A genetic algorithm to solve the resource-sharing and scheduling problem (RSSP)

Rabinowitz et al. (1991) modeled the resource-sharing and scheduling problem (RSSP) as a monolithic continuous-time mixed integer linear programming (MILP) formulation. The RSSP has the following characteristics. Each production cell may produce several products using several resources. Each product requires a set of operations with precedence relationships between them. Each operation can be performed using alternative modes which define the subset of resources needed. An operation may share different resources simultaneously. The problem is to select a single mode for each operation and, accordingly, to allocate and schedule the resources in order to minimize the makespan time. Samaddar et al. (1999) presented a customized branch and bound (B&B) algorithm to solve the RSSP. The B&B algorithm fathoms only feasible schedules and finds all optimal solutions. We present an efficient genetic algorithm (GA) that solves the RSSP for large-sized problems. We compared the performance and runtime of our GA versus Samaddar's B&B algorithm on a set of problem instances. The GA reached optimality in 33.75% of the test runs, and was not farther than 13.84% from optimality in 99% of the cases. Also, from the smallest to the largest problem instances, the runtime grows 2000 fold with the B&B algorithm, and only 10 fold with the GA.