The multi-products EMQ model

Since the introduction of the classical economic manufacturing quantities (EMQ) concept early in the twentieth century, many variants of the single-product EMQ model have been solved. These single-product EMQ models usually suppose the product is produced cyclically every T time units. This dissertation examines the general cyclical model (GCM), a generalization of the single-product EMQ. In the GCM n≥2 products are produced on a single facility according to cyclical schedules. The GCM, unlike some variants of the multiproducts, single-facility problem, permits each product i to be produced every T_i time units where it is not necessary that T_i = T_j if i ≠ j. However, a schedule of n products must be feasible; that is, only one product may occupy the facility at a time. Thus, the objective of the GCM is to find cycle times {T_i} that minimize the inventory and production costs subject to the restriction that the schedule is feasible. To mathematically address this feasibility problem, delay times {d_i} are introduced where d_i is the time at which the first use period of product i begins. Then conditions are given that are both necessary and sufficient to assure that a specified schedule {T_i, d_i} of n products is feasible. These feasibility conditions remove a major handicap suffered by previous researcher. Then delay-independent necessary and sufficient feasibility conditions are derived for the two-products and the three-products case of the GCM. Also, delay-independent necessary feasibility conditions are derived for the four-products case. Finally, an efficient algorithm is developed that finds feasible optimal schedules for the n-products model.