Mode-Based versus Activity-Based Search for a Nonredundant Resolution of the Multimode Resource-Constrained Project Scheduling Problem

[EN] This paper addresses an energy-based extension of the Multimode Resource-Constrained Project Scheduling Problem (MRCPSP) called MRCPSP-ENERGY. This extension considers the energy consumption as an additional resource that leads to different execution modes (and durations) of the activities. Consequently, different schedules can be obtained. The objective is to maximize the efficiency of the project, which takes into account the minimization of both makespan and energy consumption. This is a well-known NP-hard problem, such that the application of metaheuristic techniques is necessary to address real-size problems in a reasonable time. This paper shows that the Activity List representation, commonly used in metaheuristics, can lead to obtaining many redundant solutions, that is, solutions that have different representations but are in fact the same. This is a serious disadvantage for a search procedure. We propose a genetic algorithm(GA) for solving the MRCPSP-ENERGY, trying to avoid redundant solutions by focusing the search on the execution modes, by using the Mode List representation. The proposed GA is evaluated on different instances of the PSPLIB-ENERGY library and compared to the results obtained by both exact methods and approximate methods reported in the literature. This library is an extension of the well-known PSPLIB library, which contains MRCPSP-ENERGY test cases.This paper has been partially supported by the Spanish Research Projects TIN2013-46511-C2-1-P and TIN2016-80856-R.Morillo-Torres, D.; Barber, F.; Salido, MA. (2017). Mode-Based versus Activity-Based Search for a Nonredundant Resolution of the Multimode Resource-Constrained Project Scheduling Problem. Mathematical Problems in Engineering. 2017:1-15. https://doi.org/10.1155/2017/4627856S1152017Mouzon, G., Yildirim, M. B., & Twomey, J. (2007). Operational methods for minimization of energy consumption of manufacturing equipment. International Journal of Production Research, 45(18-19), 4247-4271. doi:10.1080/00207540701450013Hartmann, S., & Sprecher, A. (1996). A note on «hierarchical models for multi-project planning and scheduling». European Journal of Operational Research, 94(2), 377-383. doi:10.1016/0377-2217(95)00158-1Christofides, N., Alvarez-Valdes, R., & Tamarit, J. M. (1987). Project scheduling with resource constraints: A branch and bound approach. European Journal of Operational Research, 29(3), 262-273. doi:10.1016/0377-2217(87)90240-2Zhu, G., Bard, J. F., & Yu, G. (2006). A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem. INFORMS Journal on Computing, 18(3), 377-390. doi:10.1287/ijoc.1040.0121Kolisch, R., & Hartmann, S. (1999). Heuristic Algorithms for the Resource-Constrained Project Scheduling Problem: Classification and Computational Analysis. International Series in Operations Research & Management Science, 147-178. doi:10.1007/978-1-4615-5533-9_7Józefowska, J., Mika, M., Różycki, R., Waligóra, G., & Węglarz, J. (2001). Annals of Operations Research, 102(1/4), 137-155. doi:10.1023/a:1010954031930Bouleimen, K., & Lecocq, H. (2003). A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version. European Journal of Operational Research, 149(2), 268-281. doi:10.1016/s0377-2217(02)00761-0Alcaraz, J., Maroto, C., & Ruiz, R. (2003). Solving the Multi-Mode Resource-Constrained Project Scheduling Problem with genetic algorithms. Journal of the Operational Research Society, 54(6), 614-626. doi:10.1057/palgrave.jors.2601563Zhang, H., Tam, C. M., & Li, H. (2006). Multimode Project Scheduling Based on Particle Swarm Optimization. Computer-Aided Civil and Infrastructure Engineering, 21(2), 93-103. doi:10.1111/j.1467-8667.2005.00420.xJarboui, B., Damak, N., Siarry, P., & Rebai, A. (2008). A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems. Applied Mathematics and Computation, 195(1), 299-308. doi:10.1016/j.amc.2007.04.096Li, H., & Zhang, H. (2013). Ant colony optimization-based multi-mode scheduling under renewable and nonrenewable resource constraints. Automation in Construction, 35, 431-438. doi:10.1016/j.autcon.2013.05.030Lova, A., Tormos, P., Cervantes, M., & Barber, F. (2009). An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes. International Journal of Production Economics, 117(2), 302-316. doi:10.1016/j.ijpe.2008.11.002Peteghem, V. V., & Vanhoucke, M. (2010). A genetic algorithm for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problem. European Journal of Operational Research, 201(2), 409-418. doi:10.1016/j.ejor.2009.03.034Węglarz, J., Józefowska, J., Mika, M., & Waligóra, G. (2011). Project scheduling with finite or infinite number of activity processing modes – A survey. European Journal of Operational Research, 208(3), 177-205. doi:10.1016/j.ejor.2010.03.037Kolisch, R., & Hartmann, S. (2006). Experimental investigation of heuristics for resource-constrained project scheduling: An update. European Journal of Operational Research, 174(1), 23-37. doi:10.1016/j.ejor.2005.01.065Debels, D., De Reyck, B., Leus, R., & Vanhoucke, M. (2006). A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. European Journal of Operational Research, 169(2), 638-653. doi:10.1016/j.ejor.2004.08.020Paraskevopoulos, D. C., Tarantilis, C. D., & Ioannou, G. (2012). Solving project scheduling problems with resource constraints via an event list-based evolutionary algorithm. Expert Systems with Applications, 39(4), 3983-3994. doi:10.1016/j.eswa.2011.09.062Drexl, A. (1991). Scheduling of Project Networks by Job Assignment. Management Science, 37(12), 1590-1602. doi:10.1287/mnsc.37.12.1590BOCTOR, F. F. (1996). Resource-constrained project scheduling by simulated annealing. International Journal of Production Research, 34(8), 2335-2351. doi:10.1080/0020754960890502

