On the Cyclic Sequences in Mixed Model Just-in-Time Production System

Abstract

Mixed-model Just-in-Time production systems have been developed in recent years in order to reduce costs of diversified small-lot production, which involves producing only the necessary products in the necessary quantities at necessary times. This problem minimizes both the earliness and the tardiness penalties that respond to the customer demands for a variety of models without holding large inventories or incurring shortages. The problem of sequencing flexible transfer lines or mixed-model assembly lines according to the JIT philosophy can be formulated as a non-linear integer programming problem.

Minimization of the variation in demand rate for outputs of supplying processes is the output rate variation problem (ORVP) and minimization of the variation in the rate at which different products are produced on the line is the product rate variation problem (PRVP). The problem for minimizing of deviations between actual and desired production for PRVP can be solved efficiently in pseudo-polynomial time complexity. However, the ORVP with two or more levels is strongly NP-hard. But under the pegging assumption the ORVP can be solved efficiently.

In this dissertation, we implement different algorithms and heuristics to solve both ORVP and PRVP. The cyclic sequences are optimal for both sum-deviation and max-deviation PRVPs. The cyclic sequences to ORVP are presented with an example. Likewise, the existences of cyclic sequences to PRVP under different solution approaches are explored. Furthermore, several directions for further research are also explored including some emerged conjectures.