On the economic lot scheduling problem: stock-out prevention and system feasibility

The Economic Lot Scheduling Problem is a classical scheduling problem with the objective of minimising the long-run inventory and set-up costs of a single machine, multi-product inventory system. Demand rates, production rates and set-up times are assumed to be deterministic. The problem has been extensively studied and methods exist to obtain cyclic schedules which minimise total cost. In order to apply a cyclic schedule without a stock-out occurring, certain initial inventory levels are required. This paper considers the scenario where inventory levels are critically low and the cyclic schedule cannot be applied. Analytical methods are developed to determine: if the initial inventory is sufficient to prevent a stock-out from occurring; the maximum time until a stock-out will occur if a stock-out is unavoidable; and the minimum time required to obtain the necessary inventory to resume the cyclic schedule if a stock-out can be avoided.