Resource constrained shortest paths and extensions

In this thesis, we use integer programming techniques to solve the resource constrained shortest path problem (RCSPP) which seeks a minimum cost path between two nodes in a directed graph subject to a finite set of resource constraints. Although NP-hard, the RCSPP is extremely useful in practice and often appears as a subproblem in many decomposition schemes for difficult optimization problems. We begin with a study of the RCSPP polytope for the single resource case and obtain several new valid inequality classes. Separation routines are provided, along with a polynomial time algorithm for constructing an auxiliary conflict graph which can be used to separate well known valid inequalities for the node packing polytope. We establish some facet defining conditions when the underlying graph is acyclic and develop a polynomial time sequential lifting algorithm which can be used to strengthen one of the inequality classes. Next, we outline a branch-and-cut algorithm for the RCSPP. We present preprocessing techniques and branching schemes which lead to strengthened linear programming relaxations and balanced search trees, and the majority of the new inequality classes are generalized to consider multiple resources. We describe a primal heuristic scheme that uses fractional solutions, along with the current incumbent, to search for new feasible solutions throughout the branch-and-bound tree. A computational study is conducted to evaluate several implementation choices, and the results demonstrate that our algorithm outperforms the default branch-and-cut algorithm of a leading integer programming software package. Finally, we consider the dial-a-flight problem (DAFP), a new vehicle routing problem that arises in the context of on-demand air transportation and is concerned with the scheduling of a set of travel requests for a single day of operations. The DAFP can be formulated as an integer multicommodity network flow model consisting of several RCSPPs linked together by set partitioning constraints which guarantee that all travel requests are satisfied. Therefore, we extend our branch-and-cut algorithm for the RCSPP to solve the DAFP. Computational experiments with practical instances provided by the DayJet Corporation verify that the extended algorithm also outperforms the default branch-and-cut algorithm of a leading integer programming software package.Ph.D.Committee Co-Chair: George L. Nemhauser; Committee Co-Chair: Shabbir Ahmed; Committee Member: Martin W. P. Savelsbergh; Committee Member: R. Gary Parker; Committee Member: Zonghao G

Models and Solutions of Resource Allocation Problems based on Integer Linear and Nonlinear Programming

