A family of inventory models with demand met either from stock or by special production runs

This paper discusses models for a combined inventory policy where customer orders can be met either from stock or by special production runs. The daily demands are assumed to be independent random variables. No shortages may occur. Costs consist of production set-up costs, inventory holding costs, and a differential product handling cost on demand met from stock. Two models are formulated based on the following policy: If the daily demand exceeds a cutoff point P, demand is met by a special production run, otherwise it is met from stock. Stocks are replenished to a level S (a) upon depletion, or (b) jointly with a special production run provided the stock level is below a critical review point R, whichever occurs first. Computationally efficient approximations to the optimal solution are developed.