Iterative algorithms for a joint pricing and inventory control problem with nonlinear demand functions

Abstract

Price management, production planning and inventory control are important determinants of a firm's profitability. The intense competition brought about by rapid innovation, lean manufacturing time and the internet revolution has compelled firms to adopt a dynamic strategy that involves complex interplay between pricing and production decisions. In this thesis we consider some of these problems and develop computationally efficient algorithms that aim to tackle and optimally solve these problems in a finite amount of time. In the first half of the thesis we consider the joint pricing and inventory control problem in a deterministic and multiperiod setting utilizing the popular log linear demand model. We develop four algorithms that aim to solve the resulting profit maximization problem in a finite amount of time. The developed algorithms are then tested in a variety of settings ranging from small to large instances of trial data. The second half of the thesis deals with setting prices effectively when the customer demand is assumed to follow the multinomial logit demand model, which is the most popular discrete choice demand model. The profit maximization problem (even in the absence of constraints) is non-convex and hard to solve. Despite this fact we develop algorithms that compute the optimal solution efficiently. We test the algorithms we develop in a wide variety of scenarios from small to large customer segment, with and without production/inventory constraints. The last part of the thesis develops solution methods for the joint pricing and inventory control problem when costs are linear and demand follows the multinomial logit model.