Joint Pricing-Production Decisions with Stochastic Price-Dependent Demand

We present a joint decision model which combines the decisions of setting selling price and determining manufacturing batch size with an ultimate objective of maximizing a utility function, the demand for the product is both price-dependent and uncertain. We show that there exists a unique optimal selling price and manufacturing batch size, the optimal manufacturing batch size is decreasing in holding cost and increasing in demand variance, the optimal selling price is increasing in holding cost and decreasing in demand variance, the optimal objective utility function is decreasing both in holding cost and demand variance. Comparing the simultaneous decisions, we bring out that if there no demand variance, the optimal selling price and the optimal manufacturing batch size with sequential decisions is equal; if the demand is stochastic, with sequential decisions, the optimal selling price is higher, the optimal manufacturing batch size is lower, and optimal objective utility is sub-optimal with some utility loss