Production scheduling can be defined as the allocation of available production resources over time to best satisfy some set of criteria. Typically, the scheduling problem involves a set of tasks to be performed, and the criteria may involve both tradeoffs between early and late completion of a task, and between holding inventory for the task and frequent production changeovers. The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling. This paper will highlight problem areas for which there is both a significant discrepancy between practice and theory, and for which the practice corresponds closely to the theory.

A Review of Production Scheduling

The ELSP is a time-honored problem that “has been around” since 1915. It is the problem of accommodating cyclical production patterns when several products are made on a single facility. Recent contributions to its resolution resulted in either analytical approaches to a restricted problem, or heuristic approaches to the entire problem. This paper reviews critically the various contributions to the problem, and extends the analysis in the following four directions: An improved analytical approach A test for feasibility, A systematic means for escape from infeasibility, and A procedure for the determination of a basic period for a given set of multipliers to achieve a feasible schedule.

The Economic Lot Scheduling Problem (ELSP): Review and Extensions

This paper considers the Economic Lot Scheduling Problem: that is, the problem of scheduling several products on a single facility so as to minimize holding and setup costs. We develop a formulation that provides feasible schedules by allowing the lot sizes and thus the cycle times for each product to vary over time and by explicitly taking into account setup times. Our main results characterize when feasible schedules exist, quantify the insensitivity of the schedules' costs to minor adjustments, and thus show how close the schedules will be to ones with optimal equal cycle times. We also present a heuristic for finding good feasible schedules.

The Economic Lot-Scheduling Problem: Achieving Feasibility Using Time-Varying Lot Sizes

We consider the situation of a family of items sharing a common supplier or common production facility. There is a major setup header cost to make a replenishment of the family and a minor line cost for each item included in the replenishment. In such a setting it makes sense to coordinate replenishments of the various items of a family. Under the assumption of deterministic demand, several authors have suggested iterative solutions which are not necessarily guaranteed to be optimal, yet are not easy to implement. We present an alternative procedure which is extremely simple to use, yet appears to have rather small cost penalties in relation to the earlier more sophisticated methods.

A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand

Certain manufacturing situations involve a small number of items produced sequentially on the same facility with high changeover cost. Production schedules are characterized by long runs, and individual items are produced infrequently. At the same time, seasonal demand patterns require that the items be maintained in inventory in the right mix. This paper presents alternative formulations of this problem. It uses a Lagrangean relaxation approach to decouple the problem and provide lower bounds used in a branch and bound algorithm. Some experimental computations on small problems are reported.

The Deterministic Dynamic Product Cycling Problem

Most of the procedures that have been developed to find solutions to the single-machine, multi-product lot scheduling problem depend on judgment to define the desirable frequencies of production for the products. In this paper we describe an iterative procedure for directly determining near optimal frequencies of production for the products and the associated fundamental cycle time which, in many cases, can be used directly for constructing production schedules. In cases where feasible schedules cannot be constructed using the values from the iterative procedure, the procedure provides a basis for changing the production frequencies and the fundamental cycle time to obtain feasible schedules.

D. Clay Whybark

Papers

An Iterative Procedure for the Single-Machine Multi-Product Lot Scheduling Problem