A Facilities in Series Inventory Model with Nested Schedules

We consider an n-period single-product inventory model with known requirements and separable concave production and storage costs. The model is a multi-echelon structure in which N facilities, labeled 1,…,N, are arranged in series. We show that if storage and production costs are respectively nondecreasing in order of facilities and nonincreasing in time, then an optimal schedule has the property that if in a given period, facility j produces, then facility j + 1 does also. This nested structure is exploited in an algorithm for finding an optimal schedule. The computational effort increases in proportion to the cube of the number of periods and linearly with the number of facilities. For the stationary infinite horizon case an algorithm yields a periodic optimal schedule.