Pricing and capacity decisions under demand uncertainty.

Abstract

Consider a firm that has the flexibility to produce two substitutable products and must determine optimal capacity levels and prices for these products for a single-period problem. In the first case, the firm is a price taker but can determine optimal capacity levels for both products. For the second case, the firm can set the price for one product and the optimal capacity level for the other product. In the third case the capacity for both products is assumed to be fixed and the optimal pricing policy for both products is discussed. For each of these cases, the sensitivity of optimal prices and/or capacities to the problem parameters are presented for the case where both products' demands are uniformly distributed. Finally, the situation where each product is managed by a different manager trying to maximize individual product profits are analyzed. The individual optimal price and capacity decisions are then compared to the cases where the decisions are made simultaneously. Secondly, the case where a firm that is able to simultaneously set the price and capacity level of a single product in each period is considered. The demand for the product is uncertain but its mean demand is dependent on the price level that is set which in turn affects the capacity decision. The optimal pricing and capacity policy in the case where the functions to buy and sell capacity are linear is presented. A sensitivity analysis of the optimal policy to changes in the parameters of the model is presented for the case where the product's demand is uniformly distributed. The effects of deterministic and stochastic lead times on the optimal policy are also presented. In addition, the situation where there is a possibility of a change in technology that reduces the cost of buying capacity in the future is discussed in terms of its effect on the optimal pricing and capacity strategy. Numerical examples of various optimal pricing and capacity decisions are presented for the case when the cost functions are non-linear. Thirdly, optimal pricing and capacity decisions are presented for the case where there are fixed costs associated with buying and selling capacity. Sensitivity of the optimal policy to changes in the parameters of the model are also presented. Finally, optimal capacity decisions are discussed when the future selling price or the production costs are uncertain.