You manage a fleet of K identical vehicles stationed at a depot. This depot is a node in a complete directed graph whose

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You Manage A Fleet Of K Identical Vehicles Stationed At A Depot This Depot Is A Node In A Complete Directed Graph Whose 1 (67.77 KiB) Viewed 29 times

You manage a fleet of K identical vehicles stationed at a depot. This depot is a node in a complete directed graph whose other nodes are your customers. You wish to use your vehicles to fulfill some or all of a collection of orders submitted by your customers. Each order has a corresponding nonnegative reward (in dollars) on fulfillment, the warehouse is well-stocked, and any vehicle is capable of fulfilling any single order. (Notably, there is no reward for filling an order more than once.) In addition, the vehicles have a limited amount of storage- each may hold only & deliveries. Once a vehicle returns to the depot, it will not be able to go out again, so each vehicle may fulfill at most borders (and in total you may only fulfill at most b orders). There is a cost (in dollars) associated with traveling along each arc; this cost is incurred for every time a vehicle uses an arc. For given nodes i and j, note that (i, j) and (.) are distinct arcs with different traveling costs. Unlike the arc costs, which costs more per each vehicle that uses the arc, the reward per customer node can be awarded at most once. Note that while there is no reward for visiting the depot, all vehicles must return to the depot at the end of their journey. In addition to the information above, you are given the following: • G=(N, A) is the complete graph with node set N and are set A; • de N is the depot node; Gj:= cost per vehicle of traveling along arc (i, j) € A; and r := reward for visiting node i N, which may only be recieved once per node. There is one pair of customers m,n e N\ {d) which have the following requirements: (1) they both must be fulfilled, (2) they must be fulfilled by the same vehicle, and (3) n is fulfilled immediately after customer in in the driver's route. (Here, "immediately" refers only to the sequence of the deliveries for the single relevant vehicle; time should not be a factor in the model.) You are asked to maximize the total reward collected by the fleet of delivery vehicles while minimizing the total traveling cost incurred. Formulate a network-based, biobjective integer linear program (BOIP) to solve this routing problem. Figure 1: A feasible routing is shown for K 5 vehicles. Note that only the arcs belonging to the solution are shown; however, all nodes are completed as a complete graph.