Cyclic scheduling to minimize inventory in a batch flow line

This paper addresses the problem of determining a cyclic schedule for batch production on a flow line. We assume a constant supply of raw materials and a constant demand for all finished goods. Material that has completed processing at one stage is transferred to the next stage in small transfer batches. Inventory may he held before the line, at the end of the line, or between any pair of adjacent stations. The objective is to find a sequence of production and a cycle length that minimize the average cost per unit time of holding inventory. A linear programming formulation is given that determines the optimal cycle length and finishing times for a given set of sequences, one for each machine. Two heuristics are presented for finding near-optimal sequences: one is applicable to the special case of a two-machine flow line; the others are applicable to an m-machine line and focus on different aspects of the problem (e.g. cycle stock or work-in-process inventory). From a computational study, we have observed that: (1) permutation schedules, i.e. schedules with the same sequence on all machines, are nearly always optimal, (2) the heuristics produce near-optimal solutions, (3) the batching decision, i.e. the choice of cycle length, is substantially more significant than the sequencing decision for minimizing inventory costs.