In this thesis we deal with two problems of resource allocation solved through a Mixed-Integer Linear Programming approach and a Mixed-Integer Nonlinear Chance Constraint Programming approach. In the first part we propose a framework to model general guillotine restrictions in two dimensional cutting problems formulated as Mixed-Integer Linear Programs (MILP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a state of-the-art MIP solver, can tackle instances of challenging size. Our objective is to propose a way of modeling general guillotine cuts via Mixed Integer Linear Programs (MILP), i.e., we do not limit the number of stages (restriction (ii)), nor impose the cuts to be restricted (restriction (iii)). We only ask the cuts to be guillotine ones (restriction (i)). We mainly concentrate our analysis on the Guillotine Two Dimensional Knapsack Problem (G2KP), for which a model, and an exact procedure able to significantly improve the computational performance, are given. In the second part we present a Branch-and-Cut algorithm for a class of Nonlinear Chance Constrained Mathematical Optimization Problems with a finite number of scenarios. This class corresponds to the problems that can be reformulated as Deterministic Convex Mixed-Integer Nonlinear Programming problems, but the size of the reformulation is large and quickly becomes impractical as the number of scenarios grows. We apply the Branch-and-Cut algorithm to the Mid-Term Hydro Scheduling Problem, for which we propose a chance-constrained formulation. A computational study using data from ten hydro plants in Greece shows that the proposed methodology solves instances orders of magnitude faster than applying a general-purpose solver for Convex Mixed-Integer Nonlinear Problems to the deterministic reformulation, and scales much better with the number of scenarios

A Parallel Branch and Bound Algorithm for the Resource Leveling Problem with Minimal Lags

