IE-OPIM Joint Seminar
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IE-OPIM Joint Seminar 19 February 2015 at 13.40 at FENS G035

LOT SIZING PROBLEMS WITH NONLINEAR PRODUCTION COST FUNCTIONS

By

Esra Koca

 

Abstract: In this study, we consider different variations of the lot sizing problem encountered in many real life production, procurement and transportation systems. First, we consider the deterministic lot sizing problem with piecewise concave production cost functions. A piecewise concave function can be used to represent quantity discounts, subcontracting, overloading, minimum order quantities, and capacities. Computational complexity of this problem was an open question in the literature. We develop a dynamic programming (DP) algorithm to solve the problem and show that the problem is polynomially solvable when number of breakpoints of the production cost function is fixed and the breakpoints are time invariant. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of existing algorithms in the literature. Our algorithm performs quite well for small and medium instances. For larger instances, we propose a DP based heuristic to find a good quality solution in reasonable time.

Next, we consider the stochastic lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function to reflect increasing marginal costs of larger reductions. We formulate the problem as a second-order cone mixed integer program, strengthen the formulation and solve it by a commercial solver. Moreover, we obtain convex hull and computational complexity results. We conduct an extensive computational study to see the effect of controllable processing times in solution quality.

As a final problem, we study the multi-stage stochastic lot sizing problem with nervousness considerations. In multi-stage stochastic programming, different production decisions for different scenarios may lead to lack of coordination in MRP systems. We formulate the problem by considering this drawback of the approach. Some mixing set structures are observed as relaxations of our formulation, and valid inequalities are developed based on these structures.        

Bio: Esra Koca is a Ph.D. candidate in the Department of Industrial Engineering at Bilkent University. She received her B.S. and M.S. degrees in Industrial Engineering from Bilkent University in 2007 and 2010, respectively. Her research interests are mixed integer programming, stochastic optimization, convex optimization, and dynamic programming with applications in production planning and logistics.