Multiple Machine Scheduling Research Articles

Multiple-Machine Scheduling with Learning Effects and Cooperative Games

Multiple-machine scheduling problems with position-based learning effects are studied in this paper. There is an initial schedule in this scheduling problem. The optimal schedule minimizes the sum of the weighted completion times; the difference between the initial total weighted completion time and the minimal total weighted completion time is the cost savings. A multiple-machine sequencing game is introduced to allocate the cost savings. The game is balanced if the normal processing times of jobs that are on the same machine are equal and an equal number of jobs are scheduled on each machine initially.

A coupling cutting stock-lot sizing problem in the paper industry

An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.

Detecting infeasibility and generating cuts for mixed integer programming using constraint programming

We study a hybrid MIP/CP solution approach in which CP is used for detecting infeasibilities and generating cuts within a branch-and-cut algorithm for MIP. Our framework applies to MIP problems augmented by monotone constraints that can be handled by CP. We illustrate our approach on a generic multiple machine scheduling problem, and present a number of computational experiments.

Multiple-machine scheduling with earliness, tardiness and completion time penalties

We consider the problem of scheduling n jobs on m parallel and identical machines. The goal is to find an optimal permutation of the jobs and an optimal due date which jointly minimize an objective function consisting of earliness tardiness and completion time penalties. We show that the problem is NP-hard and present a polynomially solvable case. Furthermore a heuristic is developed and computationally demonstrated to be efficient in obtaining near-optimal solutions. Scope and purpose This study deals with the problem of scheduling a number of jobs on parallel machines. We assume that companies are mainly interested in two objectives, namely achieving small deviations from a common due date and short flowtimes. Therefore earliness tardiness and completion time penalties for the jobs are introduced. We are able to show that the problem is intractable and consequently develop an efficient heuristic to obtain near-optimal solutions.

Facility-Wide Planning and Scheduling of Printed Wiring Board Assembly

In the last decade, the U.S. electronics industry has experienced a 10% annual growth rate in the assembly of printed wiring boards (PWBs). For many companies, this activity represents the most profitable component of their business with revenues in the billions for the industry as a whole. The basic functions associated with PWB assembly include inventory management, materials handling, production scheduling, and quality control, all of which are subject to a host of system-wide constraints. For the Texas Instruments facility in Austin, Texas, planning and scheduling is further complicated by the need to deal with over 10,000 different components and up to 400 different board types, each with their individual routing and bill of materials. This paper describes a decision support system known as Insites designed to assist Texas Instruments in the day-to-day assembly operations of their PWB facilities. The emphasis is on the heuristic techniques used to solve the underlying multiple machine scheduling problem and the efforts undertaken to validate and deploy the system. The identified benefits, coupled with the acceptance of Insites by both shop floor personnel and management, led the way to full system integration in early 1992.

Minimization of Total Absolute Flow Time Deviation in Single and Multiple Machine Scheduling

In this note, single machine scheduling and minimizing absolute flow time deviation (TAFD) are considered. The relationship between this problem and the mean absolute deviation of job completion times about a common due date (MAD) is discussed. Based on the MAD problem optimal solutions of the TAFD problem are given. Furthermore, the generalization of the problem to the multiple machine case is discussed and an efficient algorithm for generating many optimal solutions of the problem, in the multi-machine case, is given.

Minimization of Total Absolute Flow Time Deviation in Single and Multiple Machine Scheduling

Minimization of Total Absolute Flow Time Deviation in Single and Multiple Machine Scheduling

Minimization of Total Absolute Flow Time Deviation in Single and Multiple Machine Scheduling

In this note, single machine scheduling and minimizing absolute flow time deviation (TAFD) are considered. The relationship between this problem and the mean absolute deviation of job completion times about a common due date (MAD) is discussed. Based on the MAD problem optimal solutions of the TAFD problem are given. Furthermore, the generalization of the problem to the multiple machine case is discussed and an efficient algorithm for generating many optimal solutions of the problem, in the multi-machine case, is given.

Genetic Algorithms and Random Keys for Sequencing and Optimization

In this paper we present a general genetic algorithm to address a wide variety of sequencing and optimization problems including multiple machine scheduling, resource allocation, and the quadratic assignment problem. When addressing such problems, genetic algorithms typically have difficulty maintaining feasibility from parent to offspring. This is overcome with a robust representation technique called random keys. Computational results are shown for multiple machine scheduling, resource allocation, and quadratic assignment problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Bounds for naive multiple machine scheduling with release times and deadlines

We examine an on-line polynomial time heuristic for the NP-complete problem of scheduling m identical machines to minimize the maximum lateness of jobs with release times and due dates. The main result is that for any set of jobs, the difference between the lateness given by the heuristic and the minimum possible lateness is bounded by [ (2m − 1) m ]P max , where P max is the largest processing time of any of the jobs. The conclusion is that for many applications, optimization is not necessary. We also prove that when all jobs have a common processing time P, the difference between the heuristic and the minimum lateness is bounded by P. This gives a fast estimate of the minimum possible lateness, and is useful in accelerating the practical performance of algorithms for the exact solution.