Abstract
This paper discusses dynamic methods for solving a class of multi-project scheduling problems in which rates of job performances are controllable and resources such as money, energy or manpower per time unit, are renewable and continuously divisible. The objective is to complete the projects as close to the common due date as possible. Two different ways of imposing sequential precedence relations between project jobs are explored by formulating two dynamic models and studying their relationships on the optimal solution. Efficient time-decomposition algorithms for finding either globally optimal schedules or lower bound guided near-optimal solutions are suggested and computationally tested.
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Arizono, I., Yokoi, S., and Ohta, H. 1989. The effects of varying production rates on inventory control. Journal of Operational Research Society 40: 789-796.
Bell, C. I., and Park, K. 1990. Solving resource constrained project scheduling problems by Λ* search. Naval Research Logistics 37: 41-84.
Berman, O., Larson, R., and Pinker, E. 1997. Scheduling workforce and workflow in a high volume factory. Management Science 43-2: 158-172.
Bryson, A. E., and Ho, Y.-C. 1969. Applied Optimal Control. Waltham: Ginn and Company.
Buzacott, J. A., and Ozcarahan, I. A. 1983. One-and two-stage scheduling of two products with distributed inserted idle times: the benefits of a controllable production rate. Naval Research Logistics Quarterly 657-696.
Christofides, N., Alvarez-Valdes, R., and Tamarit, J. M. 1987. Project scheduling with re source constraints: A branch and bound approach. European Journal of Operational Research 29: 262–273.
Demeulemeester, E., and Herroelen, W. 1992. Abranch and bound procedure for the multiple resource constrained project scheduling problem. Management Science 38: 1803-1818.
Janiak, A., and Stankiewicz, A. 1983. The equivalence of local and global time-optimal control of a complex of operations. International Journal of Control 38-6: 1149-1165.
Kimemia, J. G., and Gershwin, S. B. 1983. An algorithm for the computer control of a flexible manufacturing system. IEE Transactions 15-4: 353-362.
Khmelnisky, E., Kogan, K., and Maimon, O. 1995. A maximum principle based combined method for scheduling in a flexible manufacturing system. Discrete Event Dynamic Systems 5: 343-355.
Kogan, K., and Khmelnisky, E. 1996. An optimal control model for continuous-time production and setup scheduling. International Journal of Production Research 34-3: 715-725.
Kurtulus, I. S., and Davis, E. W. 1982. Multi project scheduling: Categorization of heuristic rule performance. Management Science 28: 161-172.
Leachman, R. C., Dincerler, A., and Kim, S. 1990. Resource-constrained scheduling of projects with variable intensity activities. IIE Transactions 22-1: 31-39.
Moon, I., Gallego, G., and Simchi-Levi, D. 1991. Controllable production rates in a family context. International Journal of Production Research 29: 2459-2470.
Ozdamar, L., and Ulusoy, G. 1995. A survey on the resource-constrained project scheduling problem. IIE Transactions 27: 574-586.
Roberts, A. W., and Varberg, D. E. 1973. Convex Functions. New York: Academic Press.
Stinson, J. P., Davis, E.W., and Khumawala, B.W. 1978. Multiple-resource constrained scheduling using branch and bound. AIIE Transactions 10: 252-259.
Weglarz, J. 1981. Project scheduling with continuously-divisible, doubly constrained resources. Management Science 27-9: 1040-1053.
Weglarz, J. 1979. Project scheduling with discrete and continuous resources. IEEE Trans. Systems, Man and Cybernetics 9: 644-650.
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Kogan, K. Scheduling Under Common Due Date, A Single Resource and Precedence Constraints—A Dynamic Approach. Discrete Event Dynamic Systems 8, 353–364 (1998). https://doi.org/10.1023/A:1008345132480
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DOI: https://doi.org/10.1023/A:1008345132480