A Tabu Search Algorithm for the Multi-period Inspector Scheduling Problem

This paper introduces a multi-period inspector scheduling problem (MPISP), which is a new variant of the multi-trip vehicle routing problem with time windows (VRPTW). In the MPISP, each inspector is scheduled to perform a route in a given multi-period planning horizon. At the end of each period, each inspector is not required to return to the depot but has to stay at one of the vertices for recuperation. If the remaining time of the current period is insufficient for an inspector to travel from his/her current vertex $A$ to a certain vertex B, he/she can choose either waiting at vertex A until the start of the next period or traveling to a vertex C that is closer to vertex B. Therefore, the shortest transit time between any vertex pair is affected by the length of the period and the departure time. We first describe an approach of computing the shortest transit time between any pair of vertices with an arbitrary departure time. To solve the MPISP, we then propose several local search operators adapted from classical operators for the VRPTW and integrate them into a tabu search framework. In addition, we present a constrained knapsack model that is able to produce an upper bound for the problem. Finally, we evaluate the effectiveness of our algorithm with extensive experiments based on a set of test instances. Our computational results indicate that our approach generates high-quality solutions.

An Enhanced Branch-and-bound Algorithm for the Talent Scheduling Problem

The talent scheduling problem is a simplified version of the real-world film shooting problem, which aims to determine a shooting sequence so as to minimize the total cost of the actors involved. In this article, we first formulate the problem as an integer linear programming model. Next, we devise a branch-and-bound algorithm to solve the problem. The branch-and-bound algorithm is enhanced by several accelerating techniques, including preprocessing, dominance rules and caching search states. Extensive experiments over two sets of benchmark instances suggest that our algorithm is superior to the current best exact algorithm. Finally, the impacts of different parameter settings are disclosed by some additional experiments.