Objective Of Minimizing Makespan Research Articles

A two-stage-priority-rule-based algorithm for robust resource-constrained project scheduling

Traditionally, the resource-constrained project scheduling problem (RCPSP) is modeled as a static and deterministic problem and is solved with the objective of makespan minimization. However, many uncertainties, such as unpredictable increases in processing times caused by rework or supplier delays, random transportation and/or setup, may render the proposed solution obsolete. In this paper, we present a two-stage algorithm for robust resource-constrained project scheduling. The first stage of the algorithm solves the RCPSP for minimizing the makespan only using a priority-rule-based heuristic, namely an enhanced multi-pass random-biased serial schedule generation scheme. The problem is then similarly solved for maximizing the schedule robustness while considering the makespan obtained in the first stage as an acceptance threshold. Selection of the best schedule in this phase is based on one out of 12 alternative robustness predictive indicators formulated for the maximization purpose. Extensive simulation testing of the generated schedules provides strong evidence of the benefits of considering robustness of the schedules in addition to their makespans. For illustration purposes, for 10 problems from the well-known standard set J30, both robust and non-robust schedules are executed with a 10% duration increase that is applied to the same randomly picked 20% of the project activities. Over 1000 iterations per instance problem, the robust schedules display a shorter makespan in 55% of the times while the non-robust schedules are shown to be the best performing ones in only 6% of the times.

A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem

This paper considers the multimode resource-constrained project-scheduling problem (MRCPSP) with a minimum-makespan objective. An exact branch and cut algorithm is presented based on the integer linear programming (ILP) formulation of the problem. In the preprocessing stage, lower bounds on the distance between each pair of precedence-constrained activities are derived. These bounds are used to reduce the number of variables in the model and to generate cuts that tighten the linear programming relaxation. The solution process is accelerated by an adaptive branching scheme in conjunction with a bound-tightening scheme that is called iteratively after branching. To find good feasible solutions in the early stages of the computations, a high-level neighborhood search strategy known as local branching is included. Here, a neighborhood of a feasible solution is defined by the linear inequalities in the ILP model and is searched first. As implemented, the full algorithm is exact rather than heuristic in nature. Numerical results are reported for 20- and 30-activity benchmark problems. These are the largest instances available and are generally viewed to be notoriously difficult. Up until now, there were no confirmed optimal solutions for any of the 552 30-activity instances. We were able to find several better solutions and to show that at least 506 are optimal.

Open block scheduling in optical communication networks

In this paper the process of data transmission in star coupled optical communication networks is modelled as a shop-type scheduling problem, where channels (wavelengths) are treated as machines. We formulate an Open Block problem with the minimum makespan objective ( OB | | C max ) in which a relation of a new type between the operations of each job is introduced: any two operations of a job have identical processing times and may be processed either simultaneously (in a common block) or, alternatively, at disjoint time intervals. We show that the problem is polynomially solvable for 4 machines, NP-hard for 6 machines and strongly NP-hard for a variable number of machines. For the case of a variable number of machines we present a polynomial time 2 -approximation algorithm and prove that there is no polynomial time ρ -approximation algorithm with ρ < 11 / 10 , unless P=NP. For the case when the number of machines is fixed, we show that the problem admits a linear time PTAS. In addition, we show that the two-machine problem with release dates is NP-hard in the strong sense.

STEADY-STATE SCHEDULING ON HETEROGENEOUS CLUSTERS

This paper considers steady-state scheduling techniques for heterogeneous systems, such as clusters and grids. The use of steady-state scheduling is advocated to solve a variety of important problems, which would be too difficult to tackle with the objective of makespan minimization. Several examples are given, namely master-slave tasking, mixed task and data parallelism, and pipelined macro-communications (scatter, broadcast, multicast). For each example, both the advantages and the limitations of the approach are discussed.

