Project Scheduling and Cost Minimization with Multiple Availability Constrained Resources under Stochastic Conditions

Project Scheduling and Cost Minimization with Multiple Availability Constrained Resources under Stochastic Conditions

Rui Moutinho (Department of Production and Systems Engineering, University of Minho, Guimarães, Portugal) and Anabela Tereso (Department of Production and Systems Engineering, University of Minho, Guimarães, Portugal)
DOI: 10.4018/IJHCITP.2015100103
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The authors propose a mathematical model to minimize the project total cost where there are multiple resources constrained by maximum availability. They assume the resources as renewable and the activities can use any subset of resources requiring any quantity from a limited real interval. The stochastic nature is inferred by means of a stochastic work content defined per resource within an activity and following a known distribution and the total cost is the sum of the resource allocation cost with the tardiness cost or earliness bonus in case the project finishes after or before the due date, respectively. The model was computationally implemented relying upon an interchange of two global optimization metaheuristics – the electromagnetism-like mechanism and the evolutionary strategies. Two experiments were conducted testing the implementation to projects with single and multiple resources, and with or without maximum availability constraints. The set of collected results shows good behavior in general and provide a tool to further assist project manager decision making in the planning phase.
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Literature Review

The study of the Resource-Constrained Project Scheduling Problem (RCPSP) deals with project activity scheduling regarding both precedence relationships and resource constraints. The RCPSP is a vast subject but usually the objective is to minimize the project total cost. Furthermore, when the activity durations are sensitive to the allocated resource amount, then the minimum total execution time is also part of the objective. The literature is rich with several methods solving the many aspects of the RCPSP. Next, we will summarize the most relevant to our research. We refer to Demeulemeester and Herroelen (2002) for a comprehensive overview of this subject.

The scheduling of activities is the process where the starting times for each one of them is determined while respecting any constraints, primarily the activity precedences and the resource constraints. The more commonly precedence type is the finish-to-start (FS) relationship: an activity IJHCITP.2015100103.m01 precedes IJHCITP.2015100103.m02, denoted by IJHCITP.2015100103.m03, when IJHCITP.2015100103.m04 must only start after IJHCITP.2015100103.m05 is finished. The direct application of these relationships among project activities translates the scheduling process as the determination of the earliest possible time when each activity can start. The simplest method is the serial scheduling oriented by a priority list. Priority lists are any ordering of activities respecting the precedencies. Often, different lists result in different schedules due to the effect of resource constraints. Also, each schedule would hold specific total time. Thus, it is crucial to search for the best schedule.

In the classical literature, we find the branch & bound methods (Sprecher, Hartmann, & Drexl, 1994, 1997). These aim to avoid the examination of all the possible schedules by narrowing the enumeration (of cases) through well-defined lower and upper bounds determined from the properties of the problem. Together with dominance rules, the method crawls the tree of enumeration deciding, at each branching point, the best path as returned by the application of the dominance rules. The branch & bound methods are most suitable to the determinist RCPSP and provide the optimal solution.

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