Operational Variable Job Scheduling With Eligibility Constraints: a Randomized Constraint-Graph Approach

Abstract

In this study, we consider the problem of Operational Variable Job Scheduling, also referred to as parallel machine scheduling with time windows. The problem is a more general version of the Fixed Job Scheduling problem, involving a Lime window for each job larger than its processing time. The objective is to find the optimal subset of the jobs that can be processed. An interesting application area ties in Optimal Berth Allocation, which involves the assignment of vessels arriving at the port to appropriate berths within their time windows, while maximizing the total profit from the served vessels. Eligibility constraints are also taken into consideration. We develop an integer programming model for the problem. We show that the problem is NP-hard, and develop a constraint-graph-based construction algorithm for generating near-optimal solutions. We use genetic algorithm and other improvement algorithms to enhance the solution. Computational experimentation reveals that our algorithm generates very high quality solutions in very small computation times.