A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints
Tóm tắt
In this paper, we consider the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints. For the first time, the concept of partially renewable resources is embedded in the context of projects with general temporal constraints. While partially renewable resources have already broadened the area of applications for project scheduling, the extension by general temporal constraints allows to consider even more relevant aspects of real projects. We present a branch-and-bound procedure for the problem with the objective to minimize the project duration. To improve the performance of the solution procedure, new consistency tests, lower bounds, and dominance rules are developed. Furthermore, new temporal planning procedures, based on forbidden start times of activities, are presented which can be used for any project scheduling problem with general temporal constraints independent on the considered resource type. In a performance analysis, we compare our branch-and-bound procedure with the mixed-integer linear programming solver IBM CPLEX 12.8.0 on adaptations of benchmark instances from the literature. In addition, we compare our solution procedure with the only available branch-and-bound procedure for partially renewable resources. The results of the computational experiments prove the efficiency of our branch-and-bound procedure.
Tài liệu tham khảo
Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice-Hall, Englewood Cliffs
Alvarez-Valdes R, Crespo E, Tamarit JM, Villa F (2006) A scatter search algorithm for project scheduling under partially renewable resources. J Heuristics 12(1):95–113
Alvarez-Valdes R, Crespo E, Tamarit JM, Villa F (2008) GRASP and path relinking for project scheduling under partially renewable resources. Eur J Oper Res 189(3):1153–1170
Alvarez-Valdes R, Tamarit JM, Villa F (2015) Partially renewable resources. In: Schwindt C, Zimmermann J (eds) Handbook on project management and scheduling, vol 1. Springer, Cham, pp 203–227
Artigues C (2017) On the strength of time-indexed formulations for the resource-constrained project scheduling problem. Oper Res Lett 45(2):154–159
Bartsch T, Drexl A, Kröger S (2006) Scheduling the professional soccer leagues of Austria and Germany. Comput Oper Res 33(7):1907–1937
Bartusch M, Möhring RH, Radermacher FJ (1988) Scheduling project networks with resource constraints and time windows. Ann Oper Res 16(1):201–240
Bianco L, Caramia M (2012) An exact algorithm to minimize the makespan in project scheduling with scarce resources and generalized precedence relations. Eur J Oper Res 219(1):73–85
Böttcher J, Drexl A, Kolisch R, Salewski F (1999) Project scheduling under partially renewable resource constraints. Manag Sci 45(4):543–559
Briskorn D, Fliedner M (2012) Packing chained items in aligned bins with applications to container transshipment and project scheduling. Math Methods Oper Res 75(3):305–326
De Reyck B, Herroelen W (1998) A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations. Eur J Oper Res 111(1):152–174
Dorndorf U, Pesch E, Phan-Huy T (2000a) Constraint propagation techniques for the disjunctive scheduling problem. Artif Intell 122(1):189–240
Dorndorf U, Pesch E, Phan-Huy T (2000b) A time-oriented branch-and-bound algorithm for resource-constrained project scheduling with generalised precedence constraints. Manag Sci 46(10):1365–1384
Drexl A, Salewski F (1997) Distribution requirements and compactness constraints in school timetabling. Eur J Oper Res 102(1):193–214
Drexl A, Juretzka J, Salewski F (1993) Academic course scheduling under workload and changeover constraints. Working paper 337, University of Kiel
Fest A, Möhring RH, Stork F, Uetz M (1999) Resource-constrained project scheduling with time windows: a branching scheme based on dynamic release dates. Technical report 596, revised version, Technical University of Berlin
Franck B, Neumann K, Schwindt C (2001a) Project scheduling with calendars. OR Spektrum 23(3):325–334
Franck B, Neumann K, Schwindt C (2001b) Truncated branch-and-bound, schedule-construction, and schedule-improvement procedures for resource-constrained project scheduling. OR Spektrum 23(3):297–324
Klein R, Scholl A (1999) Computing lower bounds by destructive improvement: an application to resource-constrained project scheduling. Eur J Oper Res 112(2):322–346
Knust S (2010) Scheduling non-professional table-tennis leagues. Eur J Oper Res 200(2):358–367
Kolisch R, Sprecher A (1997) PSPLIB: a project scheduling problem library. Eur J Oper Res 96(1):205–216
Kolisch R, Sprecher A, Drexl A (1995) Characterization and generation of a general class of resource-constrained project scheduling problems. Manag Sci 41(10):1693–1703
Kreter S (2016) Projektplanung mit Kalendern (project scheduling with calendars): Struktureigenschaften und Lösungsmethoden (structural characteristics and solution procedures). Shaker, Aachen
Kreter S, Rieck J, Zimmermann J (2016) Models and solution procedures for the resource-constrained project scheduling problem with general temporal constraints and calendars. Eur J Oper Res 251(2):387–403
Murty KG (1968) An algorithm for ranking all the assignments in order of increasing cost. Oper Res 16(3):682–687
Neumann K, Schwindt C (1995) Projects with minimal and maximal time lags: construction of activity-on-node networks and applications. Report WIOR-447, University of Karlsruhe
Neumann K, Schwindt C, Zimmermann J (2003) Project scheduling with time windows and scarce resources, 2nd edn. Springer, Berlin
Okubo H, Miyamoto T, Yoshida S, Mori K, Kitamura S, Izui Y (2015) Project scheduling under partially renewable resources and resource consumption during setup operations. Comput Ind Eng 83:91–99
Schirmer A (1999) Project scheduling with scarce resources: models, methods, and applications. Kovač, Hamburg
Schutt A, Feydy T, Stuckey PJ, Wallace MG (2013) Solving RCPSP/max by lazy clause generation. J Sched 16(3):273–289
Schwindt C (1996) Generation of resource-constrained project scheduling problems with minimal and maximal time lags. Report WIOR-489, University of Karlsruhe
Schwindt C (1998a) A branch-and-bound algorithm for the resource-constrained project duration problem subject to temporal constraints. Report WIOR-544, University of Karlsruhe
Schwindt C (1998b) Generation of resource-constrained project scheduling problems subject to temporal constraints. Report WIOR-543, University of Karlsruhe
Schwindt C (1998c) Verfahren zur Lösung des ressourcenbeschränkten Projektdauerminimierungsproblems mit planungsabhängigen Zeitfenstern (solution procedures for the resource-constrained project duration problem with schedule-dependent time windows). Shaker, Aachen
Talbot FB, Patterson JH (1978) An efficient integer programming algorithm with network cuts for solving resource-constrained scheduling problems. Manag Sci 24(11):1163–1174
Thesen A (1977) Measures of the restrictiveness of project networks. Networks 7(3):193–208