The peak load minimization problem in cyclic production

Abstract

The objective of this study is to determine a production schedule for a set of jobs so as to minimize the peak load for the entire planning horizon given the production duration and the cyclic frequencies of the jobs. We refer to this problem as the peak load minimization problem (PLMP). An efficient heuristic, viz. Proc. PLMP, is proposed to solve such class of problems. There are two parts for the Proc. PLMP: a greedy procedure that secures an initial production schedule and a schedule smoothing procedure that performs a local search to reduce the maximal load. Numerical experiments verify that Proc. PLMP is efficient, since its run time is of cubic order of the problem size, i.e., it is approximately an O( n 3) algorithm. A major application of Proc. PLMP is to test the feasibility of a given set of a solution for the Economic Lot Scheduling Problem using the extended basic period approach. Scope and purpose The most prominent model for cyclic production is the economic lot scheduling problem (ELSP) in which n products are produced in lots of different sizes and, thereby, require different cyclical patterns. Under the extended period approach for the ELSP, there are two major problems in its cyclic production schedules. First, feasibility test of a given set of multipliers for a specified length of the basic period is a very hard problem, and second, the basic periods are typically unevenly loaded. Cost optimization, feasibility test as well as good shop practice, require the balancing of the loads on the basic periods. This can be achieved by minimizing the maximal load, which gives rise to the peak load minimization problem (PLMP) treated here. The problem is shown more complex than NP-hard. In order to solve the PLMP, we propose an efficient heuristic, Proc. PLMP. Proc. PLMP has been tested on problems of up to n=80 products, and it runs in cubic order of the problem size. Proc. PLMP also demonstrates its successful application to solve the feasibility test problem for the ELSP.