We analyze a continuous-time, two-stage production/inventory system. In the first stage, a common intermediate product is produced in batches, and possibly stored. In the second phase, the intermediate product is fabricated into n distinct finished products. Several finished products may be included in a single production batch of limited capacity to exploit economies of scale. We propose a planning methodology to address the combined problem of joint setup costs and capacity limits (per setup). We restrict ourselves to a class of replenishment strategies with the following properties: a replenishment strategy specifies a collection of families (subsets of items) covering all end-items; if an item belongs to several families a specific fraction of its sales is assigned to each family. Each time the inventory of one item in a family is replenished, the inventories of all other items in the family are replenished as well. We derive a simple (roughly 0(n log n)) algorithm that results in a strategy whose long-run average cost comes within a few percentage points of a lower bound for the minimum achievable cost (within the above class of strategies).

Shoshana Anily and Awi Federgruen
Journal Article
Publication Date
Operations Research

Full Citation

Anily, Shoshana and Awi Federgruen
. “Capacitated two-stage multi-item production/inventory model with joint setup costs.”
Operations Research
, (January 01, 1991):