Geometrical heuristics for multiprocessor flowshop scheduling with uniform machines at each stage

We consider the multi-stage multiprocessor flowshop scheduling problem with uniform machines at each stage and the minimum makespan objective. Using a vector summation technique, three polynomial-time heuristics are developed with absolute worst-case performance guarantees. As a direct corollary, in the special case of the ordinary flowshop problem we come to the best approximation algorithms (both in absolute performance guarantee and in running time) known for this problem. Copyright © 2002 John Wiley & Sons, Ltd.

A branch and bound based heuristic for multi-product resource constrained scheduling problem in FMS environment

This paper addresses an inter-dependent multiple-product resource-constrained scheduling problem with the objective of makespan minimization in a flexible manufacturing system with resource flexibility. Both consumable and non-consumable resources are considered along with their alternative types and constrained utilization rates. A 0–1 integer linear programming formulation is presented for the problem. The complexity of the problem is observed to be at increase with the availability of alternate resources for product operations. A branch and bound based heuristic is proposed as a solution methodology. A numerical example is presented to illustrate the problem and the effectiveness of the heuristic.

Heuristics for the flow line problem with setup costs

This paper presents two new heuristics for the flowshop scheduling problem with sequence-dependent setup times (SDSTs) and makespan minimization objective. The first is an extension of a procedure that has been very successful for the general flowshop scheduling problem. The other is a greedy randomized adaptive search procedure (GRASP) which is a technique that has achieved good results on a variety of combinatorial optimization problems. Both heuristics are compared to a previously proposed algorithm based on the traveling salesman problem (TSP). In addition, local search procedures are developed and adapted to each of the heuristics. A two-phase lower bounding scheme is presented as well. The first phase finds a lower bound based on the assignment relaxation for the asymmetric TSP. In phase two, attempts are made to improve the bound by inserting idle time. All procedures are compared for two different classes of randomly generated instances. In the first case where setup times are an order of magnitude smaller than the processing times, the new approaches prove superior to the TSP-based heuristic; for the case where both processing and setup times are identically distributed, the TSP-based heuristic outperforms the proposed procedures.

The One-Machine Problem with Delayed Precedence Constraints and its Use in Job Shop Scheduling

We study the one machine scheduling problem with release and delivery times and the minimum makespan objective, in the presence of constraints that for certain pairs of jobs require a delay between the completion of the first job and the start of the second (delayed precedence constraints). This problem arises naturally in the context of the Shifting Bottleneck Procedure for the general job shop scheduling problem, as a relaxation of the latter, tighter than the standard one-machine relaxation. The paper first highlights the difference between the two relaxations through some relevant complexity results. Then it introduces a modified Longest Tail Heuristic whose analysis identifies those situations that permit efficient branching. As a result, an optimization algorithm is developed whose performance is comparable to that of the best algorithms for the standard one-machine problem. Embedding this algorithm into a modified version of the Shifting Bottleneck Procedure that uses the tighter one-machine relaxation discussed here results in a considerable overall improvement in performance on all classes of job shop scheduling problems.

A composite heuristic for the identical parallel machine scheduling problem with minimum makespan objective

This paper describes a new heuristic algorithm for the problem of scheduling n independent jobs on m identical parallel machines in order to minimize the makespan. The algorithm produces near-optimal solutions in short computation times. It outperforms alternative heuristics on a series of test problems.

New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling

In this paper search heuristics are developed for generic sequencing problems with emphasis on job shop scheduling. The proposed methods integrate problem specific heuristics common to Operations Research and local search approaches from Artificial Intelligence in order to obtain desirable properties from both. The applicability of local search to a wide range of problems, and the incorporation of problem-specific information are both properties of the proposed algorithms. Two methods are proposed, both of which are based on novel definitions of solution spaces and of neighborhoods in these spaces. Applications of the proposed methodology are developed for job shop scheduling problems, and can be easily applied with any scheduling objective. To demonstrate effectiveness, the method is tested on the job shop scheduling problem with the minimum makespan objective. Encouraging results are obtained.