Coordination of pricing, advertising, and production decisions for multiple products
This research aims to develop and propose mathematical models that can be used to facilitate cross-functional coordination between operations and marketing. We consider a dynamic problem of joint pricing, advertising, and production decisions for a profit maximizing firm that produces multiple products. We assume the firm operates in monopolistic environment, where demand for its products is a function of price and advertising expenditure. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and demand seasonality. We first model and solve the pricing problem without advertising. Later, we extend the model to include advertising as decision variables. The demand for each product is assumed to be continuous, differentiable, strictly decreasing in price and concave in advertising. We present a solution approach which can be used for constant pricing, as well as dynamic pricing strategies. Furthermore, the solution approach is more general and applicable for linear as well as nonlinear demand functions. Using real world data from a manufacturer, we create problem instances, for different demand scenarios at different capacities, and solve for optimal prices for each strategy. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and at different capacities. We compare the firm's profitability for the two pricing strategies, and show that dynamic pricing is valuable at low capacities and when at least one of the products has peak demand in the beginning of the planning horizon. We show that the optimal allocation of advertising budget across products does not change with budget changes. Moreover, the change is minimal with changes in demand seasonality. It is optimal to increase advertising in periods of higher demand and decrease in periods of lower demand. Hence, firms can use rules of thumb and need not to frequently review the allocation. Numerical results show that the proposed algorithms have good convergence properties. Finally, as it is clear from review of academic literature; there are no decision support systems that truly integrate the production/inventory and pricing decisions - specially for multi-product problems. We believe, this work makes valuable contributions in developing solution methodologies that can be incorporated in such decision support systems.