Abstract
Dynamic programming is a general technique for solving sequential problems. The first comprehensive books on the topic have been written by Bellman [13] and Howard [62]. The most important methodologies for determining an optimal policy for a Markov decision process (MDP) are backward induction, value iteration (VI), policy iteration (PI) and linear programming. As MDPs are in discrete time where transitions have the same deterministic durations many results and methodologies, such as VI, cannot be directly applied to continuous-time Markov decision processes with exponentially distributed transition times.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsBibliography
Adelman, D. (2004). A price-directed approach to stochastic inventory/routing. Operations Research, 52(4), 499–514.
Adler, P. S., Mandelbaum, A., Nguyen, V., & Schwerer, E. (1995). From project to process management: An empirically-based framework for analyzing product development time. Management Science, 41(3), 458–484.
Anavi-Isakow, S., & Golany, B. (2003). Managing multi-project environments through constant work-in-process. International Journal of Project Management, 21, 9–18.
Anderson, E. J., & Nyrenda, J. C. (1990). Two new rules to minimize tardiness in a job shop. International Journal of Production Research, 28(12), 2277–2292.
Ashtiani, B., Leus, R., & Aryanezhad, M.-B. (2011). New competitive results for the stochastic resource-constrained project-scheduling problem: Exploring the benefits of pre-processing. Journal of Scheduling, 14, 157–171.
Azaron, A., Katagiri, H., Kato, K., & Sakawa, M. (2006). Longest path analysis in networks of queues: Dynamic scheduling problems. European Journal of Operational Research, 174, 132–149.
Azaron, A., & Modarres, M. (2007). Project completion time in dynamic PERT networks with generating projects. Scientia Iranica, 14(1), 56–63.
Azaron, A., & Tavakkoli-Moghaddam, R. (2006). A multi-objective resource allocation in dynamic PERT networks. Applied Mathematics and Computation, 181, 163–174.
Baccelli, F., Liu, Z., & Towsley, D. (1993). Extremal scheduling of parallel processing with and without real-time constraints. Journal of the Association for Computing Machinery, 40(5), 1209–1237.
Ballestín, F., & Leus, R. (2009). Resource-constrained project scheduling for timely project completion with stochastic activity durations. Production and Operations Management, 18(4), 459–474.
Bard, J., Balachandra, R., & Kaufman, P. (1988). An interactive approach to R&D project selection and termination. IEEE Transactions on Engineering Management, 35, 139–146.
Bellman, R. (1957). Dynamic programming. Princeton: Princeton University Press.
Berman, E. B. (1964). Resource allocation in a PERT network under continuous activity time-cost functions. Management Science, 10(4), 734–745.
Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming. Belmont: Athena Scientific.
Boctor, F. F. (1990). Some efficient multi-heuristic procedures for resource-constrained project scheduling. European Journal of Operational Research, 49, 3–13.
Brucker, P., Drexl, A., Möhring, R., Neumann, K., & Pesch, E. (1999). Resource-constrained project scheduling: Notation, classification, models, and methods. European Journal of Operational Research, 112, 3–41.
Buss, A. H., & Rosenblatt, M. J. (1997). Activity delay in stochastic project networks. Operations Research, 45(1), 126–139.
Choi, J., Realff, M. J., & Lee, J. H. (2004). Dynamic programming in a heuristically confined state space: A stochastic resource constrained project scheduling application. Computers and Chemical Engineering, 28, 1039–1058.
Choi, J., Realff, M. J., & Lee, J. H. (2007). A Q-learning-based method applied to stochastic resource constrained project scheduling with new project arrivals. International Journal of Robust and Nonlinear Control, 17, 1214–1231.
Cohen, I., Nguyen, V., & Shtub, A. (2004). Multi-project scheduling and control: A process-based comparative study of the critical chain methodology and some alternatives. Project Management Journal, 35(2), 39–50.
Cox, D. R., & Smith, W. L. (1961). Queues. London: Methuen.
Crabill, T. B. (1972). Optimal control of a service facility with variable exponential service times and constant arrival rate. Management Science, 18(9), 560–566.
