The economic lot scheduling problem: Theory and practice

A common problem in many industries is the scheduling of many products through a single production facility where the setup times, production and demand rates of each product are different. Various heuristic solution methods have been devised for this ‘Economic Lot Scheduling Problem’ such as the Common Cycle, Basic Period and Extended Basic Period approaches. In practical operations, such as the manufacture of polypropylene film for packaging considered in this paper, there are a number of considerations to take into account in determining the ‘optimal’ schedule. The criteria of minimising the annual cost, the only criterion considered in the literature, is only one of these. For example, there is a tendency for the methods to produce excessively long cycle times, so that the assumption of stationarity of demand is no longer valid. This paper compares the alternative solution methods on a variety of problems from the literature and the case studied. It is found that a modified version of the Haessler EBP method is most appropriate for the general standard problem. In the particular situation studied, the setup times are product sequence dependent. This can be considered within the Common Cycle approach, but not the other two methods which require the use of a fixed setup cost per product. The resulting annual costs are much lower, indicating that the Common Cycle method, contrary to the general view in the literature, may be the best method for the sequence dependent setup times situation, provided the product sequence is first determined to minimise the total setup times. An efficient algorithm for solving this latter problem using Networks Flow Analysis is determined. Ways of extending the Extended Basic Period methods to include the product sequencing to minimise total setup times are suggested.