[EN] The efficient use of resources is a key factor to minimize the cost while meeting time deadlines and quality requirements; this is especially important in construction projects where field operations take fluctuations of resources unproductive and costly. Resource Leveling Problems (RLP) aim to sequence the construction activities that maximize the resource consumption efficiency over time, minimizing the variability. Exact algorithms for the RLP have been proposed throughout the years to offer optimal solutions; however, these problems require a vast computational capability ( combinatorial explosion ) that makes them unpractical. Therefore, alternative heuristic and metaheuristic algorithms have been suggested in the literature to find local optimal solutions, using different libraries to benchmark optimal values; for example, the Project Scheduling Problem LIBrary for minimal lags is still open to be solved to optimality for RLP. To partially fill this gap, the authors propose a Parallel Branch and Bound algorithm for the RLP with minimal lags to solve the RLP with an acceptable computational effort. This way, this research contributes to the body of knowledge of construction project scheduling providing the optimums of 50 problems for the RLP with minimal lags for the first time, allowing future contributors to benchmark their heuristics meth-ods against exact results by obtaining the distance of their solution to the optimal values. Furthermore, for practitioners,the time required to solve this kind of problem is reasonable and practical, considering that unbalanced resources can risk the goals of the construction project.This research was supported by the FAPA program of the Universidad de Los Andes (Colombia). The authors would like to thank the research group of Construction Engineering and Management (INgeco), especially J. S. Rojas-Quintero, and the Department of Systems Engineering at the Universidad de Los Andes. The authors are also grateful to the anonymous reviewers for their valuable and constructive suggestions.Ponz Tienda, JL.; Salcedo-Bernal, A.; Pellicer Armiñana, E. (2017). A Parallel Branch and Bound Algorithm for the Resource Leveling Problem with Minimal Lags. COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING. 32:474-498. doi:10.1111/mice.12233S47449832Adeli, H. (2000). High-Performance Computing for Large-Scale Analysis, Optimization, and Control. Journal of Aerospace Engineering, 13(1), 1-10. doi:10.1061/(asce)0893-1321(2000)13:1(1)ADELI, H., & KAMAL, O. (2008). Parallel Structural Analysis Using Threads. Computer-Aided Civil and Infrastructure Engineering, 4(2), 133-147. doi:10.1111/j.1467-8667.1989.tb00015.xAdeli, H., & Kamal, O. (1992). Concurrent analysis of large structures—II. applications. Computers & Structures, 42(3), 425-432. doi:10.1016/0045-7949(92)90038-2Adeli, H., Kamat, M. P., Kulkarni, G., & Vanluchene, R. D. (1993). High‐Performance Computing in Structural Mechanics and Engineering. Journal of Aerospace Engineering, 6(3), 249-267. doi:10.1061/(asce)0893-1321(1993)6:3(249)Adeli, H., & Karim, A. (1997). Scheduling/Cost Optimization and Neural Dynamics Model for Construction. Journal of Construction Engineering and Management, 123(4), 450-458. doi:10.1061/(asce)0733-9364(1997)123:4(450)Adeli, H., & Kumar, S. (1995). Concurrent Structural Optimization on Massively Parallel Supercomputer. Journal of Structural Engineering, 121(11), 1588-1597. doi:10.1061/(asce)0733-9445(1995)121:11(1588)ADELI, H., & VISHNUBHOTLA, P. (2008). Parallel Processing. Computer-Aided Civil and Infrastructure Engineering, 2(3), 257-269. doi:10.1111/j.1467-8667.1987.tb00150.xAdeli, H., & Wu, M. (1998). Regularization Neural Network for Construction Cost Estimation. Journal of Construction Engineering and Management, 124(1), 18-24. doi:10.1061/(asce)0733-9364(1998)124:1(18)Alsayegh, H., & Hariga, M. (2012). Hybrid meta-heuristic methods for the multi-resource leveling problem with activity splitting. Automation in Construction, 27, 89-98. doi:10.1016/j.autcon.2012.04.017Anagnostopoulos, K., & Koulinas, G. (2012). Resource-Constrained Critical Path Scheduling by a GRASP-Based Hyperheuristic. Journal of Computing in Civil Engineering, 26(2), 204-213. doi:10.1061/(asce)cp.1943-5487.0000116Anagnostopoulos, K. P., & Koulinas, G. K. (2010). A simulated annealing hyperheuristic for construction resource levelling. Construction Management and Economics, 28(2), 163-175. doi:10.1080/01446190903369907Arditi, D., & Bentotage, S. N. (1996). System for Scheduling Highway Construction Projects. Computer-Aided Civil and Infrastructure Engineering, 11(2), 123-139. doi:10.1111/j.1467-8667.1996.tb00316.xBandelloni, M., Tucci, M., & Rinaldi, R. (1994). Optimal resource leveling using non-serial dyanamic programming. European Journal of Operational Research, 78(2), 162-177. doi:10.1016/0377-2217(94)90380-8Benjaoran, V., Tabyang, W., & Sooksil, N. (2015). Precedence relationship options for the resource levelling problem using a genetic algorithm. Construction Management and Economics, 33(9), 711-723. doi:10.1080/01446193.2015.1100317Bianco, L., Caramia, M., & Giordani, S. (2016). Resource levelling in