Stochastic optimization models for a single-sink transportation problem
Tóm tắt
In this paper, we study a single-sink transportation problem in which the production capacity of the suppliers and the demand of the single customer are stochastic. Shipments are performed by capacitated vehicles, which have to be booked in advance, before the realization of the production capacity and the demand. Once the production capacity and the demand are revealed, there is an option to cancel some of the booked vehicles against a cancellation fee; if the quantity shipped from the suppliers using the booked vehicles is not enough to satisfy the demand, the residual quantity is purchased from an external company. The problem is to determine the number of vehicles to book in order to minimize the total cost. We formulate a two-stage and a multistage stochastic mixed integer linear programming models to solve this problem and test them on a real case provided by Italcementi, the primary Italian cement producer and the fifth largest cement producer in the world. We test the influence of different scenario-tree structures on the solutions of the problem, as well as sensitivity of the results with respect to the cancellation fee.
Tài liệu tham khảo
Alidaee B, Kochenberger GA (2005) A note on a simple dynamic programming approach to the single-sink, fixed-charge transportation problem. Transp Sci 39(1): 140–143
Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, New York
Dupačová J (1997) Stochastic programming: approximation via scenarios. In: Proceedings of the 3rd international conference on approximation and optimization in the caribbean. Benemérita Universidad Autónoma de Puebla, Puebla, Mexico. http://www.emis.de/proceedings/3ICAOC/index.html
Dupačová J, Consigli G, Wallace SW (2000) Scenarios for multistage stochastic programs. Ann Oper Res 100(1–4): 25–53
Herer YT, Rosenblatt MJ, Hefter I (1996) Fast algorithms for single-sink fixed charge transportation problems with applications to manufacturing and transportation. Transp Sci 30: 276–290
Kall P, Wallace SW (1994) Stochastic programming. Wiley, Chichester
Kaut M, Wallace SW (2007) Evaluation of scenario generation methods for stochastic programming. Pac J Optim 3(2): 257–271
Lamar BW, Wallace CA (1997) Revised-modified penalties for fixed charge transportation problems. Manage Sci 43(10): 1431–1436
Lamar BW, Sheffi Y, Powell WB (1990) A capacity improvement lower bound for fixed charge network design problmes. Oper Res 38(4): 704–710
Palekar US, Karwan MH, Zionts S (1990) A branch-and-bound method for the fixed charge transportation problem. Manage Sci 36(9): 1092–1105