The Research Of Robust Optimization Methodology In SCM With Retailer-Supplier Flexible Commitment Contracts

Robust optimization (RO) is a relatively recent technique as a new branch of maths programming, and it is a powerful methodology used to solve uncertain program problems. Many real-world optimization problems involve input data that are perturbed or uncertain, and the probability distributions of the uncertain data are unknown or unavailable due to measurement or modelling errors, or the unavailability of the information at the time of the decision. RO is based on a description of uncertainty via sets, as opposed to probability distributions. The uncertain parameters are only known to belong to known sets, and one associates with the uncertain problem its robust counterpart (RC) where the constraints are enforced for every possible value of the parameters within their prescribed sets; under such constraints, the worst-case value of the cost function is then minimized to obtain a"robust"solution of the problem. Different type of sets gets different type of robust counterparts, which have different complexities. What are the effects on robust solution and its optimal value when using different type of sets, and what are the relations between them, we'll try to study these problems.In this paper we take the retailer-supplier flexible commitment (RSFC) problem in supply chain management as applied background, because in RSFC there are decision problems caused by changefully demand information and fluctuant price.We study two RC of uncertain RSFC problems: Ben-Tal & Nemirovski RC and Bertsimas & Sim RC, and their essential difference and internal relations. Via the conservativeness parameters of the two RC, we derive the sufficient condition and necessary condition when they have the same solution under some premise. Furthermore, the propositions are"consrtaintwise": can be used independently in different constraint.Through case study, the RC is found to provide effective protect from the disruption of uncertain data and the robust price paid at the same time. Comparing two tests'results, it validates the sufficient and necessary conditions.The contributions of this paper are as follows:1) We introduce each contaminated constraint of Ben-Tal & Nemirovski RC a proper conservativeness parameters not only a single one, and this modifying improves optimal value without change the probability of constraint violate.2) After studying the relation between the two RC's conservativeness parameters when there are existing the same solutions, we derive the sufficient condition and necessary condition under some premise, and they are all testified by case study.3) The RC of RSFC problems with both uncertain demand and uncertain price is formulated, and by the propositions (2) above, we formulate the mixed-RC model using both two types RC.