A real-world vehicle routing and scheduling problem in which a set of known customers is served by a number of vehicles with known capacity is considered. The demand for each customer is stochastic and needs to be served within a given time window. Strict adherence to the time window constraints for customers who practice the just-in-time concept of inventory management is requisite. One or several factors of vehicle routing and scheduling problems are stochastic. This has a major impact on how the problem is both formulated and solved. A three-index model that is a mixed-integer stochastic program with recourse is proposed. A meta-heuristic algorithm for solving this problem is developed. Computation of the objective function of this model is computationally expensive. The proxies to evaluate the moves in tabu search are embedded in this heuristic algorithm. The heuristic was tested with Solomon's 100-customer Euclidean vehicle routing problems with time windows but with the customer demands and vehicle capacity excluded. The test results revealed that problem difficulty was relevant not only to the number of customers but also to the average filling coefficients. A routing schedule with a lower value of the average filling coefficient is made to serve a scattering flock of customers.