Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop

This paper describes a complex scheduling problem taken from a hospital diagnostic testing center that schedules hundreds of patients in an open shop environment consisting of multiple facilities and multiple processors. This scheduling problem, known as the multiprocessor open shop (MPOS) problem, is strongly NP-hard with few published results. Realizing that in many MPOS environments processing times are stage-dependent, not both job and stage-dependent, this paper examines a new class of problems for the MPOS—proportionate ones. This paper exploits the structural nature of the proportionate MPOS and defines new terms. Despite the enormous complexity of the MPOS problem, this work demonstrates that polynomial time algorithms exist for two special cases. Since other applications of this problem exist in service and manufacturing environments, solving the proportionate MPOS problem is not only significant in the theory of optimization, but also in many real-world applications.     

Local search algorithms for the multiprocessor flow shop scheduling problem

The multiprocessor flow shop scheduling problem is a generalization of the ordinary flow shop scheduling problem. The problem consists of both assigning operations to machines and scheduling the operations assigned to the same machine. We review the literature on local search methods for flow shop and job shop scheduling and adapt them to the multiprocessor flow shop scheduling problem. Other local search approaches we consider are variable-depth search and simulated annealing. We show that tabu search and variable-depth search with a neighborhood originated by Nowicki and Smutnicki outperform the other algorithms.     

A projective algorithm for preemptive open shop scheduling with two multiprocessor groups

We study a multiprocessor extension of the preemptive open shop scheduling problem, where the set of processors is partitioned into processor groups. We show that the makespan minimization problem is polynomially solvable for two multiprocessor groups even if preemptions are restricted to integral times.     

Routing and scheduling in a flexible job shop by tabu search

A hierarchical algorithm for the flexible job shop scheduling problem is described, based on the tabu search metaheuristic. Hierarchical strategies have been proposed in the literature for complex scheduling problems, and the tabu search metaheuristic, being able to cope with different memory levels, provides a natural background for the development of a hierarchical algorithm. For the case considered, a two level approach has been devised, based on the decomposition in a routing and a job shop scheduling subproblem, which is obtained by assigning each operation of each job to one among the equivalent machines. Both problems are tackled by tabu search. Coordination issues between the two hierarchical levels are considered. Unlike other hierarchical schemes, which are based on a one-way information flow, the one proposed here is based on a two-way information flow. This characteristic, together with the flexibility of local search strategies like tabu search, allows to adapt the same basic algorithm to different objective functions. Preliminary computational experience is reported.     

A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem

This paper deals with a general job shop scheduling problem with multiple constraints, coming from printing and boarding industry. The objective is the minimization of two criteria, the makespan and the maximum lateness, and we are interested in finding an approximation of the Pareto frontier. We propose a fast and elitist genetic algorithm based on NSGA-II for solving the problem. The initial population of this algorithm is either randomly generated or partially generated by using a tabu search algorithm, that minimizes a linear combination of the two criteria. Both the genetic and the tabu search algorithms are tested on benchmark instances from flexible job shop literature and computational results show the interest of both methods to obtain an efficient and effective resolution method.     

A modified tabu search algorithm for cost-based job shop problem

In this paper, a cost-based job shop problem (JIT-JSP) is proposed to model the multi-order processing procedure in a just-in-time (JIT) environment. The objective of JIT-JSP is to minimize three costs: work-in-process holding cost of half-finished orders, inventory holding cost of finished orders and backorder cost of unfulfilled orders. A modified tabu search (MTS) method is developed to improve the schedule quality by searching the neighbourhood of a feasible schedule iteratively. The MTS method is comprised of three components that help to ensure a more effective searching procedure: neighbourhood structure, memory structure and filter structure. Computational results show that the MTS method significantly improves the initial schedule generated by an arbitrarily selected dispatching rule.     

