Essays on Shipment Consolidation Scheduling and Decision Making in the Context of Flexible Demand

This dissertation contains three essays related to shipment consolidation scheduling and decision making in the presence of flexible demand. The first essay is presented in Section 1. This essay introduces a new mathematical model for shipment consolidation scheduling for a two-echelon supply chain. The problem addresses shipment coordination and consolidation decisions that are made by a manufacturer who provides inventory replenishments to multiple downstream distribution centers. Unlike previous studies, the consolidation activities in this problem are not restricted to specific policies such as aggregation of shipments at regular times or consolidating when a predetermined quantity has accumulated. Rather, we consider the construction of a detailed shipment consolidation schedule over a planning horizon. We develop a mixed-integer quadratic optimization model to identify the shipment consolidation schedule that minimizes total cost. A genetic algorithm is developed to handle large problem instances. The other two essays explore the concept of flexible demand. In Section 2, we introduce a new variant of the vehicle routing problem (VRP): the vehicle routing problem with flexible repeat visits (VRP-FRV). This problem considers a set of customers at certain locations with certain maximum inter-visit time requirements. However, they are flexible in their visit times. The VRP-FRV has several real-world applications. One scenario is that of caretakers who provide service to elderly people at home. Each caretaker is assigned a number of elderly people to visit one or more times per day. Elderly people differ in their requirements and the minimum frequency at which they need to be visited every day. The VRP-FRV can also be imagined as a police patrol routing problem where the customers are various locations in the city that require frequent observations. Such locations could include known high-crime areas, high-profile residences, and/or safe houses. We develop a math model to minimize the total number of vehicles needed to cover the customer demands and determine the optimal customer visit schedules and vehicle routes. A heuristic method is developed to handle large problem instances. In the third study, presented in Section 3, we consider a single-item cyclic coordinated order fulfillment problem with batch supplies and flexible demands. The system in this study consists of multiple suppliers who each deliver a single item to a central node from which multiple demanders are then replenished. Importantly, demand is flexible and is a control action that the decision maker applies to optimize the system. The objective is to minimize total system cost subject to several operational constraints. The decisions include the timing and sizes of batches delivered by the suppliers to the central node and the timing and amounts by which demanders are replenished. We develop an integer programing model, provide several theoretical insights related to the model, and solve the math model for different problem sizes

Efficient approximation schemes for Economic Lot-Sizing in continuous time

We consider a continuous-time variant of the classical Economic Lot-Sizing (ELS) problem. In this variant, the setup cost is a continuous function with lower bound K min 0 , the demand and holding costs are integrable functions of time and arbitrary replenishment policies are allowed. Starting from the assumption that certain operations involving the setup and holding cost functions can be carried out efficiently, we show that this variant admits a simple approximation scheme based on dynamic programming: if the optimal cost of an instance is OPT , we can find a solution with cost at most ( 1 + ¿ ) OPT using no more than O ( 1 ¿ 2 OPT K min log OPT K min ) of these operations. We argue, however, that this algorithm could be improved on instances where the setup costs are generally "very large" compared with K min . This leads us to introduce a notion of input-size parameter ¿ that is significantly smaller than OPT / K min on instances of this type, and then to define an approximation scheme that executes O ( 1 ¿ 2 ¿ 2 log 2 ( OPT K min ) ) operations. Besides dynamic programming, this second approximation scheme builds on a novel algorithmic approach for Economic Lot Sizing problems