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The statement of the standard vehicle routing problem cannot always capture all aspects of real-world applications. As a result, extensions or modifications to the model are warranted. Here we consider the case when customers can call in orders during the daily operations; i.e., both customer locations and demands may be unknown in advance. This is modeled as a combined dynamic and stochastic programming problem, and a heuristic solution method is developed where sample scenarios are generated, solved heuristically, and combined iteratively to form a solution to the overall problem.

This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formulations for the robust problem, each based on a different robust approach. The first formulation extends the well-known resource inequalities formulation by employing adjustable robust optimization. We propose two techniques, which, using the structure of the problem, allow to reduce significantly the number of extreme points of the uncertainty polytope. The second formulation generalizes a path inequalities formulation to the uncertain context. The uncertainty appears implicitly in this formulation, so that we develop a new cutting plane technique for robust combinatorial optimization problems with complicated constraints. In particular, efficient separation procedures are discussed. We compare the two formulations on a test bed composed of maritime transportation instances. These results show that the solution times are similar for both formulations while being significantly faster than the solutions times of a layered formulation recently proposed for the problem.

Increased fuel costs together with environmental concerns have led shipping companies to consider the optimization of vessel speeds. Given a fixed sequence of port calls, each with a time window, and fuel cost as a convex function of vessel speed, we show that optimal speeds can be found in quadratic time. © 2013 Wiley Periodicals, Inc. NETWORKS, 2013

This paper presents a humanitarian logistics decision model to be used in the event of a disaster. The operations under consideration span from opening of local distribution facilities and initial allocation of supplies, to last mile distribution of aid. A mathematical model is developed aiming to enable efficient decision making, maximizing the utility of distribution of aid amongst beneficiaries. This model is formulated as a three-stage mixed-integer stochastic programming model to account for the difficulty in predicting the outcome of a disaster.Accessibility of new information implies initiation of distinct operations in the humanitarian supply chain, be it facility location and supply allocation, or last mile distribution planning and execution. The realized level of demand, in addition to the transportation resources available to the decision maker for execution of last mile aid distribution and the state of the infrastructure, are parameters treated as random due to uncertainty.An assessment of the applicability and validity of the stochastic program is made through extensive computational testing based on several test instances. The results show that instances of considerable size are challenging to solve due to the complexity of the stochastic programming model but, still, optimal solutions may be found within a reasonable time frame. Moreover, findings prove the value of the stochastic programming model to be significant as compared with a deterministic expected value approach. Finally, the model is also applied to a case study based on the earthquake that hit Haiti in January of 2010, showing how it could be used in a realistic operation framework.