Creemers, S., Leus, R., & Lambrecht, M. (2010). Scheduling Markovian PERT networks to maximize the net present value. Operations Research Letters, 38, 51–56.
Davis, E. W., & Patterson, J. H. (1975). A comparison of heuristic and optimum solutions in resource-constrained project scheduling. Management Science, 21, 944–955.
De Boer, R. (1998). Resource-constrained multi-project management. PhD thesis, Universiteit Twente.
De Farias, D. P., & Van Roy, B. (2003). Approximate linear programming for average-cost dynamic programming. Advances in Neural Information Processing Systems, 15, 1619–1626.
De Farias, D. P., & Van Roy, B. (2003). The linear programming approach to approximate dynamic programming. Operations Research, 51(6), 850–865.
De Farias, D. P., & Van Roy, B. (2004). On constraint sampling in the linear programming approach to approximate dynamic programming. Mathematics of Operations Research, 29(3), 462–478.
Demeulemeester, E. L., & Herroelen, W. S. (2002). A research handbook (International series in operations research & management science). Boston: Kluwer Academic.
De Serres, I. (1991). Simultaneous optimization of flow control and scheduling in a single server queue with two job classes. Operations Research Letters, 10, 103–112.
De Serres, I. (1991). Simultaneous optimization of flow control and scheduling in queues. PhD thesis, McGill University, Montreal.
Dumond, J., & Mabert, V. A. (1988). Evaluating project scheduling and due date assignment procedures: An experimental analysis. Management Science, 34(1), 101–118.
Ebben, M. J. R., Hans, E. W., & Olde Weghuis, F. M. (2005). Workload based order acceptance in job shop environments. OR Spectrum, 27, 107–122.
Feinberg, E. A., & Yang, F. (2010). Optimality of trunk reservation for an M/M/k/N queue with several customer types and holding costs. Technical report, State University of New York at Stony Brook.
Fernandez, A. A., Armacost, R. L., & Pet-Edwards, J. J. A. (1996). The role of the nonanticipativity constraint in commercial software for stochastic project scheduling. Computers Industrial Engineering, 31(1/2), 233–236.
Gittins, J. C., & Jones, D. M. (1972). A dynamic allocation index for the sequential design of experiments. In J. Bolyaim (Ed.), Progress in statistics (European meeting of statisticians, Budapest) (Vol. 9). Budapest: Colloquium Mathematical Society.
Goldratt, E. M. (1997). Critical chain. Great Barrington: The North River Press.
Hans, E. W. (2001). Resource loading by branch-and-price techniques. PhD thesis, University of Twente.
Herbots, J., Herroelen, W., & Leus, R. (2007). Dynamic order acceptance and capacity planning on a single bottleneck resource. Naval Research Logistics, 54, 874–889.
Herroelen, W., & Leus, R. (2005). Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research, 165, 289–306.
Herroelen, W., De Reyck, B., & Demeulemeester, E. (1998). Resource-constrained project scheduling: A survey of recent developments. Computers and Operations Research, 25(4), 279–302.
Howard, R. (1960). Dynamic programming and Markov processes. Cambridge: MIT.
Ivanescu, C. V., Fransoo, J. C., & Bertrand, J. W. M. (2002). Makespan estimation and order acceptance in batch process industries when processing times are uncertain. OR Spectrum, 24, 467–495.
Ivanescu, V. C., Fransoo, J. C., & Betrand, J. W. M. (2006). A hybrid policy for order acceptance in batch process industries. OR Spectrum, 28, 199–222.
Kavadias, S., & Loch, C. H. (2003). Optimal project sequencing with recourse at a scarce resource. Production and Operations Management, 12(4), 433–442.
Kelley, J. E., Jr. (1963). The critical path method: Resource planning and scheduling. In Industrial scheduling. Englewood Cliffs: Prentice Hall.
Kelley, J. E., & Walker, M. R. (1959). Critical-path planning and scheduling. In 1959 Proceedings of the eastern joint computer conference, Boston (pp. 160–173).
Kemppainen, K. (2005). Priority scheduling revisited – Dominant rules, open protocols and integrated order management. PhD thesis, Helsinki School of Economics.
