A survey of variants and extensions of the resource-constrained project scheduling problem <s> Objectives Based on Nonrenewable Resources <s> The resource-constraint project scheduling problem is modeled as a zero-one integer programming model. The model considers many important characteristics of project scheduling including activity preemption, renewable and non-renewable resources, time-resource tradeoffs, and multiple objectives. Solution algorithms are developed for three single objective problems (time minimization, cost minimization, and resource leveling) and for the preemptive goal programming model that includes time, cost and resource leveling objectives. <s> BIB001 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Objectives Based on Nonrenewable Resources <s> We describe a new exact procedure for the discrete time/cost trade-off problem in deterministic activity-on-the-arc networks of the CPM type, where the duration of each activity is a discrete, nonincreasing function of the amount of a single resource (money) committed to it. The objective is to construct the complete and efficient time/cost profile over the set of feasible project durations. The procedure uses a horizon-varying approach based on the iterative optimal solution of the problem of minimising the sum of the resource use over all activities subject to the activity precedence constraints and a project deadline. This optimal solution is derived using a branch-and-bound procedure which computes lower bounds by making convex piecewise linear underestimations of the discrete time/cost trade-off curves of the activities to be used as input for an adapted version of the Fulkerson labelling algorithm for the linear time/cost trade-off problem. Branching involves the selection of an activity in order to partition its set of execution modes into two subsets which are used to derive improved convex piecewise linear underestimations. The procedure has been programmed in Visual C ++ under Windows NT and has been validated using a factorial experiment on a large set of randomly generated problem instances. <s> BIB002 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Objectives Based on Nonrenewable Resources <s> Abstract Project scheduling is concerned with single-item or small batch production where scarce resources have to be allocated to dependent activities over time. Applications can be found in diverse industries such as construction engineering, software development, etc. Also, project scheduling is increasingly important for make-to-order companies where the capacities have been cut down in order to meet lean management concepts. Likewise, project scheduling is very attractive for researchers, because the models in this area are rich and, hence, difficult to solve. For instance, the resource-constrained project scheduling problem contains the job shop scheduling problem as a special case. So far, no classification scheme exists which is compatible with what is commonly accepted in machine scheduling. Also, a variety of symbols are used by project scheduling researchers in order to denote one and the same subject. Hence, there is a gap between machine scheduling on the one hand and project scheduling on the other with respect to both, viz. a common notation and a classification scheme. As a matter of fact, in project scheduling, an ever growing number of papers is going to be published and it becomes more and more difficult for the scientific community to keep track of what is really new and relevant. One purpose of our paper is to close this gap. That is, we provide a classification scheme, i.e. a description of the resource environment, the activity characteristics, and the objective function, respectively, which is compatible with machine scheduling and which allows to classify the most important models dealt with so far. Also, we propose a unifying notation. The second purpose of this paper is to review some of the recent developments. More specifically, we review exact and heuristic algorithms for the single-mode and the multi-mode case, for the time–cost tradeoff problem, for problems with minimum and maximum time lags, for problems with other objectives than makespan minimization and, last but not least, for problems with stochastic activity durations. <s> BIB003 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Objectives Based on Nonrenewable Resources <s> Although single objective metaheuristics are widely spread and applied in many combinatorial optimisation problems, only very recently have multiobjective metaheuristics (MOMH) been designed and used in practice. They aim at obtaining good approximations of the set of nondominated solutions of a problem, in an efficient way. In this work, we have applied multiobjective versions of simulated annealing and taboo search to the resource constrained project scheduling problem (RCPSP), in order to minimise the makespan, the “weighted” lateness of activities and the violation of resource constraints. Computational experience performed on randomly generated instances shows that this general approach is flexible, effective and able to deal with multiple objectives and with variations in the problem structure. <s> BIB004 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Objectives Based on Nonrenewable Resources <s> In project management, the project duration can often be compressed by accelerating some of its activities at an additional expense. This is the so-called time–cost tradeoff problem which has been extensively studied in the past. However, the discrete version of the problem which is of great practical relevance, did not receive much attention so far. Given a set of modes (time–cost pairs) for each activity, the objective of the discrete time–cost tradeoff problem is to select a mode for each activity so that the total cost is minimized while meeting a given project deadline. ::: ::: The discrete time–cost tradeoff problem is a strongly -hard optimization problem for general activity networks. In terms of what current state-of-art algorithms can do, instances with (depending on the structure of the network and the number of processing alternatives per activity) no more than 20–50 activities can be solved to optimality in reasonable amount of time. Hence, heuristics must be employed to solve larger instances. To evaluate such heuristics, lower bounds are needed. This paper provides lower and upper bounds using column generation techniques based on “network decomposition”. Furthermore, a computational study is provided to demonstrate that the presented bounds are tight and that large and hard instances can be solved in short run-time. <s> BIB005 </s> A survey of variants and extensions of the resource-constrained project scheduling problem <s> Objectives Based on Nonrenewable Resources <s> Abstract Decisions concerning a project’s expedition, traditionally involved considerations regarding time and cost tradeoff. It was recently suggested that the quality of a project should also be taken into considerations. In this paper, we propose a meta-heuristic solution procedure for the discrete time, cost and quality tradeoff problem. This problem involves the scheduling of project activities in order to minimize the total cost of the project while maximizing the quality of the project and also meeting a given deadline. We apply a so called electromagnetic scatter search to solve this problem. In this process, we initially generate a population of feasible solutions. In so doing, we use frequency memory to well sample the feasible region. A number of these solutions are then selected and improved locally. The improved solutions are then combined to generate new set of solutions. The combination process utilizes attraction–repulsion mechanisms borrowed from the electromagnetism theory. The whole process is stopped when no significant improvement in the set of solutions are observed. The validity of the proposed solution procedure is demonstrated, and its applicability is tested on a randomly generated large and complex problem having 19,900 activities. <s> BIB006
The multi-mode RCPSP (see Section 2.4) requires that the resource capacities are not exceeded while the makespan is minimized. Analogously to the resource investment problem of Section 5.4, an alternative setting would be to impose a deadline on the project while minimizing the consumption of the nonrenewable resources. Such a nonrenewable resource-based objective has been considered by Akkan et al. BIB005 and Demeulemeester et al. BIB002 within the discrete time-cost tradeoff problem, where the only nonrenewable resource is interpreted as money. Similarly, Nudtasomboon and Randhawa BIB001 and Tareghian and Taheri BIB006 minimize the consumption of a nonrenewable resource which again represents money. Nudtasomboon and Randhawa BIB001 and Viana and de Sousa BIB004 suggest to minimize the consumed nonrenewable resource units that exceed the capacities. These objectives can be specified by γ = ∑ c k f (r k (S)) in the notation of Brucker et al. BIB003 , where f is a function of the consumption r k (S) of nonrenewable resource k in schedule S.