Resource Constrained Project Scheduling

7 Key excerpts on "Resource Constrained Project Scheduling"

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  Production Scheduling

  • Pierre Lopez, François Roubellat, Pierre Lopez, François Roubellat(Authors)
  • 2013(Publication Date)
  • Wiley-ISTE

    (Publisher)

  Finally, a natural hybrid flow shop extension consists of considering that an operation may require several types of machine for its execution, and for each machine type, a certain number of machines. If we consider that machines are no longer organized in stages, then we obtain a multi-resource (each operation requires more than one type of resource) cumulative (each operation may require more than one resource unit per resource type) problem. In addition, if precedence constraints between operations are not chains (job constraints), but given by a graph of precedence, then we obtain a problem called “Resource Constrained Project Scheduling”.

  9.3. RCPSP: presentation and state of the art

  The Resource Constrained Project Scheduling Problem (RCPSP) is widely studied in other works [BRU 99, DEM 02, WEG 05, ART 08]. It consists of scheduling a given number of tasks over one or more limited capacity resources. Each task is defined by a processing time, consumption of each resource, and a series of tasks called predecessors, i.e. a task cannot start before the end of all its predecessors. The goal is then to find feasible schedules, i.e. task start times which satisfy resource constraints as well as precedence constraints, and that optimize given criteria, such as the project completion time for example. Many works have shown that this problem can be used to solve real life applications, and several extensions have been proposed. See [BRU 99, OZD 95, KOL 97, DEM 02, WEG 05, ART 08] for a description of solving methods which consider variations of the RCPSP.

  Many heuristic methods have been proposed for solving the RCPSP: priority rule-based methods [KLE 00], neighborhood and large neighborhood search [PIN 94, BOU 03, DEB 06, FLE 04, GOD 05, KOC 03, PAL 04, VAL 03], population-based method [MER 02, VAL 04], activity-insertion-based methods [ART 00, ART 03], etc. Experimental evaluation of some of these methods has been recently presented [KOL 06].

  Authors have also proposed efficient lower bounds [MING 98, BRU 98a, BRU 00, CAR 03, CAR 07, DAM 05, DEM 05].

  In this chapter we present the traditional form of the problem (section 9.3.1 ), along with the main exact resolution methods (section 9.3.2 ).

  9.3.1. A simple model including shop problems

  The RCPSP generalizes traditional scheduling problems such as job shop or flow shop. This time, a task may have a certain number of predecessors and/or successors. However, the graph associated with precedence constraints between tasks should not have a directed cycle in order for the problem to accept a solution. In addition, tasks are no longer executed on a machine, but require one or more cumulative resources. This problem is characterized by:

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  Discrete Optimization

  The State of the Art

  • E. Boros, P.L. Hammer(Authors)
  • 2003(Publication Date)
  • JAI Press

    (Publisher)

  Section 7 contains conclusions and gives an overview on implementations of solution procedures for scheduling problems in which constraint propagation techniques are applied. 2. Scheduling models The resource-constrained project scheduling problem (RCPSP) is one of the basic scheduling problems. In Section 2.1 we introduce this problem and some of its gen-eralizations. Machine scheduling problems which may be considered as special cases are introduced in Section 2.2. 2.1. The RCPSP and generalizations The resource-constrained project scheduling problem (RCPSP) may be formulated as follows. Given are η activities i= are r (renewable) resources k — l,...,r. A constant amount of R k units of resource k is available at any time. Activity / must be processed for /?,- time units. During this time period a constant amount of r ik units of resource k is occupied. Furthermore, precedence constraints are defined between activities. These are given by relations i —• y, where i —• j means that activity j cannot start before activity / is completed. The objective is to determine starting times 5/ for the activities / = in such a way that • at each time / the total resource demand is less than or equal to the resource availability for each resource type, (2.1) • the given precedence constraints are fulfilled, and (2.2) P. Brueker I Discrete Applied Mathematics 123 (2002) 227-256 229 Ri = 5 R 2 = 7 Pi ; 5 6 9 4 R , -I 1 2 2 2 R ,-2 5 2 4 3 * 1 2 3 4 Fig. 1. Project with 4 activities and 2 resources. • the makespan C m ax = max =1 Q is minimized, where C/:=5/ + /?/ is assumed to be the completion time of activity /. The fact that an activity which starts at time 5/ finishes at time £,· + pi implies that activities are not preempted. We may relax this condition by allowing preemp-tion (activity splitting). In this case the processing of any activity may be interrupted and resumed at a later date. It will be stated explicitly if we consider models with preemptions.

