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In a recently published article in EJOR, Christofides et al. (CAT) present a depth-first search, branch-and-bound solution procedure for the multiple-resource constrained, single project scheduling problem. While there are many important... more
In a recently published article in EJOR, Christofides et al. (CAT) present a depth-first search, branch-and-bound solution procedure for the multiple-resource constrained, single project scheduling problem. While there are many important contributions in this paper, we show by ...
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We describe an integer programming algorithm for determining scheduled start and finish times for the activities of a project subject to resource limitations during each period of the schedule duration. The objective is to maximize the... more
We describe an integer programming algorithm for determining scheduled start and finish times for the activities of a project subject to resource limitations during each period of the schedule duration. The objective is to maximize the net present value of the project to the firm. A depth-first branch and bound solution procedure searches over the feasible set of finish or completion times for each of the activities of the project. Fathoming criteria based upon the concept of a network cut originally developed to solve the duration minimization version of this problem are extended in this paper to solve the net present value problem. These fathoming decision rules prevent many potentially inferior solutions from being explicitly evaluated. Computational experience reported demonstrates the efficacy of the approach.
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Research Interests:
In service organizations, heterogeneity in workforce skills can lead to variation in end-product/service quality. The multi-mode, resource-constrained, project scheduling problem (MRCPSP), which assumes similar skills among resources in a... more
In service organizations, heterogeneity in workforce skills can lead to variation in end-product/service quality. The multi-mode, resource-constrained, project scheduling problem (MRCPSP), which assumes similar skills among resources in a given resource pool, accounts for differences in quality levels of individuals by assigning different activity durations depending on the skill level used. This approach is often inadequate to model the problem type investigated here. Using typical projects from the customer training division of a large telecommunications company (which motivated this research), a labor assignment problem using a successive work–time concept is formulated and solved using integer programming optimization procedures. The setting represents a multiple-project environment where projects are separate and independent, but require the same renewable resource mix for their completion. The paper demonstrates how the output of the model can be used to identify bottlenecks (...
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In this brief note, we comment upon a statement made by E. M. Dar-El on the “computational impracticality” of a precedence matrix, enumeration method for balancing assembly lines,and show through an examination of several randomly... more
In this brief note, we comment upon a statement made by E. M. Dar-El on the “computational impracticality” of a precedence matrix, enumeration method for balancing assembly lines,and show through an examination of several randomly generated, large problems, that the technique involved may indeed be quite effective in balancing assembly lines involving numerous individual work elements in a reasonable amount of computation time.
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In this paper we describe an integer programming algorithm for allocating limited resources to competing activities (jobs, tasks, etc.) of a project such that the completion time of the project is minimal among all possible completion... more
In this paper we describe an integer programming algorithm for allocating limited resources to competing activities (jobs, tasks, etc.) of a project such that the completion time of the project is minimal among all possible completion times. Typical of such problems is the minimization of the completion time of projects of the PERT/CPM variety where limits on resource availability force the postponement of selected activities during project performance. Also included in this class of problems for which our procedure is applicable is the assignment of jobs to machines such that the elapsed time for completing all jobs (makespan) is a minimum over all possible job-machine assignments. The procedure developed consists of a systematic evaluation (enumeration) of all possible job finish times for each task in the project. To limit the number of task assignments which have to be explicitly evaluated, an artifice called a network cut is developed which removes from consideration the evalua...
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Research Interests:
In this paper, we describe an integer programming algorithm for assigning tasks on an assembly line to work stations in such a way that the number of work stations is minimal for the rate of production desired. The procedure insures that... more
In this paper, we describe an integer programming algorithm for assigning tasks on an assembly line to work stations in such a way that the number of work stations is minimal for the rate of production desired. The procedure insures that no task is assigned to a work station before all tasks which technologically must be performed before it have been assigned (precedence restrictions are not violated), and that the total time required at each work station performing the tasks assigned to it does not exceed the time available (cycle time restrictions are not violated). The procedure is based on a systematic evaluation (enumeration) of all possible task assignments to work stations. Significant portions of the enumeration process are performed implicitly, however, by utilizing tests described in the paper which are based on the specific structure of the line balancing problem. An artifice termed a network cut is also developed which eliminates from explicit consideration the assignmen...