project scheduling with generalized precedence relationships and variable execution intensities. OR Spectrum, 38(2), 405-425. doi:10.1007/s00291-016-0435-1Chakroun, I., & Melab, N. (2015). Towards a heterogeneous and adaptive parallel Branch-and-Bound algorithm. Journal of Computer and System Sciences, 81(1), 72-84. doi:10.1016/j.jcss.2014.06.012Christodoulou, S. E., Ellinas, G., & Michaelidou-Kamenou, A. (2010). Minimum Moment Method for Resource Leveling Using Entropy Maximization. Journal of Construction Engineering and Management, 136(5), 518-527. doi:10.1061/(asce)co.1943-7862.0000149Clausen, J., & Perregaard, M. (1999). Annals of Operations Research, 90, 1-17. doi:10.1023/a:1018952429396Coughlan, E. T., Lübbecke, M. E., & Schulz, J. (2010). A Branch-and-Price Algorithm for Multi-mode Resource Leveling. Lecture Notes in Computer Science, 226-238. doi:10.1007/978-3-642-13193-6_20Coughlan, E. T., Lübbecke, M. E., & Schulz, J. (2015). A branch-price-and-cut algorithm for multi-mode resource leveling. European Journal of Operational Research, 245(1), 70-80. doi:10.1016/j.ejor.2015.02.043Crainic, T. G., Le Cun, B., & Roucairol, C. (s. f.). Parallel Branch-and-Bound Algorithms. Parallel Combinatorial Optimization, 1-28. doi:10.1002/9780470053928.ch1Damci, A., Arditi, D., & Polat, G. (2013). Resource Leveling in Line-of-Balance Scheduling. Computer-Aided Civil and Infrastructure Engineering, 28(9), 679-692. doi:10.1111/mice.12038Damci, A., Arditi, D., & Polat, G. (2013). Multiresource Leveling in Line-of-Balance Scheduling. Journal of Construction Engineering and Management, 139(9), 1108-1116. doi:10.1061/(asce)co.1943-7862.0000716Damci, A., Arditi, D., & Polat, G. (2015). Impacts of different objective functions on resource leveling in Line-of-Balance scheduling. KSCE Journal of Civil Engineering, 20(1), 58-67. doi:10.1007/s12205-015-0578-7De Reyck, B., & Herroelen, W. (1996). On the use of the complexity index as a measure of complexity in activity networks. European Journal of Operational Research, 91(2), 347-366. doi:10.1016/0377-2217(94)00344-0Hossein Hashemi Doulabi, S., Seifi, A., & Shariat, S. Y. (2011). Efficient Hybrid Genetic Algorithm for Resource Leveling via Activity Splitting. Journal of Construction Engineering and Management, 137(2), 137-146. doi:10.1061/(asce)co.1943-7862.0000261Drexl, A., & Kimms, A. (2001). Optimization guided lower and upper bounds for the resource investment problem. Journal of the Operational Research Society, 52(3), 340-351. doi:10.1057/palgrave.jors.2601099Easa, S. M. (1989). Resource Leveling in Construction by Optimization. Journal of Construction Engineering and Management, 115(2), 302-316. doi:10.1061/(asce)0733-9364(1989)115:2(302)El-Rayes, K., & Jun, D. H. (2009). Optimizing Resource Leveling in Construction Projects. Journal of Construction Engineering and Management, 135(11), 1172-1180. doi:10.1061/(asce)co.1943-7862.0000097Florez, L., Castro-Lacouture, D., & Medaglia, A. L. (2013). Sustainable workforce scheduling in construction program management. Journal of the Operational Research Society, 64(8), 1169-1181. doi:10.1057/jors.2012.164Gaitanidis, A., Vassiliadis, V., Kyriklidis, C., & Dounias, G. (2016). Hybrid Evolutionary Algorithms in Resource Leveling Optimization. Proceedings of the 9th Hellenic Conference on Artificial Intelligence - SETN ’16. doi:10.1145/2903220.2903227Gather, T., Zimmermann, J., & Bartels, J.-H. (2010). Exact methods for the resource levelling problem. Journal of Scheduling, 14(6), 557-569. doi:10.1007/s10951-010-0207-8Georgy, M. E. (2008). Evolutionary resource scheduler for linear projects. Automation in Construction, 17(5), 573-583. doi:10.1016/j.autcon.2007.10.005Hariga, M., & El-Sayegh, S. M. (2011). Cost Optimization Model for the Multiresource Leveling Problem with Allowed Activity Splitting. Journal of Construction Engineering and Management, 137(1), 56-64. doi:10.1061/(asce)co.1943-7862.0000251Harris, R. B. (1990). Packing Method for Resource Leveling (Pack). Journal of Construction Engineering and Management, 116(2), 331-350. doi:10.1061/(asce)0733-9364(1990)116:2(331)Hegazy, T. (1999). Optimization of Resource Allocation and Leveling Using Genetic Algorithms. Journal of Construction Engineering and Management, 125(3), 167-175. doi:10.1061/(asce)0733-9364(1999)125:3(167)Heon Jun, D., & El-Rayes, K. (2011). Multiobjective Optimization of Resource Leveling and Allocation during Construction Scheduling. Journal of Construction Engineering and Management, 137(12), 1080-1088. doi:10.1061/(asce)co.1943-7862.0000368Hiyassat, M. A. S. (2000). Modification of Minimum Moment Approach in Resource Leveling. Journal of Construction Engineering and Management, 126(4), 278-284. doi:10.1061/(asce)0733-9364(2000)126:4(278)Hiyassat, M. A. S. (2001). Applying Modified Minimum Moment Method to Multiple Resource Leveling. Journal of Construction Engineering and Management, 127(3), 192-198. doi:10.1061/(asce)0733-9364(2001)127:3(192)Ismail, M. M., el-raoof, O. abd, & Abd EL-Wahed, W. F. (2014). A Parallel Branch and Bound Algorithm for Solving Large Scale Integer Programming Problems. Applied Mathematics & Information Sciences, 8(4), 1691-1698. doi:10.12785/amis/080425Kolisch, R., & Sprecher, A. (1997). PSPLIB - A project scheduling problem library. European Journal of Operational Research, 96(1), 205-216. doi:10.1016/s0377-2217(96)00170-1Koulinas, G. K., & Anagnostopoulos, K. P. (2013). A new tabu search-based hyper-heuristic algorithm for solving construction leveling problems with limited resource availabilities. Automation in Construction, 31, 169-175. doi:10.1016/j.autcon.2012.11.002Lai, T.