الگوریتم شاخه و قیمت برای برنامه زمانبندی چند دوره ای دوره ای

This paper considers the multi-period service scheduling problem with an aperiodic service policy. In this problem, a set of customers who periodically require service over a finite time horizon is given. To satisfy the service demands, a set of operators is given, each with a fixed capacity in terms of the number of customers that can be served per period. With an aperiodic policy, customers may be served before the period were the service would be due. Two criteria are jointly considered in this problem: the total number of operators, and the total number of ahead-of-time periods. The task is to determine the service periods for each customer in such a way that the service requests of the customers are fulfilled and both criteria are minimized. A new integer programming formulation is proposed, which outperforms an existing formulation. Since the computational effort required to obtain solutions considerably increases with the size of the instances, we also present a reformulation suitable for column generation, which is then integrated within a branch-and-price algorithm. Computational experiments highlight the efficiency of this algorithm for the larger instances.