A construction of knowledge rules for reactive planning of job-mix assignment to homogeneous serial batch machines

In high-mix, low-volume production, assigning jobs to parallel machines is an important operation management decision. In manufacturing environments with disruptive unplanned events, reactive job-machine assignment is common in practice but has received little research attention. In this paper, knowledge rules for reactive assignment are constructed analytically for Poisson job arrivals and homogeneous serial batch machines. In serial batching operation, jobs that arrive stochastically are batched by type and then sent to machine queues. This paper has three parts. The effect of job mixes under batching is first analyzed. The probability of setup is derived for the first-come-first-serve, time-based batching, and job-based batching policies. It is shown that uneven mixings of job types produce better results than even mixings under all three batching policies for the performance criterion of minimizing the total number of machine setups. In the second part, knowledge rules that specify partial orderings of job mixings are constructed and proven for singe machine. In the last part, the knowledge rules are applied to the case of parallel machines in situations of disruptive events to demonstrate their utility in dynamic revision of assignment plans.