Kleywegt, A. J., & Papastavrou, J. D. (1998). The dynamic and stochastic knapsack problem. Operations Research, 1, 17–35.
Kleywegt, A. J., & Papastavrou, J. D. (2001). The dynamic and stochastic knapsack problem with random sized items. Operations Research, 49(1), 26–41.
Klimov, G. P. (1974). Time-sharing service systems I. Theory of Probability and its Applications, 19(3), 532–551.
Knudsen, N. C. (1972). Individual and social optimization in a mutliserver queue with a general cost-benefit. Econometrica, 40(3), 515–528.
Kolisch, R. (1996). Efficient priority rules for the resource-constrained project scheduling problem. Journal of Operations Management, 14, 179–102.
Koole, G., & Pot, A. (2005). Approximate dynamic programming in multi-skill call centers. In M. E. Kuhl, N. M. Steiger, F. B. Armstrong, & J. A. Joines (Eds.), Proceedings of the 2005 winter simulation conference, Orlando.
Kulkarni, V. G., & Adlakha, V. G. (1986). Markov and Markov-regenerative PERT networks. Operations Research, 34, 769–781.
Kumar, P. R., & Seidman, T. I. (1990). Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Transactions on Automatic Control, 35(3), 289–298.
Kurtulus, I. S., & Davis, E. W. (1982). Multi-project scheduling: Categorization of heuristic rule performance. Management Science, 28(2), 161–172.
Kurtulus, I. S., & Narula, S. C. (1985). Multi-project scheduling: Analysis of project performance. IIE Transactions, 17(1), 58–66.
Kutanoglu, E., & Sabuncuoglu, I. (1999). An analysis of heuristics in a dynamic job shop with weighted tardiness objectives. International Journal of Production Research, 37(1), 165–187.
Lawrence, S. R., & Morton, T. E. (1993). Resource-constrained multi-project scheduling with tardy costs: Comparing myopic, bottleneck, and resource pricing heuristics. European Journal of Operational Research, 64, 168–187.
Lee, H., & Suh, H.-W. (2008). Estimating the duration of stochastic workflow for product development process. International Journal of Production Economics, 111, 105–117.
Levy, N., & Globerson, S. (1997). Improving multiproject management by using a queueing theory approach. Project Management Journal, 28(4), 40–46.
Lippman, S. A. (1975). Applying a new device in the optimization of exponential queueing systems. Operations Research, 23, 687–710.
Loch, C. H., & Kavadias, S. (2002). Dynamic portfolio selection of NPD programs using marginal returns. Management Science, 48(10), 1227–1241.
Loch, C. H., Pich, M. T., Urbschat, M., & Terwiesch, C. (2001). Selecting R&D projects at BMW: A case study of adopting mathematical programming methods. IEEE Transactions Engineering Management, 48(1), 70–80.
Meyn, S. (2008). Control techniques for complex networks. Cambridge: Cambridge University Press.
Möhring, R. H., Radermacher, F. J., & Weiss, G. (1984). Stochastic scheduling problems I. Zeitschrift für Operations Research, 28, 193–260.
Morton, T. E., & Pentico, D. W. (1993). Heuristic scheduling systems (Wiley series in engineering & technology management). New York: Wiley.
Naor, P. (1969). The regulation of queue size by levying tolls. Econometrica, 37(1), 15–24.
Nguyen, V. (1993). Processing networks with parallel and sequential tasks: Heavy traffic analysis and brownian limits. The Annals of Applied Probability, 3(1), 28–55.
Nguyen, V. (1994). The trouble with diversity: Fork-join networks with heterogeneous customer populations. The Annals of Applied Probability, 4(1), 1–25.
Nino-Mora, J. (2005). Stochastic scheduling. In P. M. Pardalos (Ed.), Encyclopedia of optimization (Vol. V, pp. 367–372). Dordrecht: Kluwer Academic.
Perry, T. C., & Hartman, J. C. (2004). Allocating manufacturing capacity by solving a dynamic, stochastic multiknapsack problem. Technical report ISE 04T-009, Lehigh University, Pennsylvania.
Powell, W. B. (2007). Approximate dynamic programming. Hoboken: Wiley.
