In the aftermath of a large disaster, the routing of vehicles carrying critical supplies can greatly impact the arrival times to those in need. Since it is critical that the deliveries are both fast and fair to those being served, it is not clear that the classic cost-minimizing routing problems properly reflect the priorities relevant in disaster relief. In this paper, we take the first steps in developing new methodologies for these problems. We focus specifically on two alternative objective functions for the TSP and VRP: one that minimizes the maximum arrival time (minmax) and one that minimizes the average arrival time (minavg). To demonstrate the potential impact of using these new objective functions, we bound the worst case performance of optimal TSP solutions with respect to these new variants and extend these bounds to include multiple vehicles and vehicle capacity. Similarly, we examine the potential increase in routing costs that result from using these alternate objectives. We present solution approaches for these two variants of the TSP and VRP which are based on well known insertion and local search techniques. These are used in a series of computational experiments to help identify the types of instances where TSP and VRP solutions can be significantly different from optimal minmax and minavg solutions.

Many companies with consumer direct service models, especially grocery delivery services, have found that home delivery poses an enormous logistical challenge due to the unpredictability of demand coupled with strict delivery windows and low profit margin products. These systems have proven difficult to manage effectively and could benefit from new technology, particularly to manage the interaction between order capture and promise and order delivery. In this paper, we define routing and scheduling problems that capture important features of this emerging business model and propose algorithms, based on insertion heuristics, for their solution. The emphasis is on profit maximization. The vendor has to decide which requests to accept and in which time slot to guarantee delivery, for those that are accepted. Computational experiments demonstrate the importance of an integrated approach to order capture and promise and order delivery and the quality and value of the proposed algorithms. 3 Literature Research is emerging that analyzes routing strategies for unattended home deliveries where time slots are not of concern. In (Punakivi 2000), the routing options studied include the use of fixed routes and the optimal sequencing of the deliveries on routes as soon as all deliveries are known. The results demonstrate the importance of optimization in CD with savings from optimal routing

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