Variable neighborhood search for minimum cost berth allocation

The berth allocation problem is to allocate space along the quayside to incoming ships at a container terminal in order to minimize some objective function. We consider minimization of total costs for waiting and handling as well as earliness or tardiness of completion, for all ships. We assume ships can arrive at any given time, i.e., before or after the berths become available. The resulting problem, which subsumes several previous ones, is expressed as a linear mixed 0–1 program. As it turns out to be too time-consuming for exact solution of instances of realistic size, a Variable Neighborhood Search (VNS) heuristic is proposed, and compared with Multi-Start (MS), a Genetic Search algorithm (GA) and a Memetic Search algorithm (MA). VNS provides optimal solutions for all instances solved to optimality in a previous paper of the first two authors and outperforms MS, MA and GA on large instances.     

Single-machine scheduling with waiting-time-dependent due dates

We consider a single-machine scheduling problem in which due dates are linear functions of the job waiting-times and the objective is to minimize the maximum lateness. An optimal sequence is constructed by implementing an index-based priority rule for a fixed value of the due date normalizing constant k. We determine in polynomial time all the k value ranges so that the optimal sequence remains the same within each range. The optimal due dates are computed as linear functions of the global optimal value of k. The overall procedure is illustrated in a numerical example.     

Pareto optima for total weighted completion time and maximum lateness on a single machine

We consider the single-machine bicriterion scheduling problem of enumerating the Pareto-optimal sequences with respect to the total weighted completion time and the maximum lateness objectives. We show that the master sequence concept originally introduced for 1|r_j|∑w_jU_j by Dauzère-Pérès and Sevaux is also applicable to our problem and a large number of other sequencing problems. Our unified development is based on exploiting common order-theoretic structures present in all these problems. We also show that the master sequence implies the existence of global dominance orders for these scheduling problems. These dominance results were incorporated into a new branch and bound algorithm, which was able to enumerate all the Pareto optima for over 90% of the 1440 randomly generated problems with up to n=50 jobs. The identification of each Pareto optimum implicitly requires the optimal solution of a strongly NP-hard problem. The instances solved had hundreds of these Pareto solutions and to the best of our knowledge, this is the first algorithm capable of completely enumerating all Pareto sequences within reasonable time and space for a scheduling problem with such a large number of Pareto optima.     

2-approximation algorithm for minmax absolute maximum lateness scheduling-location problem

The problem of minmax absolute scheduling-location is investigated on trees with interval edge length. Jobs are located at vertices and must travel to the machine. The goal is to find a machine location and simultaneously a schedule to minimize the maximum lateness in the worst-case. We derive a result that could reduce the robust versions to deterministic problems. An efficient algorithm is developed to solve special cases. A 2-approximation algorithm is proposed for the robust problem on the underlying tree.