Izak Duenyas

Optimal Admission Control and Sequencing in a Make-to-Stock/Make-to-Order Production System

In this paper, we address the problem of admission control and sequencing in a production system that produces two classes of products. The first class of products is made-to-stock, and the firm is contractually obliged to meet demand for this class of products. The second class of products is made-to-order, and the firm has the option to accept (admit) or reject a particular order. The problem is motivated by suppliers in many industries who sign contracts with large manufacturers to supply them with a given product and also can take on additional orders from other sources on a make-to-order basis.We model the joint admission control/sequencing decision in the context of a simple two-classM/ M/1 queue to gain insight into the following problems: 1. How should a firm decide (a) when to accept or reject an additional order, and (b) which type of product to produce next? 2. How should a firm decide what annual quantity of orders to commit to when signing a contract to produce the make-to-stock products?

Optimal Policies for Inventory Systems with Priority Demand Classes

We consider a periodic review inventory system with two priority demand classes, one deterministic and the other stochastic. The deterministic demand must be met immediately in each period. However, the units of stochastic demand that are not satisfied during the period when demand occurs are treated as lost sales. At each decision epoch, one has to decide not only whether an order should be placed and how much to order, but also how much demand to fill from the stochastic source. The firm has the option to ration inventory to the stochastic source (i.e., not satisfy all customer demand even though there is inventory in the system).We first characterize the structure of the optimal policy. We show that, in general, the optimal order quantity and rationing policy are state dependent and do not have a simple structure. We then propose a simple policy, called ( s, k, S) policy, wheres andS (ordering policy) determine when and how much to order, whilek (rationing policy) specifies how much of the stochastic demand to satisfy. We report the results of a numerical study, which shows that this simple policy works extremely well and is very easy to compute.

Integrated maintenance and production control of a deteriorating production system

We consider a make-to-stock production/inventory system consisting of a single deteriorating machine which produces a single item. We formulate the integrated decisions of maintenance and production using a Markov Decision Process. The optimal dynamic policy is shown to have a rather complex structure which leads us to consider more implementable policies. We present a double-threshold policy and derive exact and approximate methods for evaluating the performance of this policy and computing its optimal parameters. A detailed numerical study demonstrates that the proposed policy and our approximate method for computing its parameters perform extremely well. Finally, we show that policies which do not address maintenance and production control decisions in an integrated manner can perform rather badly.

Existence of Coordinating Transshipment Prices in a Two-Location Inventory Model

We consider a two-location production/inventory model where each location makes production decisions and is subject to uncertain capacity. Each location optimizes its own profits. Transshipment (at a cost) is allowed from one location to another. We focus on the question of whether one can globally set a pair of coordinating transshipment prices, i.e., payments that each party has to make to the other for the transshipped goods, that induce the local decision makers to make inventory and transshipment decisions that are globally optimal. A recent paper suggests, for a special case of our model, that there always exists a unique pair of coordinating transshipment prices. We demonstrate through a counterexample that this statement is not correct and derive sufficient and necessary conditions under which it would hold. We show that in some conditions, coordinating prices may exist for only a narrow range of problem parameters and explore conditions when this can happen. Finally, we study the effects of demand and capacity variability on the magnitude of coordinating transshipment prices.

OPTIMAL CONTROL OF A TWO-STAGE TANDEM QUEUING SYSTEM WITH FLEXIBLE SERVERS

We consider the optimal control of two parallel servers in a two-stage tandem queuing system with two flexible servers. New jobs arrive at station 1, after which a series of two operations must be performed before they leave the system. Holding costs are incurred at rate h1 per unit time for each job at station 1 and at rate h2 per unit time for each job at station 2.The system is considered under two scenarios; the collaborative case and the noncollaborative case. In the prior, the servers can collaborate to work on the same job, whereas in the latter, each server can work on a unique job although they can work on separate jobs at the same station. We provide simple conditions under which it is optimal to allocate both servers to station 1 or 2 in the collaborative case. In the noncollaborative case, we show that the same condition as in the collaborative case guarantees the existence of an optimal policy that is exhaustive at station 1. However, the condition for exhaustive service at station 2 to be optimal does not carry over. This case is examined via a numerical study.

Setting Single-Period Optimal Capacity Levels and Prices for Substitutable Products

In this paper, we consider how a company that has the flexibility to produce two substitutable products would determine optimal capacity levels and prices for these products in a single-period problem. We first consider the case where the firm is a price taker but can determine optimal capacity levels for both products. We then consider the case where the firm can set the price for one product and the optimal capacity level for the other. Finally, we consider the case where capacity is fixed for both products, but the firm can set prices. For each case, we examine the sensitivity of optimal prices and capacities to the problem parameters. Finally, we consider the case where each product is managed by a product manager trying to maximize individual product profits rather than overall firm profits and analyze how optimal price and capacity decisions are affected.

Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity

In this paper, we address the optimal joint control of inventory and transshipment for a firm that produces in two locations and faces capacity uncertainty. Capacity uncertainty (e.g., due to downtime, quality problems, yield, etc.) is a common feature of many production systems, but its effects have not been explored in the context of a firm that has multiple production facilities. We first characterize the optimal production and transshipment policies and show that uncertain capacity leads the firm to ration the inventory that is available for transshipment to the other location and characterize the structure of this rationing policy. Then, we characterize the optimal production policies at both locations, which are defined by state-dependent produce-up-to thresholds. We also describe sensitivity of the optimal production and transshipment policies to problem parameters and, in particular, explain how uncertain capacity can lead to counterintuitive behavior, such as produce-up-to limits decreasing for locations that face stochastically higher demand. We finally explore, through a numerical study, when the optimal policy is most likely to yield significant benefits compared to simple policies.

Estimating the throughput of an exponential CONWIP assembly system

We consider a production system consisting of several fabrication lines feeding an assembly station where both fabrication and assembly lines consist of multiple machine exponential workstations and the CONWIP (CONstant Work-In-Process) mechanism is used to regulate work releases. We model this system as an assembly-like queue and develop approximations for the throughput and average number of jobs in queue. These approximations use an estimate of the time that jobs from each line spend waiting for jobs from other lines before being assembled. We use our approximations to gain insight into the related problems of capacity allocation, bottleneck placement and WIP setting.

Stochastic scheduling of a batch processing machine with incompatible job families

We consider the control of a single batch processing machine with random processing times and incompatible job families (jobs from different families cannot be processed together in the same batch). Holding costs are incurred for each unit of time that a job waits in the system before being served, and the objective is to minimize the long-run average cost per unit time. We first determine optimal policies for the static problem where all jobs are available simultaneously. We next characterize the optimal policies for certain problems with dynamic arrivals of jobs under the restriction that the machine is not allowed to idle. Finally, we develop a simple heuristic scheduling policy to control the machine. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances and to compare its performance with existing heuristics.

Planning and scheduling in Japanese semiconductor manufacturing

Abstract Described are some methods used by Japanese semiconductor manufacturing companies for long-term planning and short-term scheduling and shop floor control. Tools and techniques used for planning and scheduling in wafer fabrication are identified. General findings are discussed, and specific efforts at four companies are described in detail.