Knowledge that Transforms

This paper presents the experimental performance of three elementary rules for sequencing jobs through a single production facility. The problem is a variant of the “traveling salesman problem.” It is presented in terms of the job sequencing problem because of practical constraints on problem solving methods encountered in this situation. The objective of the sequencing decision is to minimize the facility downtime or setup time over a finite batch of jobs. The study consists of examining the performance of the three heuristic rules in terms of two criteria. The first is the optimal downtime obtained by the branch and bound algorithm. The second is the downtime which results from a random sequencing of jobs through the facility. The sampling procedure considers different values of the variance of between-job setup times, the number of jobs in the sequencing batch, and the form of the distribution of setup times.

A simulator is developed which enables a variety of forecasting procedures to be tested on any given time series. The simulator determines the standard deviation of the forecast error for each of the procedures tried, indicates the procedure which is optimal in the sense of lowest standard deviation of forecast error, and presents projections and graphs of actual versus predicted values. The time series under study can be either a real time series read into the simulator or a time series generated by the simulator.

A number of packaging problems involve optimization of costs subject to constraints imposed by the geometry of the alternatives. One such problem arises in those consumer goods warehousing systems which pack a large number of similar products, differing in size, into individual boxes for warehousing and subsequent shipment to the ultimate consumer. Box cardboard costs and warehouse space costs are minimized if boxes exactly fit each product size; on the other hand, box inventory, handling, and purchase costs are minimized if only one box size is used for all product sizes. The problem is to select the optimum number and sizes of boxes which minimize the total system costs. An integer programming formulation of the problem is given, and the results obtained from the application of a heuristic procedure to a specific problem are described.

The economic lot size programming problem, as studied originally by A. S. Manne and later by B. P. Dzielinski, C. T. Baker and A. S. Manne, is the problem of making economic lot size, inventory and work force decisions in a multi-production process. When several thousand distinct items are involved, the large number of equations that result from the linear programming formulation makes computation infeasible. Also, a large number of variables are involved because of inclusion of alternative set-up sequences for each item. In this paper, the application of the Dantzig and Wolfe decomposition principle and a method for creating alternative set-up sequences as they are needed by means of a computation of the Wagner and Whitin type is described as a method for overcoming the computational difficulty. A digital computer program has been developed using these methods. The results of some experiments where production was planned for a large number of distinct items are described.

Remarks on “Inventory Valuations—An Analytic Technique” Management Science, Vol. 8, No. 1 (October 1961), pp. 58–86 by Harlan D. Mills.