-H., & Sahni, S. (1984). Anomalies in parallel branch-and-bound algorithms. Communications of the ACM, 27(6), 594-602. doi:10.1145/358080.358103Leu, S.-S., Yang, C.-H., & Huang, J.-C. (2000). Resource leveling in construction by genetic algorithm-based optimization and its decision support system application. Automation in Construction, 10(1), 27-41. doi:10.1016/s0926-5805(99)00011-4Li, H., Xu, Z., & Demeulemeester, E. (2015). Scheduling Policies for the Stochastic Resource Leveling Problem. Journal of Construction Engineering and Management, 141(2), 04014072. doi:10.1061/(asce)co.1943-7862.0000936Lim, T.-K., Yi, C.-Y., Lee, D.-E., & Arditi, D. (2014). Concurrent Construction Scheduling Simulation Algorithm. Computer-Aided Civil and Infrastructure Engineering, 29(6), 449-463. doi:10.1111/mice.12073Menesi, W., & Hegazy, T. (2015). Multimode Resource-Constrained Scheduling and Leveling for Practical-Size Projects. Journal of Management in Engineering, 31(6), 04014092. doi:10.1061/(asce)me.1943-5479.0000338Neumann, K., Schwindt, C., & Zimmermann, J. (2003). Project Scheduling with Time Windows and Scarce Resources. doi:10.1007/978-3-540-24800-2Neumann, K., & Zimmermann, J. (1999). Methods for Resource-Constrained Project Scheduling with Regular and Nonregular Objective Functions and Schedule-Dependent Time Windows. International Series in Operations Research & Management Science, 261-287. doi:10.1007/978-1-4615-5533-9_12Neumann, K., & Zimmermann, J. (2000). Procedures for resource leveling and net present value problems in project scheduling with general temporal and resource constraints. European Journal of Operational Research, 127(2), 425-443. doi:10.1016/s0377-2217(99)00498-1Nübel, H. (2001). The resource renting problem subject to temporal constraints. OR-Spektrum, 23(3), 359-381. doi:10.1007/pl00013357Perregaard, M., & Clausen, J. (1998). Annals of Operations Research, 83, 137-160. doi:10.1023/a:1018903912673Ponz-Tienda, J. L., Pellicer, E., Benlloch-Marco, J., & Andrés-Romano, C. (2015). The Fuzzy Project Scheduling Problem with Minimal Generalized Precedence Relations. Computer-Aided Civil and Infrastructure Engineering, 30(11), 872-891. doi:10.1111/mice.12166Ponz-Tienda, J. L., Yepes, V., Pellicer, E., & Moreno-Flores, J. (2013). The Resource Leveling Problem with multiple resources using an adaptive genetic algorithm. Automation in Construction, 29, 161-172. doi:10.1016/j.autcon.2012.10.003Pritsker, A. A. B., Waiters, L. J., & Wolfe, P. M. (1969). Multiproject Scheduling with Limited Resources: A Zero-One Programming Approach. Management Science, 16(1), 93-108. doi:10.1287/mnsc.16.1.93Ranjbar, M. (2013). A path-relinking metaheuristic for the resource levelling problem. Journal of the Operational Research Society, 64(7), 1071-1078. doi:10.1057/jors.2012.119Rieck, J., & Zimmermann, J. (2014). Exact Methods for Resource Leveling Problems. Handbook on Project Management and Scheduling Vol.1, 361-387. doi:10.1007/978-3-319-05443-8_17Rieck, J., Zimmermann, J., & Gather, T. (2012). Mixed-integer linear programming for resource leveling problems. European Journal of Operational Research, 221(1), 27-37. doi:10.1016/j.ejor.2012.03.003Saleh, A., & Adeli, H. (1994). Microtasking, Macrotasking, and Autotasking for Structural Optimization. Journal of Aerospace Engineering, 7(2), 156-174. doi:10.1061/(asce)0893-1321(1994)7:2(156)Saleh, A., & Adeli, H. (1994). Parallel Algorithms for Integrated Structural/Control Optimization. Journal of Aerospace Engineering, 7(3), 297-314. doi:10.1061/(asce)0893-1321(1994)7:3(297)Son, J., & Mattila, K. G. (2004). Binary Resource Leveling Model: Activity Splitting Allowed. Journal of Construction Engineering and Management, 130(6), 887-894. doi:10.1061/(asce)0733-9364(2004)130:6(887)Son, J., & Skibniewski, M. J. (1999). Multiheuristic Approach for Resource Leveling Problem in Construction Engineering: Hybrid Approach. Journal of Construction Engineering and Management, 125(1), 23-31. doi:10.1061/(asce)0733-9364(1999)125:1(23)Tang, Y., Liu, R., & Sun, Q. (2014). Two-Stage Scheduling Model for Resource Leveling of Linear Projects. Journal of Construction Engineering and Management, 140(7), 04014022. doi:10.1061/(asce)co.1943-7862.0000862Wah, Guo-jie Li, & Chee Fen Yu. (1985). Multiprocessing of Combinatorial Search Problems. Computer, 18(6), 93-108. doi:10.1109/mc.1985.1662926Yeniocak , H. 2013 An efficient branch and bound algorithm for the resource leveling problem Ph.D. dissertation, Middle East Technical University, School of Natural and Applied SciencesYounis, M. A., & Saad, B. (1996). Optimal resource leveling of multi-resource projects. Computers & Industrial Engineering, 31(1-2), 1-4. doi:10.1016/0360-8352(96)00116-

