Minimizing variation of production rates in just-in-time systems: A survey

In the past several years, there has been growing interest in scheduling problems where jobs are penalized both for being early and for being tardy. This notable deviation from previous work, in which finishing early is generally regarded as being at least a desirable as finishing on time, is perceived to be the one that well captures the scheduling dimension of JIT production systems. A number of excellent surveys on these problems has appeared over the last four years. There is, however, another important scheduling objective in JIT production systems which is to minimize variation of rates at which processes supply their outputs. These scheduling problems are, for example, of primary concern in the Toyota JIT system. Thus far, most research efforts in this area have been focused on minimizing variation of the rate at which different products are being produced on the final multi-model assembly line which itself is a supplying process. The paper shall review the results of this research, and relate them to the due date based scheduling problems. Extensions and open problems will also be reviewed. Schedules that minimize variations of the rate at which different products are being produced on the line do not necessarily minimize variation in the line demand for outputs of processes that supply it. Few heuristics for the problem of minimizing the variation are available and hardly anything is known on its complexity as well as exact algorithms to tackle it. The paper shall review a mathematical programming model of the problem and open questions that result from it.