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  Project Management in Practice, International Adaptation

  • Jack R. Meredith, Scott M. Shafer, Samuel J. Mantel, Jr., Margaret M. Sutton(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  Just as projects may compete for resources, different activities of the same project may compete. Two or more concurrent activities might require the same personnel, or equipment, or even workspace. One activity will be given priority, and the other(s) must wait. In order to manage resources in such a way as to optimize the use of a limited supply, trade- offs must be made. The interaction of project scheduling and resource scheduling is clear, but we will examine several different solutions to the allocation problem. Those include the critical path method (CPM), Goldratt’s “critical chain” (1997), and many different priority rules for allocating scarce resources. The primary cause of concern is resource scarcity. If some resources (includ- ing time) were not scarce, the resource-allocation problem would be concerned solely with profit maximization—a relatively easy problem. In Chapter 5 we evaluated project durations solely in terms of time. A project was either on time or not. Now we must also consider when and for what purposes scarce people, equipment, material, and facilities are used. The PM’s performance is judged by the skill with which the trade- offs of time, resources, and scope are managed, so the PM must make constant use of cost/ benefit analysis. There are countless questions to be answered. “If we come in late on this project, we face a $1,000 per day penalty. How much project slack do we need and what resources at what costs are required to get it?” “If I hire Cheatham Engineering Associates as design consul- tants, can I improve project performance by 3 percent without extending the project’s due date?” “Adding project slack and hiring a consultant require monetary resources that could be used for other things. Are these the best uses for the dollars?” Trade-Offs

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  Managing Aviation Projects from Concept to Completion

  • Triant G. Flouris, Dennis Lock(Authors)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  15Principles of Resource Scheduling

  Resource scheduling, otherwise known as resource allocation or resource leveling, is a process that follows on from the initial planning calculations made with critical path network analysis (described in the previous two chapters). When the initial network scheduling has been completed successfully the project manager will know:

  • all the project tasks that need to be scheduled and progressed; • the estimated duration of each task and, where appropriate, the optimum level of resources to be employed on the task (which usually means how many people of each relevant skill); • the earliest possible times when each task could be expected to start and finish; • the latest permissible times when each task can be allowed to start and finish if the project is not to be delayed; • the amount of total float possessed by each task.

  Now comes the question of blending the project organization’s resources to the plan. This usually means considering people of different qualifications and skills, and timing their tasks so that the demand for each type of resource is kept as level as possible. The aim must be to avoid alternating overloads and idle periods that would result in inefficient working. But the project must still be completed on time if that is possible with the resources available. A perfect solution is seldom possible because when one resource is scheduled it can throw out the best timetable for activities using other resources. Attempts to reach a near perfect solution covering all resources are known as resource optimization. Broadly speaking, the greater the number of project tasks, the more likely it will be that a smooth schedule can be produced.

  When several projects are active at the same time in an organization, clearly all of them will have to be put into one resource scheduling pot, so that one project is not scheduled well at the expense of all the others. Fortunately that aspect of resource scheduling, which will be described later in these chapters, is just as easy to accomplish as single project scheduling, provided good software is available and is used with commonsense.

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  Project Management in Practice

  • Jack R. Meredith, Scott M. Shafer, Samuel J. Mantel, Jr., Margaret M. Sutton(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  CHAPTER 6 189 Allocating Resources to the Project I n this chapter we consider the problem of allocating physical and human resources to projects.* The physical and human resources are granted to and used by the proj-ect in order to meet the project’s objectives. The amount of resources that can be allo-cated, of course, depends on the timing of the allocation as well as on the total supply of resources available for allocation. Mainly, resource allocation concerns how we allocate specific, limited resources to specific activities (or projects) when there are competing demands for the same limited resources. Projects compete with each other for the same resources in two different ways. First, consider a resource that is limited but is not consumed when used, the services of a specific technical specialist, for instance. The problem here is which project gets to use the resource first and which must wait. Second, consider a resource that is limited and is consumed when used, a specific chemical reagent for instance. In this case, the second project may have to wait until more of the reagent can be purchased and deliv-ered. In both cases, the project that must wait may suffer a schedule delay that makes it late. Just as projects may compete for resources, different activities of the same project may compete. Two or more concurrent activities might require the same personnel, or equipment, or even workspace. One activity will be given priority, and the other(s) must wait. In order to manage resources in such a way as to optimize the use of a limited supply, trade-offs must be made. The interaction of project scheduling and resource scheduling is clear, but we will examine several different solutions to the allocation problem. Those include the critical path method (CPM), Goldratt’s “critical chain” (1997), and many different priority rules for allocating scarce resources.