Railway scheduling reduces the expected project makespan.

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.Railway scheduling; Roadrunner scheduling; Feeding buffer; Priority list; Resource availability;

A modied branch and cut procedure for resource portfolio problem under relaxed resource dedication policy

Multi-project scheduling problems are characterized by the way resources are managed in the problem environment. The general approach in multi-project scheduling literature is to consider resource capacities as a common pool that can be shared among all projects without any restrictions or costs. The way the resources are used in a multi-project environment is called resource management policy and the aforementioned assumption is called Resource Sharing Policy in this study. The resource sharing policy is not a generalization for multi-project scheduling environments and different resource management policies maybe defined to identify characteristics of different problem environments. In this study, we present a resource management policy which prevents sharing of resources among projects but allows resource transfers when a project starts after the completion of another one. This policy is called the Relaxed Resource Dedication (RRD) Policy in this study. The general resource capacities might or might not be decision variables. We will treat here the case where the general available amounts of resources are decision variables to be determined subject to a limited budget. We call this problem as the Resource Portfolio Problem (RPP). In this study, RPP is investigated under RRD policy and a modified Branch and Cut (B&C)procedure based on CPLEX is proposed. The B&C procedure of CPLEX is modified with different branching strategies, heuristic solution approaches and valid inequalities. The computational studies presented demonstrate the effectiveness of the proposed solution approaches

Stability and resource allocation in project planning.

The majority of resource-constrained project scheduling efforts assumes perfect information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule is executed. In reality, project activities are subject to considerable uncertainty, which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed resource allocation problem. We report on computational results obtained on a set of benchmark problems.Constraint satisfaction; Information; Model; Planning; Problems; Project management; Project planning; Project scheduling; Resource allocati; Scheduling; Stability; Uncertainty; Variability;