Powell, W. B. (2011). Approximate dynamic programming (2nd ed.). Hoboken: Wiley.
Pritsker, A. A. B., Watters, L. J., & Wolfe, P. M. (1969). Multiproject scheduling with limited resources: A zero-one programming approach. Management Science, 16, 93–107.
Ramasesh, R. (1990). Dynamic job shop scheduling: A survey of simulation research. OMEGA International Journal of Operations and Production Management, 18(1), 43–57.
Roemer, T. A., & Ahmadi, R. (2004). Concurrent crashing and overlapping in product development. Operations Research, 52(4), 606–622.
Ross, K. W., & Tsang, D. H. K. (1989). Optimal circuit access policies in an ISDN environment: A Markov decision approach. IEEE Transactions on Communications, 37(9), 934–939.
Roubos, D., & Bhulai, S. (2007). Average-cost approximate dynamic programming for the control of birth-death processes. Technical report, VU University Amsterdam.
Schweitzer, P. J., & Seidman, A. (1985). Generalized polynomial approximations in Markovian decision processes. Journal of Mathematical Analysis and Applications, 110, 568–582.
Sennot, L. I. (1999). Stochastic dynamic programming and the control of queueing systems (Wiley series in probability and statistics). New York: Wiley.
Slotnick, S., & Morton, T. (2007). Order acceptance with weighted tardiness. Computers and Operations Research, 34, 3029–3042.
Sobel, M. J., Szmerekovsky, J. G., & Tilson, V. (2009). Scheduling projects with stochastic activity duration to maximize expected net present value. European Journal of Operational Research, 198, 697–705.
Stork, F. (2001). Stochastic resource-constrained project scheduling. PhD thesis, Technische Universität Berlin.
Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning. Cambridge: MIT.
Talla Nobibon, F., Herbots, J., & Leus, R. (2009). Order acceptance and scheduling in a single-machine environment: Exact and heuristic algorithms. Technical report, Faculty of Business and Economics, KU Leuven.
Talla Nobibon, F., & Leus, R. (2011). Exact algorithms for a generalization of the order acceptance and scheduling problem in a single-machine environment. Computers and Operations Research, 38(1), 367–378.
Tsai, D. M., & Chiu, H. N. (1996). Two heuristics for scheduling multiple projects with resource constraints. Construction Management and Economics, 14, 325–340.
van Foreest, N. D., Wijngaard, J., & van der Vaart, J. T. (2010). Scheduling and order acceptance for the customized stochastic lot scheduling problem. International Journal of Production Research, 48(12), 3561–3578.
Veatch, M. H. (2009). Approximate dynamic programming for networks: Fluid models and constraint reduction. Technical report, Gordon College.
Veatch, M. H., & Walker, N. (2008). Approximate linear programming for network control: Column generation and subproblems. Technical report, Gordon College.
Vepsalainen, A. P. J., & Morton, T. E. (1987). Priority rules for job shops with weighted tardiness costs. Management Science, 33(8), 1035–1047.
Vyzas, E. (1997). Approximate dynamic programming for some queueing problems. Master’s thesis, Massachusetts Institute of Technology.
Wester, F. A. W., Wijngaard, J., & Zijm, W. H. M. (1992). Order acceptance strategies in a production-to-order environment with setup time and due-dates. International Journal of Production Research, 30(6), 1313–1326.
Yaghoubi, S., Noori, S., Azaron, A., & Tavakkoli-Moghaddam, R. (2011). Resource allocation in dynamic PERT networks with finite capacity. European Journal of Operational Research, 215, 670–678.
Yechiali, U. (1969). On optimal balking rules and toll charges in the GI/M/1 queueing process. Operations Research, 19, 349–370.
Yechiali, U. (1972). Customers’ optimal joining rules for the GI/M/s queue. Manage, 18, 434–443.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Melchiors, P. (2015). Literature Review. In: Dynamic and Stochastic Multi-Project Planning. Lecture Notes in Economics and Mathematical Systems, vol 673. Springer, Cham. https://doi.org/10.1007/978-3-319-04540-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-04540-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04539-9
Online ISBN: 978-3-319-04540-5
eBook Packages: Business and EconomicsBusiness and Management (R0)