Instant satisfaction is the effect of brick-and-mortar stores, whereas online purchases take time waiting for delivery. Online sellers, such as Amazon, are contemplating ways to deliver goods in the minimum possible time. Amazon has introduced a service in urban areas to deliver within an hour for a price, or free in two hours. Instacart offers a similar service for grocery delivery. In urban areas where there is higher customer density, same-day delivery is offered. Same-day service is managed by a fleet of vehicles dedicated to that purpose. The request arrives dynamically and there is an associated time window for delivery. Vehicles are loaded from a point and multiple requests are delivered at a time. The objective is to make the maximum number of deliveries within a stipulated time window. This problem is called the same-day delivery problem (SDDP). Routing efficiency can increase the number of deliveries. If probabilistic information about delivery requests and vehicle availability are incorporated into the model, the resulting solution will be improved. Probabilistic information may allow for the vehicle to do more services on the way. Also, based on future requests, decisions can be made on which requests should be served immediately and which should be served at a future time. The article provides a Markov decision process model to handle SDDP. The problem is solved using a heuristic solution approach based on sample planning. An extensive set of computational tests are used to demonstrate the strength of the solution methodology.
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