Stochastic optimization models for a single-sink transportation problem |
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Authors: | Francesca Maggioni Michal Kaut Luca Bertazzi |
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Institution: | (1) Department of Mathematics, Statistic, Computer Science and Applications, Bergamo University, Via dei Caniana 2, 24127 Bergamo, Italy;(2) Molde University College, P.O. Box 2110, 6402 Molde, Norway;(3) Department of Quantitative Methods, Brescia University, Contrada S. Chiara 50, 25122 Brescia, Italy |
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Abstract: | 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. |
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Keywords: | Single-sink transportation problem Stochastic programming Scenario trees |
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