Decomposition Algorithm in Fixed Charge Time-Space Network Flow Problems

A wide range of network flow problems primarily used in transportation is categorized as time-space fixed charge network flow (FCNF) problems. In this family of networks, each node is associated with a specific time and is replicated across all time-periods. The cost structure in these problems consists of variable and fixed costs where continuous and binary variables are required to formulate the problem as a mixed integer linear programming. FCNF problems are classified as NP-hard problems, therefore, adding another component (i.e., time) to this type of problem results in a complex problem which is time-consuming and CPU and memory intensive. Various exact and heuristic methods have been proposed and implemented to solve FCNF problems. In this work, a decomposition heuristic is proposed that subdivides the problem into various time epochs to create smaller and more manageable subproblems. These subproblems are solved sequentially to find an overall solution for the original problem. To evaluate the capability and efficiency of the decomposition method vs. exact method, a total of 1600 problems is generated and solved using Gurobi MIP solver, which runs parallel branch & bound algorithm. Statistical analysis indicates that depending on the problem specification, the average solution time in decomposition methods is improved by up to four orders of magnitude. While statistically, there is a significant difference between the mean objective value of exact method and each TPV configuration in both decomposition methods, however, the average difference (0-2.16% in decomposition and 1.55-7.85% in decomposition method with relaxation) may not be a serious concern for many practical large-scale problems. This shows great promise for decomposition method to significantly reduce the solution time which has been an outstanding issue in complicated large-scale problems

Decomposition methods for large-scale network expansion problems

Network expansion problems are a special class of multi-period network design problems in which arcs can be opened gradually in different time periods but can never be closed. Motivated by practical applications, we focus on cases where demand between origin-destination pairs expands over a discrete time horizon. Arc opening decisions are taken in every period, and once an arc is opened it can be used throughout the remaining horizon to route several commodities. Our model captures a key timing trade-off: the earlier an arc is opened, the more periods it can be used for, but its fixed cost is higher, since it accounts not only for construction but also for maintenance over the remaining horizon. An overview of practical applications indicates that this trade-off is relevant in various settings. For the capacitated variant, we develop an arc-based Lagrange relaxation, combined with local improvement heuristics. For uncapacitated problems, we develop four Benders decompositi

Modeling and Optimization of Resource Allocation in Supply Chain Management Problems

Resource allocation in supply chain management studies how to allocate the limited available resources economically/optimally to satisfy the demands. It is an important research area in operations research. This dissertation focuses on the modeling and optimization of three problems. The first part of the dissertation investigates an important and unique problem in a supply chain distribution network, namely minimum cost network flow with variable lower bounds (MCNF-VLB). This type of network can be used to optimize the utilization of distribution channels (i.e., resources) in a large supply network, in order to minimize the total cost while satisfying flow conservation, lower and upper bounds, and demand/supply constraints. The second part of the dissertation introduces a novel method adopted from multi-product inventory control to optimally allocate the cache space and the frequency (i.e., resources) for multi-stream data prefetching in computer science. The objective is to minimize the cache miss level (backorder level), while satisfying the cache space (inventory space) and the total prefetching frequency (total order frequency) constraints. Also, efforts have also been made to extend the model for a multi-level, multi-stream prefetching system. The third part of the dissertation studies the joint capacity (i.e., resources) and demand allocation problem in a service delivery network. The objective is to minimize the total cost while satisfying a required service reliability, which measures the probability of satisfying customer demand within a delivery time interval