A tabu search experience in production scheduling

During the last four years, tabu search has been shown to be a remarkably effective method in solving difficult combinatorial optimization problems. Nowhere has this success been more marked than in the timely and very important area of production scheduling. In this paper, we review some of the research that has contributed to that success. We also give a synthesis of the various tabu search mechanisms that have been employed, giving special attention to advances that have led to major improvements. In the final section of the paper, we suggest directions for future research.     

A tabu search algorithm for scheduling pharmaceutical packaging operations

This paper addresses a practical scheduling problem arising in the packaging department of a pharmaceutical industrial plant. The problem is modeled as a multi-purpose machine scheduling problem with setup and removal times, release and due dates and additional constraints related to the scarce availability of tools and human operators. The objective functions are minimization of makespan and maximum tardiness in lexicographic order. Representing a solution with a directed graph allows us to devise an effective tabu search algorithm to solve the problem. Computational experiments, carried on real and randomly generated instances, show the effectiveness of this approach.     

A tabu search heuristic for ship routing and scheduling

The purpose of this paper is to solve a planning problem faced by many shipping companies dealing with the transport of bulk products. These shipping companies are committed to carrying some contract cargoes and will try to derive additional revenue from optional spot cargoes. An efficient tabu search algorithm has been developed to ensure quick decision support for the planners. The solutions generated by the tabu search heuristic are compared with those produced by a previously published multi-start local search heuristic. Computational results show that the tabu search heuristic yields optimal or near-optimal solutions to real-life instances within reasonable time. For large and tigthly constrained cases, the tabu search heuristic provides much better solutions than the multi-start local search heuristic. A version of the tabu search heuristic will be integrated as an improved solver in a prototype decision support system used by several shipping companies.     

A tabu search algorithm for solving economic lot scheduling problem

The economic lot scheduling problem has driven considerable amount of research. The problem is NP-hard and recent research is focused on finding heuristic solutions rather than searching for optimal solutions. This paper introduces a heuristic method using a tabu search algorithm to solve the economic lot scheduling problem. Diversification and intensification schemes are employed to improve the efficiency of the proposed Tabu search algorithm. Experimental design is conducted to determine the best operating parameters for the Tabu search. Results show that the tabu search algorithm proposed in this paper outperforms two well known benchmark algorithms.     

A local search method for permutation flow shop scheduling

It is well known that a local search method, a widely used approach for solving the permutation flow shop scheduling problem, can easily be trapped at a local optimum. In this paper, we propose two escape-from-trap procedures to move away from local optima. Computational experiments carried out on a standard set of instances show that this heuristic algorithm generally outperforms an effective approximation algorithm.     

Polynomial time approximation schemes for general multiprocessor job shop scheduling

We study preemptive and non-preemptive versions of the general multiprocessor job shop scheduling problem: Given a set of n tasks each consisting of at most μ ordered operations that can be processed on different (possibly all) subsets of m machines with different processing times, compute a schedule (preemptive or non-preemptive, depending on the model) with minimum makespan where operations belonging to the same task have to be scheduled according to the specified order. We propose algorithms for both preemptive and non-preemptive variants of this problem that compute approximate solutions of any positive ε accuracy and run in O(n) time for any fixed values of m, μ, and ε. These results include (as special cases) many recent developments on polynomial time approximation schemes for scheduling jobs on unrelated machines, multiprocessor tasks, and classical open, flow and job shops.     

A comparison of local search methods for flow shop scheduling

Local search techniques are widely used to obtain approximate solutions to a variety of combinatorial optimization problems. Two important categories of local search methods are neighbourhood search and genetic algorithms. Commonly used neighbourhood search methods include descent, threshold accepting, simulated annealing and tabu search. In this paper, we present a computational study that compares these four neighbourhood search methods, a genetic algorithm, and a hybrid method in which descent is incorporated into the genetic algorithm. The performance of these six local search methods is evaluated on the problem of scheduling jobs in a permutation flow shop to minimize the total weighted completion time. Based on the results of extensive computational tests, simulated annealing is found to generate better quality solutions than the other neighborhood search methods. However, the results also indicate that the hybrid genetic descent algorithm is superior to simulated annealing.     

