Capacity expansion planning with congestion

Sukgon Kim, Purdue University

Abstract

This thesis consists of two parts. In the first part, we use nonlinear clearing functions that relate the expected output of a production resource in a planning period to the expected work in process (WIP) inventory level over that period to develop improved formulations for capacity expansion problems. We exploit the properties of the clearing function to develop a pseudo-polynomial time solution for the single stage capacity expansion problem. This procedure then forms the basis for two constructive greedy heuristics and a Lagrangian heuristic for the multistage problem. The latter procedure also provides lower bounds on the optimal value. We present computational experiments showing that the proposed heuristics obtain high-quality solutions in modest CPU times. As an alternative solution for the multistage problem, we propose a column generation procedure that employs the pseudo-polynomial time algorithm for the single-stage problem to solve sub-problems and generate new columns. The fractional solution to the LP relaxation obtained by column generation is then used to construct a feasible solution. Computational experiments on randomly generated test problems show that the procedure consistently produces near-optimal solutions in shorter CPU times than the Lagrangian heuristic. We also use the column generation formulation to obtain lower bounds in an exact branch and bound algorithm, and show that this new procedure is able to obtain exact solutions to problems that are significantly larger than those that were solved with previous methods. In the second part of the thesis, we present a planning model that allocates production capacity between production and engineering activity to capture the tradeoff between engineering activity that results in increased output in the future, and production that meets demand and generates revenue immediately. The effect of engineering activity is modeled as a concave function of the total number of engineering lots processed to date, while the production facility is represented by a clearing function capturing the nonlinear relationship between resource utilization and lead time. We analyze the optimality conditions of the model to develop structural results and illustrate its behavior with numerical example.

Degree

Ph.D.

Advisors

Uzsoy, Purdue University.

Subject Area

Industrial engineering

COinS