Problem

(Zavi 1976) Consider the economic lot size model with infinite horizon and deterministic demand D items per unit of time. When the inventory level is zero, production of Q items starts at a rate of P items per unit of time, P ≥ D. The setup cost is K$ and the holding cost is h$/item/time. Every time production starts at a level of P items/time, we incur a cost of αP, α > 0.

(a) What is the optimal production rate?

(b) Suppose that due to technological constraints, P must satisfy 2D ≤ P ≤ 3D. What are the optimal production rate and the optimal order quantity?