Optimal supply chain planning problems with nonlinear revenue and cost functions

This dissertation studies problems arising in certain stages of a supply chain. We specifically focus on problems that have nonlinearity in revenue or cost functions, and problems that can be written as mixed-integer linear programming problems. There are four main chapters that provide contributions to the supply chain operations literature.;We first consider the allocation of a limited budget to a set of investments in order to maximize net return from investment. In a number of practical contexts, the net return from investment in an activity is effectively modeled using an S-Curve, where increasing returns to scale exist at small investment levels, and decreasing returns to scale occur at high investment levels. We formulate the problem as a knapsack problem with S-Curve return functions and demonstrate that it is NP -Hard. We provide a pseudo-polynomial time algorithm for the integer variable version of the problem, and develop efficient solution methods for special cases of the problem. We also discuss a fully-polynomial-time approximation algorithm for the integer variable version of the problem. Then, we consider a stochastic knapsack problem with random item weights that follow a Poisson distribution. We assume that a penalty cost is incurred when the sum of realized weights exceeds capacity. Our aim is to select the items that maximize expected profit. We provide an effective solution method and illustrate the advantages of this approach.;We then consider a supply chain setting where a set of customers with a single product are assigned to multiple uncapacitated facilities. The majority of literature on such problems requires assigning all of any given customer's demand to a single facility. While this single-sourcing strategy is optimal under certain cost structures, it will often be suboptimal under the nonlinear costs that arise in the presence of safety stock costs. Our primary goal is to characterize the incremental costs that result from a single-sourcing strategy. We propose a general model that uses a cardinality constraint on the number of supply facilities that may serve a customer. The result is a complex mixed-integer nonlinear programming problem. We provide a generalized Benders decomposition algorithm to solve the model. Computational results for the model permit characterizing the costs that arise from a single-sourcing strategy.;Finally, we consider a multi-period component procurement-planning and product-line design problem with product substitutions and multiple customer segments. Each customer segment has a preferred product and a set of alternative products. If a customer's preferred product is not made available, demand can be satisfied using an alternative product at a substitution cost. We assume each product is assembled-to-order from a set of components, and inventory is held at the component level. Our aim is to determine a product portfolio, substitution plan, and procurement plan in order to maximize profit. We develop a large-scale mixed-integer linear programming formulation, prove that the problem is NP -Hard and propose a Benders decomposition-based exact algorithm. We conclude the dissertation by discussing our contributions to the literature, and provide some future research directions based on our results. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)...