Fleet sizing and routing of healthcare automated guided vehicles

This paper proposes techniques to improve the efficiency of transportation activities within hospitals. Transportation is a major activity in hospitals which requires management efforts to improve its efficiency and increase the quality of patient services. One of the most powerful ways of achieving more efficiency of transportation systems in hospitals is via the labor-saving technology of logistics processes using automated guided vehicles (AGVs). In this paper, we study the fleet sizing and routing problem with synchronization for AGVs with dynamic demands (FSRPS-AGV) in the context of a real-life application. The goal is to simultaneously optimize the number and types of carts and AGVs needed to perform all daily requests in a hospital while optimizing AGVs’ routes and respecting time constraints. Different requests require different types of carts, which are transported by the AGVs. Each request is composed of several tasks consisting of moving material from a pickup point to a delivery point. Operation synchronization among the tasks of the same request (task 1 must be performed before task 2, possibly by different AGVs but using the same cart) and movement synchronization with respect to AGVs and carts (an AGV may drop off a cart, and later another AGV picks up the cart to continue serving the same or another request) are major challenges of the addressed problem. In this paper, we describe, model, and solve the FSRPS-AGV. We introduce a mathematical formulation and propose a powerful matheuristic based on a fast and efficient dynamic reoptimization of the routes upon the arrival of new requests. We compare the performance of our matheuristic under different scenarios, including against the solutions obtained by an oracle, showing that it can handle dynamism of demand very well and achieve near-optimal solutions. We assess our methods using small and large instances generated based on real data from an industrial partner. We demonstrate that significant performance improvements and important savings can be achieved with a small degree of flexibility in timing constraints and less conservative speed estimations (while taking into account safety concerns). Finally, we provide managerial insights with respect to the number of AGVs and carts that should be acquired by our industrial partner.