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Open vehicle routing problems, as a variant of vehicle routing problem (VRP), define that the vehicles are not required to return to the depot after completing service. In this paper, we extend the problem to include process control due to the uncertainty of customer demands. Each customer has a demand and each customer must be serviced by a single vehicle and no vehicle may serve a set of customers whose total demand exceeds its capacity. Each vehicle route must start at the depot and end at the last customer it serves. The objective is to define the set of vehicle routes that minimizes the total costs. We solve the stochastic model using a strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method. This strategy is used to force the appropriate non-integer basic variables to move to their neighborhood integer points.

Mixed Integer Program for Tackling Process Control Demand in The Capacitated Open Vehicle Routing Problems