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For over three decades, researchers have sought effective solution procedures for PERT/CPM types of scheduling problems under conditions of limited resource availability. This paper presents a procedure for this problem which takes... more
For over three decades, researchers have sought effective solution procedures for PERT/CPM types of scheduling problems under conditions of limited resource availability. This paper presents a procedure for this problem which takes advantage of the emerging technology provided by multiple parallel processors to find and verify an optimal schedule for a project under conditions of multiple resource constraints. In our approach, multiple solutions trees are searched simultaneously in the quest for a minimum duration schedule. Global upper and lower bound information in common memory is shared among processors, enabling one or several processors to prune potentially significant portions of its search tree based upon bounds discovered by a processor using a different search tree. Computational experience is reported both for problems in which resources are available in constant amounts per period, as well as the much more difficult problem in which the resources available are allowed to...
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... 1. Introduction The application of project planning and other related network techniques to cost control has lagged far behind applications of these techniques to resource leveling and minimizing project duration under resource... more
... 1. Introduction The application of project planning and other related network techniques to cost control has lagged far behind applications of these techniques to resource leveling and minimizing project duration under resource constraints. ...
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Page 1. MANAGEMENT SCIENCE Vol. 20, No. 6, February, 1974 Printed in USA A HORIZON-VARYING, ZERO-ONE APPROACH TO PROJECT SCHEDULING* JAMES H. PATTERSONt AND WALTER D. HUBER? Bounding ...
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Page 1. MANAGEMENT SCIENCE Vol. 30, No. 1, January 1984 Printed in USA AN INTEGER PROGRAMMING ALGORITHM WITH NETWORK CUTS FOR SOLVING THE ASSEMBLY LINE BALANCING PROBLEM* F. BRIAN ...
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... 1909/84/3007/0854$01.25 Copyright ?U 1984, The Institute of Management Sciences ... subsets, and the very logic of the Stinson procedure in advancing the "clock" to ... Three optimization approaches for... more
... 1909/84/3007/0854$01.25 Copyright ?U 1984, The Institute of Management Sciences ... subsets, and the very logic of the Stinson procedure in advancing the "clock" to ... Three optimization approaches for solving the single project, multiple-constrained resource, project scheduling ...
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Research Interests:
This research examines a heuristic, rule-based approach for setting due dates in a multiproject, multijob, or assembly shop. Due date estimation is a challenging problem because the operating environment is capacitated, involves the... more
This research examines a heuristic, rule-based approach for setting due dates in a multiproject, multijob, or assembly shop. Due date estimation is a challenging problem because the operating environment is capacitated, involves the allocation of multiple resources, and allows for the preemption of resources from one project or job to another. The dynamic, continuous arrival of new jobs or orders frequently results in the preemption of resources through the application of managerially determined priority policies. These preemption policies have a significant impact on the ultimate completion time of a job or a project.A three-factor, full-factorial computer simulation experiment is used to assess the relative effectiveness of combinations of four due date setting heuristics, five resource assignment heuristics, and three resource preemption heuristics. Recommendations are made for the selection of due date and resource assignment heuristic combinations under the three preemption pol...
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Page 1. Scheduling a Project Under Multiple Resource Constraints: A Zero-One Programming Approach JAMES H. PATTERSON The Pennsylvania State University University Park, PA 16802 GLENN W. ROTH Carnegie-Mellon Umversity Pittsburgh, PA 1521 3... more
Page 1. Scheduling a Project Under Multiple Resource Constraints: A Zero-One Programming Approach JAMES H. PATTERSON The Pennsylvania State University University Park, PA 16802 GLENN W. ROTH Carnegie-Mellon Umversity Pittsburgh, PA 1521 3 ...
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Page 1. MANAGEMENT SCIENCE Vol. 21, No. 8, April, 1975 Printed in USA A COMPARISON OF HEURISTIC AND OPTIMUM SOLUTIONS IN RESOURCE-CONSTRAINED PROJECT SCHEDULING* EDWARD W. DAVISt AND JAMES H. PATTERSON? ...
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Two heuristic assembly line balancing procedures (the precedence matrix, enumeration method of Hoffman [Hoffman, Thomas R. 1963. Assembly line balancing with a precedence matrix. Management Sci. 9 (4, July).] and the biased sampling... more
Two heuristic assembly line balancing procedures (the precedence matrix, enumeration method of Hoffman [Hoffman, Thomas R. 1963. Assembly line balancing with a precedence matrix. Management Sci. 9 (4, July).] and the biased sampling procedure of Arcus [Arcus, Alpert L. 1966. COMSOAL: A computer method for sequencing operations for assembly lines. E. S. Buffa, ed. Readings in Production and Operations Management.