USING SIMULATION TO EXAMINE CUTTING POLICIES FOR A STEEL FIRM

Minimizing the cost of filling demand is a problem that reaches back to the foundation of operations research. Here we use simulation to investigate various heuristic policies for a one-dimensional, guillotine cutting stock problem with stochastic demand and multiple supply and demand locations. The policies investigated range from a random selection of feasible pieces, to a more strategic search of pieces of a specific type, to a new policy using dual values from a linear program that models a static, deterministic demand environment. We focus on an application in the steel industry and we use real data in our model. We show that simulation can effectively model such a system, and further we exhibit the relative performance of each policy. Our results demonstrate that this new policy provides statistically significant savings over the other policies investigated

Effective Design and Operation of Supply Chains for Remnant Inventory Systems

This research considers a stochastic supply chain problem that (a) has applications in anumber of continuous production industries, and (b) integrates elements of several classicaloperations research problems, including the cutting stock problem, inventory management,facility location, and distribution. The research also uses techniques such as stochasticprogramming and Benders' decomposition. We consider an environment in which a companyhas geographically dispersed distribution points where it can stock standard sizes of a productfrom its plants. In the most general problem, we are given a set of candidate distributioncenters with different fixed costs at the di®erent locations, and we may choose not to operate facilities at one or more of these locations. We assume that the customer demand for smaller sizes comes from other geographically distributed points on a continuing basis and this demand is stochastic in nature and is modeled by a Poisson process. Furthermore, we address a sustainable manufacturing environment where the trim is not considered waste, but rather, gets recycled and thus has an inherent value associated with it. Most importantly, the problem is not a static one where a one-time decision has to be made. Rather, decisions are made on a continuing basis, and decisions made at one point in time have a significant impact on those made at later points. An example of where this problem would arise is a steel or aluminum company that produces product in rolls of standard widths. The decision maker must decide which facilities to open, to find long-run replenishment rates for standard sizes, and to develop long-run policies for cutting these into smaller pieces so as to satisfy customer demand. The cutting stock, facility-location, and transportation problems reside at the heart of the research, and all these are integrated into the framework of a supply chain. We can see that, (1) a decision made at some point in time a®ects the ability to satisfy demand at a later point, and (2) that there might be multiple ways to satisfy demand. The situation is further complicated by the fact that customer demand is stochastic and that this demand could be potentially satisfied by more than one distribution center. Given this background, this research examines broad alternatives for how the company's supply chain should be designed and operated in order to remain competitive with smaller and more nimble companies. The research develops a LP formulation, a mixed-integer programming formulation, and a stochastic programming formulation to model di®erent aspects of the problem. We present new solution methodologies based on Benders' decomposition and the L-shaped method to solve the NP-hard mixed-integer problem and the stochastic problem respectively. Results from duality will be used to develop shadow prices for the units in stock, and these in turn will be used to develop a policy to help make decisions on an ongoing basis. We investigate the theoretical underpinnings of the models, develop new, sophisticated computational methods and interesting properties of its solution, build a simulation model to compare the policies developed with other ones commonly in use, and conduct computational studies to compare the performance of new methods with their corresponding existing methods