On project scheduling with irregular starting time costs

Möhring, Rolf H.; Schulz, Andreas S.; Stork, Frederik; Uetz, Marc

doi:10.1016/s0167-6377(01)00064-5

Cited by 44 publications

(25 citation statements)

References 27 publications

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“…u n 1 . This ordering condition is also shared by the by-variable formulations [6][7][8][9][10][11][12], which explains why they lead to balanced branch-and-bound trees. Moreover, it is explicitly imposed in other more complicated ad-hoc formulations for piecewise-linear functions [20][21][22][23] and probabilistic constraints [24,25].…”

Section: Incremental Formulationsmentioning

confidence: 99%

“…In this setting, we can use an alternative set of binary variables that instead indicate whether the activity is executed in period i or before. These new variables are sometimes called by-variables and lead to balanced branch-and-bound trees that can significantly reduce solution times [6][7][8][9][10][11][12]. The third approach proposes to model n alternatives with a number of binary variables that is logarithmic in n [5, [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Incremental and encoding formulations for Mixed Integer Programming

Yıldız

Vielma

2013

Operations Research Letters

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The standard way to represent a choice between n alternatives in Mixed Integer Programming is through n binary variables that add up to one. Unfortunately, this approach commonly leads to unbalanced branch-and-bound trees and diminished solver performance. In this paper, we present an encoding formulation framework that encompasses and expands existing approaches to mitigate this behavior. Through this framework, we generalize the incremental formulation for piecewise linear functions to any finite union of polyhedra with identical recession cones.

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Section: Incremental Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Incremental and encoding formulations for Mixed Integer Programming

Yıldız

Vielma

2013

Operations Research Letters

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“…This problem, or special cases thereof, has been addressed frequently in the literature. [50] give an overview of these results. As it turns out, the project scheduling problem with starttime dependent costs can be efficiently solved as a minimum cut problem in a directed graph.…”

Section: 23mentioning

confidence: 94%

Planning and scheduling in the process industry

Kallrath¹

2002

OR Spectrum

311

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Since there has been tremendous progress in planning and scheduling in the process industry during the last 20 years, it might be worthwhile to give an overview of the current state-of-the-art of planning and scheduling problems in the chemical process industry. This is the purpose of the current review which has the following structure: we start with some conceptional thoughts and some comments on special features of planning and scheduling problems in the process industry. In Section 2 the focus is on planning problems while in Section 3 different types of scheduling problems are discussed. Section 4 presents some solution approaches especially those applied to a benchmark problem which has received considerable interest during the last years. Section 5 allows a short view into the future of planning and scheduling. In the appendix we describe the WestenbergerKallrath problem which has already been used extensively as a benchmark problem for planning and scheduling in the process industry.

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“…Maniezzo and Mingozzi [49] and Möhring et al [50,51] considered costs for each activity dependent on the activity's start time and their objective is to minimize the sum of these costs. Achuthan and Hardjawidjaja [52] minimized total project costs which consist of earliness and tardiness costs with regard to due dates as well as costs related to the durations of the activities.…”

Section: Financial Indicatorsmentioning

confidence: 99%

An Entropy-Based Upper Bound Methodology for Robust Predictive Multi-Mode RCPSP Schedules

Chen¹,

Liang

Padilla

2014

Entropy

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Abstract:Projects are an important part of our activities and regardless of their magnitude, scheduling is at the very core of every project. In an ideal world makespan minimization, which is the most commonly sought objective, would give us an advantage. However, every time we execute a project we have to deal with uncertainty; part of it coming from known sources and part remaining unknown until it affects us. For this reason, it is much more practical to focus on making our schedules robust, capable of handling uncertainty, and even to determine a range in which the project could be completed. In this paper we focus on an approach to determine such a range for the Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP), a widely researched, NP-complete problem, but without adding any subjective considerations to its estimation. We do this by using a concept well known in the domain of thermodynamics, entropy and a three-stage approach. First we use Artificial Bee Colony (ABC)-an effective and powerful meta-heuristic-to determine a schedule with minimized makespan which serves as a lower bound. The second stage defines buffer times and creates an upper bound makespan using an entropy function, with the advantage over other methods that it only considers elements which are inherent to the schedule itself and does not introduce any subjectivity to the buffer time generation. In the last stage, we use the ABC algorithm with an objective function that seeks to maximize robustness while staying within the makespan boundaries defined OPEN ACCESSEntropy 2014, 16 5033 previously and in some cases even below the lower boundary. We evaluate our approach with two different benchmarks sets: when using the PSPLIB for the MRCPSP benchmark set, the computational results indicate that it is possible to generate robust schedules which generally result in an increase of less than 10% of the best known solutions while increasing the robustness in at least 20% for practically every benchmark set. And, in an attempt to solve larger instances with 50 or 100 activities, we also used the MRCPSP/max benchmark sets, where the increase of the makespan is approximately 35% with respect to the best known solutions at the same time as with a 20% increase in robustness.

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On project scheduling with irregular starting time costs

Cited by 44 publications

References 27 publications

Incremental and encoding formulations for Mixed Integer Programming

Incremental and encoding formulations for Mixed Integer Programming

Planning and scheduling in the process industry

An Entropy-Based Upper Bound Methodology for Robust Predictive Multi-Mode RCPSP Schedules

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