Stochastic optimization models for a single-sink transportation problem

Francesca Maggioni; Michal Kaut; Luca Bertazzi

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SPEPS Preprint

Author(s):	Francesca Maggioni, Bergamo University Michal Kaut, Molde University College Luca Bertazzi, Brescia University
Title:	Stochastic optimization models for a single-sink transportation problem
Date of Acceptance:	06.03.2008
Submission Date:	29.11.2007
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10086948)
Keywords (eng):	stochastic programming, scenario tree, single-sink transportation problem
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Abstract (eng):

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 clinker producer and the 5th 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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