Capacitated lot-sizing with sequence dependent setup costs

In this paper we consider a single-stage system where a number of different items have to be manufactured on one machine. Expenditures for the setups depend on the sequence in which items are scheduled on the machine. Holding costs are incurred for holding items in inventory. The demand of the items has to be satisfied without delay, i.e. shortages are not allowed. The objective is to compute a schedule such that the sum of holding and setup costs is minimized with respect to capacity constraints. For this problem which we call capacitated lot-sizing problem with sequence dependent setup costs (CLSD) we formulate a new model. The main differences between the new model and the discrete lot-sizing problem with sequence dependent setup costs (DLSDSD), introduced by Fleischmann, is that continuous lot-sizes are allowed and the setup state can be preserved overidle time. For the solution of the new model we present a heuristic which applies a priority rule. Since the priority values are affected by two significant parameters, we perform a local search in the parameter space to obtain low cost solutions. The solution quality is analyzed by a computational study. The comparison with optimal solutions of small instances shows that the solution quality of our heuristic is acceptable. The Fleischmann approach for the DLSPSD computes upper bounds for our new problem. On the basis of larger instances we show that our heuristic is more efficient to solve the CLSD.