Two models for the generalized assignment problem in uncertain environment


Hamidreza Haddad, Hossein Mohammadi and Hedieh Pooladkhan


The generalized assignment problem (GAP) is a unique extended form of the Knapsack problem, which is tremendously practical in optimization fields. For instance, resource allocation, sequencing, supply chain management, etc. This paper tackles the GAP in uncertain environment in which the assignment costs and capacity of agents are fuzzy numbers. Two models are presented for this problem and a novel hybrid algorithm is offered using simulated annealing (SA) method and max-min fuzzy in order to obtain near optimal solution. Computational experiments validate the efficiency of proposed method.


DOI: j.msl.2011.11.005

Keywords: Simulated annealing ,Max-min fuzzy ,Generalized assignment problem Resource allocation

How to cite this paper:

Haddad, H., Mohammadi, H & Pooladkhan, H. (2012). Two models for the generalized assignment problem in uncertain environment.Management Science Letters, 2(2), 623-630.


References

Avella, P., Boccia, M., & Vasilyev, I. (2010). A computational study of exact knapsack separation for the generalized assignment problem. Computational Optimization and Applications, 45, 543–555.

Chu, P.C., & Beasley J.E. (1997). A genetic algorithm for the generalized assignment problem. Computers & Operations Research, 24, 17–23.

Cohen, R., Katzir, L., & Raz, D. (2006). An efficient approximation for the generalized assignment problem. Information Processing Letters, 100, 162–166.

Diaz, J. A., & Fernandez, E. ( 2001). A tabu search heuristic for the generalized assignment problem. European Journal of Operational Research, 132, 22–38.

Fisher, M.L., Jaikumar, R, & Van Wassenhove L.N. (1986). A multiplier adjustment method for the generalized assignment problem. Management Science, 32, 1095–1103.

Haddadi, S, & Ouzia, H. (2004). Effective algorithm and heuristic for the generalized assignment problem., European Journal of Operational Research, 153, 184–190.

Haddadi, S., & Ouzia, H. (2001). An effective Lagrangian heuristic for the generalized assignment problem., Informs, 39, 351–356.

Laguna, M., Kelly, M., Gonzalez-Velarde, Jl., & Glover, F. (1995). Tabu search for the multilevel generalized assignment problem., European Journal of Operational Research, 82, 176–189.

Lai, Y.J, & Hwang C.L. (1994). Fuzzy Mathematical Programming, Springer, 1994, chapter4.

Liu B, Iwamura, K. (1998). Chance constrained programming with fuzzy parameters. Fuzzy Sets and Systems, 94(2), 227-237.

Lourenc¸ HO., & Serra, D. (2002). Adaptive search heuristics for the generalized assignment problem. Mathware and Soft Computing, 9, 209–234.

Mitrovic-Minic, S., & Punnen, A. (2009). Local search intensified: Very large-scale variable neighborhood search for the multi-resource generalized assignment problem. Discrete Optimization, 6, 370-377.

Nauss, RM. (2003). Solving the generalized assignment problem: An optimizing and heuristic approach. INFORMS Journal on Computing, 15, 249–266.

Özbakir L, Baykasoǧlu A, & Tapkan P. (2010). Bees algorithm for generalized assignment problem. Applied Mathematics and Computation, 215, 3782–3795.

Rainwater, Geunes, J., & Romeijn, H.E., (2009). The generalized assignment problem with flexible jobs. Chase Discrete Applied Mathematics, 157, 49–67.

Sharkey T, Romeijn E , (2010) ,Greedy approaches for a class of nonlinear Generalized Assignment Problems, Discrete Applied Mathematics 158, 559_572.

Wen Zhang, C., & Liong Ong, H. (2007). An efficient solution to bi-objective generalized assignment problem. Advances in Engineering Software, 38, 50–58.

Woodcock, A. J., & Wilson, J.M. (2010). A hybrid tabu search/branch & bound approach to solving the generalized assignment problem. European Journal of Operational Research, 207, 566–578.

Yagiura, M., Ibaraki, T., & Glover, F. (2004). An ejection chain approach for the generalized assignment problem, INFORMS J. Computing, 16, 133–151.

Yagiura, M., Ibaraki, T., & Glover, F. (2005). A path relinking approach with ejection chains for the generalized assignment problem. European Journal of Operational Research, 169, 548–569.

Zimmermann H.-J. (1996). Fuzzy sets theory and its application., Kluwer Academic publishers, Boston.