Overtime*

Traditional approaches for modeling economic production lot‐sizing problems assume that a single, fixed equipment setup cost is incurred each time a product is run, regardless of the quantity manufactured. This permits multiple days of production from one production setup. In this paper, we extend the model to consider additional fixed charges, such as cleanup or inspection costs, that are associated with each time period's production. This manufacturing cost structure is common in the food, chemical, and pharmaceutical industries, where process equipment must be sanitized between item changeovers and at the end of each day's production. We propose two mathematical problem formulations and optimization algorithms. The models' unique features include regular time production constraints, a fixed charge for each time period's production, and the availability of overtime production capacity. Experimental results indicate the conditions under which our algorithms' performance is superior to traditional approaches. We also test the procedures on a set of lot‐sizing problems facing a national food processor and document their potential economic benefit.     

Vendor Selection with Bundling*

Product bundling has become increasingly prevalent not only in consumer goods but also in the industrial sector. We study a purchasing problem in which a buyer must obtain necessary numbers of various stock items from a variety of vendors who charge different prices, have limited capacities and different levels of quality, and offer bundled products at discounted prices. We examine relationships among different bundling scenarios and show that the most general scenario is one in which free items are given to the buyer when sufficient quantities are purchased. We develop a mixed integer linear program that finds the purchasing strategy for the buyer that minimizes the total purchase cost. We present computational results which indicate that the problem is very tractable to solve optimally on a personal computer with standard optimization software. Finally, three extensions of the model are discussed.     

THE IMPACT OF EXTREME OBSERVATIONS ON SIMPLE FORECASTING METHODS*

In general linear modeling, an alternative to the method of least squares (LS) is the least absolute deviations (LAD) procedure. Although LS is more widely used, the LAD approach yields better estimates in the presence of outliers. In this paper, we examine the performance of LAD estimators for the parameters of the first-order autoregressive model in the presence of outliers. A simulation study compared these estimates with those given by LS. The general conclusion is that LAD does not deal successfully with additive outliers. A simple procedure is proposed which allows exception reporting when outliers occur.     

Distinguishing Features of Just-in-Time Systems in the Make-to-Order/Assemble-to-Order Environment*

Few studies of just-in-time (JIT) implementation examine their significance in make-to-order manufacturing environments. This study examines the relative importance of several operating variables that are characteristic features of JIT systems within such environments in North America. The results suggest that the most salient features of JIT for make-to-order and assemble-to-order firms are the elimination of waste (in the form of time and defects), reduced setup time, reduced lotsize, and a smaller pool of suppliers. In addition, the results suggest that the use of non-domestic suppliers can possibly hinder efforts at JIT implementation of materials procurement.     

Manufacturing Proactiveness and Performance*

Since Skinner's [40] landmark article depicting the manufacturing function as the “missing link” in corporate strategic processes, a portion of the blame for inferior performance in many firms has been attributed to the subordinate strategic position of manufacturing. It has been argued that part of the solution to misalignments between the capabilities possessed by manufacturing and the requirements dictated by customers is for manufacturing to take a more proactive stance. However, little research has been reported which examines manufacturing proactiveness empirically. In this paper, we address this gap by developing an operational definition of manufacturing proactiveness and testing empirically whether a link exists between proactiveness and performance based on data collected from a sample of manufacturers. Based on the manufacturing strategy literature, we identify two major dimensions of manufacturing proactiveness: (1) the degree of manufacturing's involvement in the strategic processes of the business unit; and (2) the degree of commitment to a long-term program of investments in manufacturing structure and infrastructure aimed at building capabilities in anticipation of their need. We develop reliable scales for measuring each of the dimensions of proactiveness and use the data to provide evidence of a clear link between manufacturing proactiveness and business performance. We show that investments in structural programs coupled with either high levels of manufacturing involvement in strategic processes or planned investments in infrastructural programs correlate with higher than average performance.     

Concepts,Theory, and Techniques THE LOT-SIZE REORDER-POINT MODEL WITH UPSTREAM-DOWNSTREAM UNCERTAINTY*

One assumption in the classical lot-size problem is certainty in the amount requisitioned. In many practical situations, however, the amount received may be a random variable. In this paper, we discuss a lot-size inventory problem in which the quantity received does not necessarily match the quantity requisitioned. We develop explicit and approximate solutions for the back-orders case by assuming that the standard deviation of the amount received is linearly related to the quantity requisitioned.     

PROCEDURES FOR DETERMINING RELATIVE FREQUENCIES OF PRODUCTION/ORDER IN MULTISTAGE ASSEMBLY SYSTEMS*

We show that the problems of determination lot sizes in a multistage assembly system for the case of instantaneous production and constant demand for the end item can be reduced to the problems of determining relative frequenceis of production/order for items at each production stage. We further show that such frequencies are independent of the demand levels. Optimal and near-optimal solution procedures for this reduced problem are provided. The near-optimal procedure successively treats each stage of production as a final production stage while simulatenously incorporating decisions made at lower stages into decisions made at higher stages. Experimental results show that the near-optimal procedure results in optimal solutions 75 percent of the time and performs considerably better than representative heuristics available in the literature. Further, its performance is relatively less susceptible to product/structural characteristics of the system.