Stochastic optimization models for a single-sink transportation problem
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.
KeywordsSingle-sink transportation problem Stochastic programming Scenario trees
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- Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, New YorkGoogle Scholar
- 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
- Kall P, Wallace SW (1994) Stochastic programming. Wiley, ChichesterGoogle Scholar
- Kaut M, Wallace SW (2007) Evaluation of scenario generation methods for stochastic programming. Pac J Optim 3(2): 257–271Google Scholar