Candace Arai Yano

Lot Sizing with Random Yields: A Review

This paper reviews the literature on quantitatively-oriented approaches for determining lot sizes when production or procurement yields are random. We discuss issues related to the modeling of costs, yield uncertainty, and performance in the context of systems with random yields. We provide a review of the existing literature, concentrating on descriptions of the types of problems that have been solved and important structural results. We identify a variety of shortcomings of the literature in addressing problems encountered in practice, and suggest directions for future research.

Coordinated Pricing and Production/Procurement Decisions: A Review

It has been nearly 50 years since researchers began to develop analytical models to aid in simultaneous decisions regarding pricing strategy, which influences demands, and production/procurement decisions, which determine the cost of satisfying those demands. In this chapter, we provide a comprehensive review of analytical models on this topic, focusing on models in which external demand is price-sensitive. We review models in both continuous and discrete-time frameworks, considering both constant and time-varying demand functions, with and without demand uncertainty. Although our emphasis is on decision problems facing a single firm, we also provide a brief overview of models involving multiple firms or multiple decision-makers. We also offer suggestions for future research.

Joint Production and Pricing Decisions with Setup Costs and Capacity Constraints

We consider the problem of setting prices and choosing production quantities for a single product over a finite horizon for a capacity-constrained manufacturer facing price-sensitive demands. There is a fixed cost per production run and a variable cost per unit produced, both of which may vary by period. We characterize properties of the optimal solution, considering cases with constant and time-varying capacity, and with and without speculative motive for holding inventory. We show that, counter to intuition, optimal prices may increase as the capacity increases, even when capacity is constant over the horizon. We also show that increases in capacity do not always exhibit diminishing marginal returns. Our procedure produces solutions with much higher profits than can be obtained from a sophisticated sequential procedure in which a well-informed and optimum-seeking marketing department makes pricing decisions and the manufacturing department seeks to satisfy the resulting demands at minimum cost. Our results also suggest that firms with seasonal demand and tight capacity constraints should be more aggressive in setting prices to manage their demands than what is typically done in practice. Finally, we discuss how a decision maker can use our procedure as an aid in solving multiproduct versions of the problem.

Algorithms for a class of single-machine weighted tardiness and earliness problems

Abstract We address the problem of determining schedules for static, single-machine scheduling problems where the objective is to minimize the sum of weighted tardiness and weighted earliness. We develop optimal and heuristic procedures for the special case of weights that are proportional to the processing times of the respective jobs. The optimal procedure uses dominance properties to reduce the number of sequences that must be considered, and some of the heuristic use these properties as a basis for constructing good initial sequences. A pairwise interchange procedure is used to improve the heuristic solutions. An experimental study shows that the heuristic procedures perform very well.

The economic lot and delivery scheduling problem: The single item case*

We have studied the problem of determining the frequency of production of a single component and the frequency of delivery of that component to a customer which uses this component at a constant rate. The objective is to minimize the average cost per unit time of production setup costs, inventory holding costs at both the supplier and the customer, and transportation costs. The model allows positive production setup times. We prove that the ratio between the production interval and delivery interval must be an integer in an optimal solution. This provides the basis for a very simple, optimal solution procedure. We use these results to characterize situations in which it is optimal to have synchronized production and delivery, and discuss the ramifications of these conditions on strategies for setup cost and setup time reductions.

Scheduling Direct and Indirect Trains and Containers in an Intermodal Setting

The focus of our research is on rail transportation of intermodal containers. We address the problem of determining day-of-week schedules for both direct and indirect (via a hub) trains and allocating containers to these trains for the rail (linehaul) portion of the intermodal trip. The goal is to minimize operating costs, including a fixed charge for each train, variable transportation and handling costs for each container and yard storage costs, while meeting on-time delivery requirements. We formulate the problem as an integer program and develop a novel decomposition procedure to find near-optimal solutions. We also develop a method to provide relatively tight bounds on the objective function values. Finally, we compare our solutions to those obtained with heuristics designed to mimic current operations, and show that a savings of between 5 and 20% can be gained from using our solution procedure.

Minimizing mean tardiness and earliness in single‐machine scheduling problems with unequal due dates

We consider a single-machine scheduling problem with the objective of minimizing the mean (or equivalently, total) tardiness and earliness when due dates may differ among jobs. Some properties of the optimal solution are discussed, and these properties are used to develop both optimal and heuristic algorithms. Results of computational tests indicate that optimal solutions can be found for problems with up to 20 jobs, and that two of the heuristic procedures provide optimal or very near optimal solutions in many instances.

LOT SIZING IN ASSEMBLY SYSTEMS WITH RANDOM COMPONENT YIELDS

We investigate the problem of choosing optimal lot sizes in assembly systems when component manufacturing or procurement yields, and possibly assembly yields, are random. For a single-period setting, we analyze two models. The first has components with identical yield distributions and costs, random demand and an imperfect assembly stage. We analyze this two-stage problem, and highlight the implications of the results for the single-stage case where the final product is just a set of good components. The second model is a single-stage system where components have non-identical yield distributions and costs. We analyze a two-component system with known demand, identify conditions for concavity, and derive the optimality conditions.

The economic lot and delivery scheduling problem: the common cycle case

We analyze the interface between a supplier and an assembly facility, where direct shipments are made from one to the other. The final manufacturing step at the supplier involves multiple components produced on a single machine or production line. The assembly facility uses these components at a constant rate. The supplier incurs a sequence-independent setup cost and/or setup time each time the production line is changed over from one component to another. On the other hand, setup costs and times for the assembly facility are negligible. We consider two types of delivery cost: a fixed charge for each delivery, and a fixed-charge-per-truck cost. We develop a heuristic procedure to find a ‘just-in-time’ schedule in which one production run of each product and a subsequent delivery of these products to the assembly facility occur in each cycle. The objective is to find the cycle duration that minimizes the average cost per unit time of transportation, inventory at both the supplier and the assembly facility,...

Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty

We consider a problem faced by a contract assembler that both assembles finished goods and procures the associated component parts for one of its major customers. Because of rapid changes in technology and ongoing engineering changes, all parts subject to obsolescence are purchased only for the current customer order. The procurement lead times of the components are random. Moreover, although the order for the finished product has a defined due date, the contract allows the customer to change the order quantity. Consequently, the assembler also faces a random demand. The assembler must determine how much to order and when to order each component part. The objective is to minimize the total expected cost, including the cost of holding components prior to their assembly, penalties for tardiness visa-vis the assembly due date, and overage and underage costs in satisfying the demand quantity. We present some structural results and discuss insights regarding optimal policies. We also present several simple heuristic policies and compare them to optimal policies. Computational results indicate that ignoring lead time variability can be costly, but relatively simple heuristics that consider lead time variability perform quite well.