Optimal batch provisioning to customers subject to a delay-limit

This work deals with batch provisioning and order aggregation. Two examples are: (i) a manufacturer that has to deliver items to customers in a remote destination, and (ii) a company that provides repair and replacement service to its clients. In both cases the remoteness of customers suggests order aggregation – a batch delivery in the first example, and a batch-visits journey in the other; the alternative is to provide individual services to customers. A key element is a contractual obligation of the company to provide service within an agreed delay-limit, and in that view the main decision problem is to determine the moments at which a batch service should be executed. That decision would depend on (random) demand-arrival patterns, the costs associated with the two service modes (batch and individual), as well as the model used to describe operating conditions. This paper proposes and investigates several service-provision policies, with a simple enough structure to make them appealing for real-life implementation. Optimal service-provision procedures are obtained for these policies, minimizing the long-run expected cost per unit of time. The optimal costs of the proposed policies are compared and their relative performance is evaluated with respect to the global minimal cost (of the optimal policy) on one hand, and basic policies that employ either only batch or only individual services on the other hand. Finally, a range of model generalizations of interest is presented and the relationship of the problem here to broader issues is discussed.