In this paper, we consider bicriterion scheduling problems involving job completion times and job waiting times in a nonpreemptive single machine environment. As an example, we seek to determine a schedule that yields both a low mean and a low variation of completion time. Such a schedule is attractive when the system has the dual objectives of minimizing in-process inventory and providing different jobs the same quality of service. Similarly, we seek a schedule that performs well on both the mean and variation of waiting time. As the measure of variation, we use the sum of absolute pairwise differences. We present an efficient algorithm for minimizing the variation of waiting time. Next, we assume that the total scheduling cost is a function of the mean and variation of completion time alone, and is linear. We give an efficient algorithm for minimizing this total cost. Finally, we consider parametric analysis of this cost function and present simple procedures for generating all or some of the optimal schedules. All the results are extended to the case where job waiting times are substituted for job completion times.
Abstract:The scheduling problem addressed in this paper concerns a manufacturer who produces a variety of product types and operates in a make-to-order environment. Each customer order consists of known quantities of the different product types, and must be delivered as a single shipment. Periodically the manufacturer schedules the accumulated and unscheduled customer orders. Instances of this problem occur across industries in manufacturing as well as in service environments. In this paper we show that the problem of minimizing the weighted sum of customer order delivery times is unary NP-hard. We characterize the optimal schedule, solve several special cases of the problem, derive tight lower bounds, and propose several heuristic solutions. We report the results of a set of computational experiments to evaluate the lower bounding procedures and the heuristics, and to determine optimal solutions.
We show in this study, through analysis and examples, the impact on stockouts and stockout risk if the variability of lead time in independent demand systems is ignored. In calculating safety stocks, we recommend that the compound distribution of demand during lead time, or a good approximation to it, be used. We motivate the article by a case study on lead‐time variability at the U.S. Air Force and show the impact of lead‐time variability by means of numerical examples and by marginal analysis. Having established that it is essential to consider lead‐time variability, we take advantage of theoretical developments and show how to calculate reorder points and safety stocks in some common situations.
It is important to use the proper form for the compound distribution of demand during lead time. A normal approximation to it will often yield significant errors. This is because the true distribution is usually very much skewed to the right.
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