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  Construction Management

  • Daniel W. Halpin, Bolivar A. Senior, Gunnar Lucko(Authors)
  • 2017(Publication Date)
  • Wiley

    (Publisher)

  10 152 chapter Resource-Related and Advanced Linear Scheduling Techniques 10.1 Resource Scheduling The term resources in construction planning and scheduling can refer to the “triplet” of materials, labor (i.e., workers), or equipment, or even crews, which are combinations of equipment with their operators. However, in the context of analyzing and optimizing resources, it typically does not refer to materials, which are consumed in the process of building and are either permanent— forming part of the final structure—or on a temporary basis supporting it (e.g., formwork and falsework). Rather, it refers to the latter two productive resources, primarily to labor. The labor resource typically has a limited availability in the local marketplace in which a project is built, and may be subject to additional constraints such as nonworking periods (e.g., approved vaca- tion, unavailability due to working on another project, etc.). It is therefore necessary to carefully consider resources when developing a realistic schedule. Methods are available for creating such resource-loaded schedules. Two different approaches, resource allocation and resource leveling, may be used depending on whether the goal of the deci- sion maker is to adhere to a given availability or improve the workflow. Their basic differences lie in which project duration value is assumed to be held fixed and which one is allowed to vary. 10.2 Resource Allocation Resource allocation begins with a known availability over time. It asks the question “How long will the project have to be, given this resource availability?” Consider Figure 10.1, which shows a schedule that is being developed for the dashed availability “ceiling” of first six, then four laborers of a particular type and skill level. Each activity can be treated like a bar from a bar chart that must be fitted underneath the availability ceiling. Activities are added in the sequence that is known from the network schedule.

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  Handbook of Military Industrial Engineering

  • Adedeji B. Badiru, Marlin U. Thomas, Adedeji B. Badiru, Marlin U. Thomas(Authors)
  • 2009(Publication Date)
  • CRC Press

    (Publisher)

  The provide more realistic handling of project scheduling beyond the conventional PERT/CPM network analysis. The conventional CPM and PERT approaches assume unlimited resource availability in project network analysis. In realistic projects, both the time and resource requirements of activities should be consid-ered in developing network schedules. Projects are subject to three major constraints: time limitations, resource constraints, and performance requirements. Since these constraints are difficult to satisfy simultaneously, trade-offs must be made. The smaller the resource base, the longer the project schedule. The CRD and RS charts are simple extensions of very familiar management tools. They are simple to use, and they convey resource information quickly. They can be used to complement existing resource management tools. CRD can be modified for specific resource planning, scheduling, and control needs in both small and large projects. References 1. Ashok Kumar, V.K. and L.S. Ganesh. 1998. Use of petri nets for resource allocation in projects. IEEE Transactions on Engineering Management , 45(1), 49–56. 2. Badiru, A.B. 1992. Critical resource diagram: A new tool for resource management. Industrial Engineering, 24(10), 58–59, 65. 3. Badiru, A.B. 1993. Activity resource assignment using critical resource diagramming. Project Management Journal, 24(3), 15–21. 4. Badiru, A.B. 1995. Incorporating learning curve effects into critical resource diagramming. Project Management Journal, 26(2), 38–45. 5. Campbell, G.M. 1999. Cross-utilization of workers whose capabilities differ . Management Science, 45(5), 722–32. 6. Carraway, R.L. and R.L. Schmidt. 1991. An improved discrete dynamic programming algorithm for allocating resources among interdependent projects. Management Science, 37(9), 1195–200. 7. Cui, W., J. Qin, X. Cao, C. Yue, and Z. Yin. 2006. Critical resources identification in constant resource constrained projects.

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