Scheduling N products on a single facility with allowed backordering

Abstract

There are N products, each demanded at a fixed rate r_j per period, and a single facility which, if assigned to product j, will produce p_j (>r_j ) units per period. Given the initial inventory for each product and a finite planning horizon, then the problem is to identify the production schedule with the minimum inventory holding and backordering costs.

Dominance relations between the products and a strong lower bound on the optimal cost are derived; together, they are used in a search procedure to generate the optimal schedule. The procedure is illustrated by a numerical example and tested on a set of 36 problems with varying parameters. For a problem of 8 products with a planning horizon of length 30 periods, the CPU time is less than half a minute.