Routing open shop and flow shop scheduling problems

We consider a generalization of the classical open shop and flow shop scheduling problems where the jobs are located at the vertices of an undirected graph and the machines, initially located at the same vertex, have to travel along the graph to process the jobs. The objective is to minimize the makespan. In the tour-version the makespan means the time by which each machine has processed all jobs and returned to the initial location. While in the path-version the makespan represents the maximum completion time of the jobs. We present improved approximation algorithms for various cases of the open shop problem on a general graph, and the tour-version of the two-machine flow shop problem on a tree. Also, we prove that both versions of the latter problem are NP-hard, which answers an open question posed in the literature.     

A 3/2-Approximation for the proportionate two-machine flow shop scheduling with minimum delays

We study the two-machine flow shop problem with minimum delays. The problem is known to be strongly NP-hard even in the case of unit processing times and to be approximable within a factor of 2 of the length of an optimal schedule in the general case. The question whether there exists a polynomial-time algorithm with a better approximation ratio has been posed by several researchers but still remains open. In this paper, we improve the above bound to 3/2 for the special case of the problem when both operations of each job have equal processing times (this case of flow shop is known as the proportionate flow shop). Our analysis of the algorithm relies upon a nontrivial generalization of the lower bound established by W. Yu for the case of unit processing times.     

A tabu search tutorial based on a real-world scheduling problem

We apply a tabu search method to a scheduling problem of a company producing cables for cars: the task is to determine on what machines and in which order the cable jobs should be produced in order to save production costs. First, the problem is modeled as a combinatorial optimization problem. We then employ a tabu search algorithm as an approach to solve the specific problem of the company, adapt various intensification as well as diversification strategies within the algorithm, and demonstrate how these different implementations improve the results. Moreover, we show how the computational cost in each iteration of the algorithm can be reduced drastically from O(n ³) (naive implementation) to O(n) (smart implementation) by exploiting the specific structure of the problem (n refers to the number of cable orders).     

Evaluating the performance of tabu search procedures for flow shop sequencing

We address the problem of minimising makespan in a flow shop by using tabu search procedures. By combining different neighbourhood structures, neighbourhood examinations, and stopping conditions we obtain alternative tabu search procedures. Starting from a common initial solution we evaluate the relative performance of such procedures considering both the solution quality and computational effort.     

A new tabu search heuristic for the open vehicle routing problem

In this paper, another version of the vehicle routing problem (VRP)—the open vehicle routing problem (OVRP) is studied, in which the vehicles are not required to return to the depot, but if they do, it must be by revisiting the customers assigned to them in the reverse order. By exploiting the special structure of this type of problem, we present a new tabu search heuristic for finding the routes that minimize two objectives while satisfying three constraints. The computational results are provided and compared with two other methods in the literature.     

A tabu search algorithm for the multi-trip vehicle routing and scheduling problem

This paper describes a novel tabu search heuristic for the multi-trip vehicle routing and scheduling problem (MTVRSP). The method was developed to tackle real distribution problems, taking into account most of the constraints that appear in practice. In the MTVRSP, besides the constraints that are common to the basic vehicle routing problem, the following ones are present: during each day a vehicle can make more than one trip; the customers impose delivery time windows; the vehicles have different capacities considered in terms of both volume and weight; the access to some customers is restricted to some vehicles; the drivers' schedules must respect the maximum legal driving time per day and the legal time breaks; the unloading times are considered.     

Job shop scheduling with beam search

Beam Search is a heuristic method for solving optimization problems. It is an adaptation of the branch and bound method in which only some nodes are evaluated in the search tree. At any level, only the promising nodes are kept for further branching and remaining nodes are pruned off permanently. In this paper, we develop a beam search based scheduling algorithm for the job shop problem. Both the makespan and mean tardiness are used as the performance measures. The proposed algorithm is also compared with other well known search methods and dispatching rules for a wide variety of problems. The results indicate that the beam search technique is a very competitive and promising tool which deserves further research in the scheduling literature.