Multi-product capacity-constrained lot sizing with economic objectives

The capacity-constrained lot-sizing problem with stochastic lot arrivals is especially relevant within batch production environments. Progress has previously been made in minimizing queue times and flow times under generalized queueing assumptions. This paper introduces extensions incorporating economic criteria for the single machine case. Holding costs related to queueing delays are considered along with traditional EOQ cost components. Relationships are developed to determine lot sizes that minimize costs for the single and multiple product cases when the production rate is specified. As well, relationships to determine both lot sizes and throughput rates that maximize profits are examined.