Single capacitated production facilities where multiple products are produced pose particularly challenging scheduling problems. The traditional economic lot size calculation reflects the optimum production batch size in the light of the tradeoff between inventory carrying costs and order preparation/setup costs. However, these calculations are straightforward only when applied to a single product. When multiple products are produced on the same facility, the production quantities must be translated into a schedule which is within the capacity of the facility and results in the timely satisfaction of demand for each product. Previously published solution procedures directly address the capacity issue. A far less tractable issue is the stockout concern. This issue has previously been addressed by either (1) imposing (often overly restrictive) constraints a priori to guarantee feasibility from the outset possibly eliminating more economic schedule alternatives from consideration or (2) heuristic enumeration procedures where trial solutions are evaluated for feasibility a posteriori but the escape from infeasibility often poses algorithmic difficulties. In this paper, the focus is on providing a workable production sequence through a posteriori tests. Mathematical programming approaches are defined which include alternative formulations to better address the stockout concern. Goal programming procedures are proposed which provide a mechanism to directly examine the tradeoffs between scheduling efficiency and delivery performance.
