Optimization Algorithms for Vehicle Routing and Packing Problems

Abstract

Many optimization problems can be formulated as monolithic mathematical models (e.g., mixed-integer linear programs), which are ready to be solved by the state-of-the-artoptimization solvers. However, by exploiting the problem structures, one may design specialized solution approaches that can manage to efficiently solve problems of a muchlarger size. In this thesis, we develop tailored branch-and-bound algorithms for solving complex problems that arise in supply chain logistics as well as object packing. The primary focus of this thesis is on the mathematical modeling and algorithmic development for addressing vehicle routing problems. We consider the following four settings: (i) continuous-time inventory routing, which integrates inventory management, vehicle routing, and delivery-scheduling decisions; (ii) full truckload pickup and delivery, which entails full truckload shipments between distribution centers and delivery locations; (iii) marginal cost estimation, which seeks for the average routing cost of serving an individual customer in a stochastic supply chain system; (iv) routing under uncertainty, which incorporates customer demand and/or travel time uncertainty while designing delivery routes. The second part of the thesis is focused on global optimization with application to cutting and packing problems. In particular, we are interested in two variants of packing problems: shape nesting and circle packing. The former entails irregular polygons while the latter involves circles. The goal is to identify a feasible configuration for these objects to be packed in a container such that no overlap exists among these objects and the materialwaste is minimized. Modeling both problems is simple, however, solving the resulting mathematical models is extremely challenging due to the presence of non-overlapping constraints. For each of the aforementioned problems, we explore its intrinsic structure and proposea specialized algorithm. Through extensive computational studies on benchmark instances, we demonstrate the effectiveness and efficiency of our proposed methods.