The multimode resource constrained multiproject scheduling problem: Alternative formulations

Abstract

in Wiley InterScience (www.interscience.wiley.com).Tactical management of development pipelines is concerned with the allocation of resources and scheduling of tasks. Though these decisions have to be made in the presence of uncertainty, to make the problem solvable it is customary to use deterministic MILP formulations of the multi-mode RCMPSP that are reevaluated after important uncertainties are realized. In spite of the major simplifications attained by down-playing the stochastic nature of the problem, the curse of dimensionality limits the exact solution of the formulations to very small systems. The curse is mainly caused by 3 factors: the indexing of the task execution modes the indexing of time periods, and the discrete character of the resources. Three models that attempt to overcome these limitations are proposed and compared. Results show that despite the theoretical advantages of the strategies used, the alternative formulations are limited to problems in the same range of applicability of the conventional multi-mode formulation.

MIP formulations for an application of project scheduling in human resource management

“…The results of the comparative study in Naber and Kolisch (2014) indicate that an MIP formulation based on Bianco and Caramia (2013) dominates all other DT formulations. In the study of Zapata et al (2008), alternative DT and CT formulations for the MRCPSP with multiple projects are compared. The authors conclude that the best MIP formulation depends on the specific characteristics of each problem instance.…”

Event Based Approaches for Solving Multi-mode Resource Constraints Project Scheduling Problem

“…The standard MRCPSP requires sequencing the project activities, so that the precedence constraints are met, the execution mode for each activity is determined, the resource constraints are met and the project duration is minimized. In spite of having several mathematical models for MRCPSP [2] and [13], the model from Talbot [14] is still being used as a basis for discrete time approach and hence is employed throughout this paper as the discrete time (DT) approach for comparing with our proposed models. In the MRCPSP model, a binary decision variable is defined to be 1 if activity starts at mode m at time instant , and 0 otherwise.…”

“…A variant of RCPSP is known as the Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and for it each activity can be performed using one out of a set of different resources (known as modes), with specific activity durations and resource requirements. MRCPSP provides the most comprehensive framework for realistically representing the flexibilities that decision makers have [2]. MRCPSPs have many applications within computer integrated manufacturing, planning in make-to-order production, as well as other production planning problems, such as flow shop and job shop scheduling problem.…”

“…For reducing the number of binary decision variables, in those models, we have considered continuous time or time-independent approaches that are known as 'Start/End Event based formulation (SEE) and 'On/Off Event based formulation (OOE)'. The proposed formulations are variants of that of Zapata et al [2], but with fewer variables. Thus, instead of the 3 binary variables for Zapata et al [2], it took 2 variables for SEE and binary variables for OEE, where m represents number of modes and n represents the number of activities.…”

“…The proposed formulations are variants of that of Zapata et al [2], but with fewer variables. Thus, instead of the 3 binary variables for Zapata et al [2], it took 2 variables for SEE and binary variables for OEE, where m represents number of modes and n represents the number of activities. It was conjectured from the earlier researchers that the solution time of integer programming can be bounded as an exponential function of the number of variables [12].…”