Optimal joint pricing and lot sizing with fixed and variable capacity

This paper examines previously unexplored fixed and variable capacity problems of jointly determining an item's price and lot size for a profit-maximizing firm facing constant but price-dependent demands over a planning horizon. We apply geometric programming to these constrained nonlinear maximization problems with nonconcave objective functions and obtain global optimal solutions. Using Karush–Kuhn–Tucker condition, marginal and sensitivity analyses, we investigate model interactions, provide managerial implications on the optimal capacity decisions, and explore the postoptimal behavior of the price, lot size, and capacity expansion and reduction size. Some findings cast interesting insights, different from previous just-in-time management studies without pricing consideration.