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In this article, the following stochastic vehicle routing problem is considered. Each customer has a known probability of presence and a random demand. This problem arises in several contexts, e.g., in the design of less-than-truckload collection routes. Because of uncertainty, it may not be possible to follow vehicle routes as planned. Using a stochastic programming framework, the problem is solved in two stages. In a first stage, planned collection routes are designed. In a second stage, when the set of present customers is known, these routes are followed as planned by skipping the absent customers. Whenever the vehicle capacity is attained or exceeded, the vehicle returns to the depot and resumes its collections along the planned route. This generates a penalty. The problem is to design a first stage solution in order to minimize the expected total cost of the second state solution. This is formulated as a stochastic integer program, and solved for the first time to optimality by means of an integer L-shaped method.

This paper considers a version of the stochastic vehicle routing problem where customers are present at locations with some probabilities and have random demands. A tabu search heuristic is developed for this problem. Comparisons with known optimal solutions on problems whose sizes vary from 6 to 46 customers indicate that the heuristic produces an optimal solution in 89.45% of cases, with an average deviation of 0.38% from optimality.