LP-based subgradient algorithm for joint pricing and inventory control problems

Abstract

It is important for companies to manage their revenues and -reduce their costs efficiently. These goals can be achieved through effective pricing and inventory control strategies. This thesis studies a joint multi-period pricing and inventory control problem for a make-to-stock manufacturing system. Multiple products are produced under shared production capacity over a finite time horizon. The demand for each product is a function of the prices and no back orders are allowed. Inventory and production costs are linear functions of the levels of inventory and production, respectively. In this thesis, we introduce an iterative gradient-based algorithm. A key idea is that given a demand realization, the cost minimization part of the problem becomes a linear transportation problem. Given this idea, if we knew the optimal demand, we could solve the production problem efficiently. At each iteration of the algorithm, given a demand vector we solve a linear transportation problem and use its dual variables in order to solve a quadratic optimization problem that optimizes the revenue part and generates a new pricing policy. We illustrate computationally that this algorithm obtains the optimal production and pricing policy over the finite time horizon efficiently. The computational experiments in this thesis use a wide range of simulated data. The results show that the algorithm we study in this thesis indeed computes the optimal solution for the joint pricing and inventory control problem and is efficient as compared to solving a reformulation of the problem directly using commercial software. The algorithm proposed in this thesis solves large scale problems and can handle a wide range of nonlinear demand functions.