Generating alternative solutions within the supply chain optimization model BOSS: a mathematical programming approach

Busschers, Roxanne (2012) Generating alternative solutions within the supply chain optimization model BOSS: a mathematical programming approach.

Abstract:ORTEC offers the software tool BOSS, which is used for supply chain optimization studies and decision support at a strategic and tactical level. To find the optimal configuration of a supply chain, BOSS uses mathematical programming. In mathematical programming, it is generally assumed that all data necessary to solve the model is accurately known at the moment of decision. However, in supply chain modeling, parameters like actual demand for products (right-hand side uncertainty) and prices of products (cost parameter uncertainty) are not precisely known when critical decisions have to be made. Furthermore, a mathematical model is generally a simplification of a real business problem. Such a model typically leaves out details that are difficult to express by formal expressions or that make the model hard to solve. Also, some optimization criteria are inherently subjective and difficult to quantify. This thesis describes research into improving the capabilities of BOSS to deal with data and model uncertainties. Modeling to Generate Alternatives (MGA) has been proposed as a framework for dealing with complex problems for which there are important unmodeled issues (Chang et al., 1983). MGA techniques are designed to provide the decision maker a set of alternative solutions that are good with respect to the modeled objectives and different from each other in the decisions they make. Literature describes several methods to generate such alternatives. We propose to apply an approach based on the Hop, Skip, and Jump (HSJ) method by Brill et al. (1982), which we refer to as the Generalized HSJ (GHSJ) framework. The GHSJ framework uses mathematical optimization with a different objective function than the original model uses. A constraint is added to this new model to ensure that the cost of an alternative solution does not exceed the optimal value by more than a pre-specified percentage. Furthermore, the constraints of the original model should hold. We propose four realizations of the GHSJ method that all use a different objective function, depending on the purpose of the method with respect to the obtained alternative solutions: 1. to obtain maximally different solutions, we apply the Standard HSJ method; 2. to obtain a large number of alternative solutions, we apply the Random HSJ method; 3. to obtain alternative solutions that perform better in case of cost parameter uncertainty, we apply the Cost uncertain HSJ method; 4. to obtain alternative solutions that are more robust against right-hand side uncertainty, we apply two versions of the Robust HSJ method. Thus, the four approaches of the GHSJ method deal with both model uncertainty (method 1 and 2) and data uncertainty (method 3 and 4). To test the proposed methods, we use two test cases based on studies performed for customers of ORTEC. The test results are promising and show that each method is able to obtain the type of alternative solutions that it aims for. Based on these results, we recommend ORTEC to implement all four methods in BOSS. When doing a strategic network study for a customer with BOSS, we advise ORTEC to always use the Standard HSJ method. This method provides insight to the decision maker in the existence of solutions that are close to optimal, but with very different strategic decisions. We recommend to use the Random HSJ method, when cost may only increase from optimality by a small amount, for example 0.5%, and the Standard HSJ finds too few solutions. When cost uncertainty plays a role, even if there is only a slight presumption that actual cost may be different than assumed, we recommend to apply the Cost uncertain HSJ method. Initial results should point out whether there exist alternatives that outperform the initial solution. Also, if the Cost uncertain HSJ does not find good alternatives, the method still serves a purpose, since the decision maker gets more confidence in the proposed solution. We recommend applying the Robust HSJ method (version 1) if a customer wants to consider alternatives that allocate unused capacity di�erently over production facilities and distribution locations. Finally, when the customer indicates that he prefers capacity to be not fully utilized for all production or distribution locations, we recommend to apply the Robust HSJ method (version 2).
Item Type:Essay (Master)
Faculty:BMS: Behavioural, Management and Social Sciences
Subject:85 business administration, organizational science
Programme:Industrial Engineering and Management MSc (60029)
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