Supply decisions for unknown linearly increasing demand

• Published in: Engineering costs and production economics Vol. 17; no. 1; pp. 389 - 393
• Main Author: Reyniers, Diane J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.1989; Elsevier
• Series: Engineering Costs and Production Economics
• ISSN: 0167-188X; 1878-4011
• DOI: 10.1016/0167-188X(89)90088-8

We consider the problem of a supplier faced with unknown but deterministic future demand. We assume that demand {itD t} increases linearly over time: D t = D+ αt. The supplier knows demand D in period 0 with certainty but is ignorant about the rate of increase α. In each period t he will supply a certain quantity S t and as a consequence he gets information about demand. If there is a stockout ( S t</D t ), he only knows that he underestimated the trend α. If, on the other hand, supply exceeds demand ( S t> t ), he knows exactly what demand was from the amount leftover and from then onwards he will set supply equal to demand. In addition to the asymmetry in information feed-back, the costs are asymmetric. The cost of oversupply is the production cost or unit cost price whereas the cost of undersupply is an opportunity cost of lost profits. We find the min-max cost and the supplier's optimal strategy.