Production Scheduling for an Arbitrary Number of Periods Given the Sales Forecast in the form of a Probability Distribution

Abstract

In this paper a mathematical model is presented for solving an optimum production scheduling problem. The optimum program is not dependent on the sale price as long as the production is forced to fulfill all the sales orders. The sales forecast is given in the form of a probability distribution for a number of periods. The costs consist of ordinary production costs, overtime production costs, and costs for carrying inventory. The importance of a unique policy for the calculation of the program is pointed out. Three different policies have been treated (1) scheduling for one period each time, (2) scheduling over two periods every second period, and (3) scheduling over as many periods as the enterprise is expected to last. The three different policies give different optimal programs. A numerical example has been carried out analytically where the differences are shown. Policy (1) above gives the lowest cost because all information about the inventories is known at the beginning of each of the periods. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.