×

A probabilistic bi-level linear multi-objective programming problem to supply chain planning. (English) Zbl 1137.90659

Summary: Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels.
In most of the real life problems in mathematical programming, the parameters are considered as random variables. The branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called “stochastic programming”.
Supply chain planning problems are concerned with synchronizing and optimizing multiple activities involved in the enterprise, from the start of the process, such as procurement of the raw materials, through a series of process operations, to the end, such as distribution of the final product to customers.
Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using “multi-level programming” principles.
In this paper, we consider a “probabilistic bi-level linear multi-objective programming problem” and its application in enterprise-wide supply chain planning problem where (1) market demand, (2) production capacity of each plant and (3) resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not. This probabilistic model is first converted into an equivalent deterministic model in each level, to which fuzzy programming technique is applied to solve the multi-objective nonlinear programming problem to obtain a compromise solution.

MSC:

90C29 Multi-objective and goal programming
90B50 Management decision making, including multiple objectives
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Emam, O.E., A fuzzy approach for bi-level integer non-linear programming problem, Appl. math. comput., (2005) · Zbl 1169.90408
[2] Colson, Benoıˆt; Marcotte, Patrice; Savard, Gilles, Bilevel programming: A survey, A quarterly journal of operations research, (2005), Springer-Verlag · Zbl 1134.90482
[3] Bellman, R.E.; Zadeh, L.A., Decision making in a fuzzy environment, Manage. sci., 17, 141-164, (1970) · Zbl 0224.90032
[4] Charnes, A.; Cooper, W.W., Chance constrained programming, Manage. sci., 6, 73-79, (1959) · Zbl 0995.90600
[5] Contini, B., A stochastic approach to goal programming, Oper. res., 16, 576-586, (1978) · Zbl 0211.22501
[6] Hanan, E.L., On fuzzy goal programming, Decision sci., 12, 522-531, (1981)
[7] Kolbin, V.V., Stochastic programming, (1977), D. Reidel Publishing Company Dordrecht · Zbl 0359.90043
[8] Leberling, H., On finding compromise solution in multi-criteria problems using the MIN-operator, Fuzzy sets syst., 6, 105-118, (1981) · Zbl 0465.90081
[9] Leclercq, J.P., Stochastic programming: an interactive multi-criteria approach, Eur. J. oper. res., 10, 33-41, (1982) · Zbl 0484.90078
[10] Narasimhan, R., Goal programming in a fuzzy environment, Decision sci., 11, 325-336, (1980)
[11] Abdelaziz, F.B.; Aouni, B.; El Fayedh, R., Multi-objective stochastic programming for portfolio selection, Eur. J. oper. res., 4-6, (2005)
[12] Sengupta, J.K., Stochastic programming: methods and applications, (1972), North-Holland Amsterdam · Zbl 0262.90049
[13] Stancu-Minasian, I.M.; Wets, M.J., A research bibliography in stochastic programming 1955-1975, Oper. res., 24, 1078-1119, (1976) · Zbl 0343.90033
[14] Sullivan, R.S.; Fitzsimmoms, J.A., A goal programming model for readiness and optimal deployment of resources, Socio-economic planning sci., 12, 215-220, (1978)
[15] Teghem, J.; Dufrance, D.; Thauvoye, M.; Kunch, P., Strange: an interactive method for multi-objective linear programming under uncertainty, Eur. J. oper. res., 26, 5-82, (1986) · Zbl 0602.90080
[16] Zimmermann, H.J., Fuzzy programming and linear programming with several objective functions, Fuzzy sets syst., 1, 45-55, (1978) · Zbl 0364.90065
[17] Ryu, Jun-Hyung; Dua, Vivek; Pistikopoulos, Efstratios N., A bilevel programming framework for enterprise-wide process networks under uncertainty, Comput. chem. eng., 28, 1121-1129, (2004) · Zbl 1048.90159
[18] T. Backx, O. Bosgra, W. Marquardt, Towards intentional dynamics in supply chain conscious process operation, in: Proceedings of the Third International Conference on Foundations of Computer-aided Process Operations, 1998.
[19] Tsiakis, P.; Shah, N.; Pantelides, C.C., Design of multiechelon supply chain networks under demand uncertainty, Ind. eng. chem. res., 40, 3585-3604, (2001)
[20] Gupta, A.; Maranas, C.D., A two-stage modeling and solution framework for multisite midterm planning under uncertainty, Ind. eng. chem. res., 39, 3799-3813, (2000)
[21] Gupta, A.; Maranas, C.D.; McDonald, C.M., Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management, Comput. chem. eng., 24, 2613-2621, (2000)
[22] McDonald, C.M.; Karimi, I.A., Planning and scheduling of parallel semicontinuous processes. part 1. production planning, Ind. eng. chem. res., 36, 2691-2700, (1997)
[23] Lee, H.L.; Padmanabhan, V.; Whang, S., The bullwhip effect in supply-chains, Sloan manage. rev., 38, 93-102, (1997)
[24] Gjerdrum, J.; Shah, N.; Papageorgiou, L.G., Transfer prices for multienterprise supply chain optimization, Ind. eng. chem. res., 40, 1650-1660, (2001)
[25] Zhou, Z.; Cheng, S.; Hua, B., Supply chain optimization of continuous process industries with sustainability considerations, Comput. chem. eng., 24, 1151-1158, (2000)
[26] Perea-Lopez, E.; Grossmann, I.E.; Ydstie, E.; Tahmassebi, T., Dynamic modeling and classical control theory for supply chain management, Comput. chem. eng., 24, 1143-1149, (2000)
[27] Bose, S.; Pekny, J.F., A model predictive framework for planning and scheduling problem: a case study of consumer goods supply chain, Comput. chem. eng., 24, 329-335, (2000)
[28] M.E. Flores, D.E. Rivera, V. Smith-Daniels, Supply chain management using model predictive control, in: AIChE Annual Meeting, Los Angeles, 2000.
[29] Osman, M.S.; Abo-Sinna, M.A.; Amer, A.H., A multi-level non-linear multi-objective decision-making under fuzziness, Appl. math. comput., 153, 239-252, (2004) · Zbl 1049.90032
[30] Sinha, S.B.; Hulsurkar, Suwarna; Biswal, M.P., Fuzzy programming approach to multi-objective stochastic programming problems when bi’s follow joint normal distribution, Fuzzy sets syst., 109, 91-96, (2000) · Zbl 0949.90099
[31] Sakawa, M., Fuzzy sets and interactive multi-objective optimization, (1993), Plenum Press New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.