Robust Cross-dock Location Model Accounting for Demand Uncertainty

The objective of this thesis was to develop optimization models to locate cross-docks in supply chain networks. Cross-docks are a type of intermediate facility which aid in the consolidation of shipments, in which the goods spend little or no time in storage. Instead, the goods are quickly and efficiently moved from the inbound trucks to the outbound docks. Two deterministic facility location models were developed. One followed the p-median facility problem type, where only p facilities were opened in order to minimize total network costs. In the second model, as many cross-docks as necessary were opened and facility location costs were considered while minimizing total network costs. In order to account for uncertainty in demands, a robust optimization model was created based on the initial deterministic one. Robust counterparts were developed for each equation that contained the demand term. The robust model allowed for the creation of a network with the ability to handle variations in demand due to factors such as inclement weather, seasonal variations, and fuel prices. Numerical analysis was performed extensively on both the deterministic and robust models, following the p-median facility problem type, using three networks and parameters coherent with industry standards. The results showed that accounting for uncertainty in demands had a real effect on the facilities which were opened and total network costs. While the deterministic network was less expensive, it was unable to handle increases in demand due to uncertainty, whereas the robust network had no capacity shortages in any scenario. Simple demand inflation, along with the use of a robust model for baseline comparison, also proved to be a legitimate strategy to account for uncertainties in demand among small freight carriers

Supply Chain Network Design with Concave Costs: Theory and Applications

Many practical decision models can be formulated as concave minimization problems. Supply chain network design problems (SCNDP) that explicitly account for economies-of-scale and/or risk pooling often lead to mathematical problems with a concave objective and linear constraints. In this thesis, we propose new solution approaches for this class of problems and use them to tackle new applications. In the first part of the thesis, we propose two new solution methods for an important class of mixed integer concave minimization problems over a polytope that appear frequently in SCNDP. The first is a Lagrangian decomposition approach that enables a tight bound and a high quality solution to be obtained in a single iteration by providing a closed-form expression for the best Lagrangian multipliers. The Lagrangian approach is then embedded within a branch-and-bound framework. Extensive numerical testing, including implementation on three SCNDP from the literature, demonstrates the validity and efficiency of the proposed approach. The second method is a Benders approach that is particularly effective when the number of concave terms is small. The concave terms are isolated in a low dimensional master problem that can be efficiently solved through enumeration. The subproblem is a linear program that is solved to provide a Benders cut. Branch-and-bound is then used to restore integrality if necessary. The Benders approach is tested and benchmarked against commercial solvers and is found to outperform them in many cases. In the second part, we formulate and solve the problem of designing a supply chain for chilled and frozen products. The cold supply chain design problem is formulated as a mixed-integer concave minimization problem with dual objectives of minimizing the total cost, including capacity, transportation, and inventory costs, and minimizing the global warming impact that includes, in addition to the carbon emissions from energy usage, the leakage of high global-warming-potential refrigerant gases. Demand is modeled as a general distribution, whereas inventory is assumed managed using a known policy but without explicit formulas for the inventory cost and maximum level functions. The Lagrangian approach proposed in the first part is combined with a simulation-optimization approach to tackle the problem. An important advantage of this approach is that it can be used with different demand distributions and inventory policies under mild conditions. The solution approach is verified through extensive numerical testing on two realistic case studies from different industries, and some managerial insights are drawn. In the third part, we propose a new mathematical model and a solution approach for the SCNDP faced by a medical sterilization service provider serving a network of hospitals. The sterilization network design problem is formulated as a mixed-integer concave minimization program that incorporates economies of scale and service level requirements under stochastic demand conditions, with the objective of minimizing long-run capacity, transportation, and inventory holding costs. To solve the problem, the resulting formulation is transformed into a mixed-integer second-order cone programming problem with a piecewise-linearized cost function. Based on a realistic case study, the proposed approach was found to reach high quality solutions efficiently. The results reveal that significant cost savings can be achieved by consolidating sterilization services as opposed to decentralization due to better utilization of resources, economies of scale, and risk pooling