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SINGLE VEHICLE ROUTING PROBLEMS WITH A PREDEFINED CUSTOMER ORDER, UNIFIED LOAD AND STOCHASTIC DISCRETE DEMANDS

Published online by Cambridge University Press:  18 December 2012

Dimitrios G. Pandelis ,
Constantinos C. Karamatsoukis  and
Epaminondas G. Kyriakidis
Dimitrios G. Pandelis
Affiliation:
Department of Mechanical Engineering, University of Thessaly, Volos, Greece E-mail: d_pandelis@mie.uth.gr
Constantinos C. Karamatsoukis
Affiliation:
Department of Financial and Management Engineering, University of the Aegean, Chios, Greece E-mail: k.karamatsoukis@fme.aegean.gr
Epaminondas G. Kyriakidis
Affiliation:
Department of Statistics, Athens University of Economics and Business, Athens, Greece E-mail: ekyriak@aueb.gr
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Abstract

We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers that are served according to a particular order. It is assumed that the demands of the customers for each product are discrete random variables, and the total demand of each customer for all products cannot exceed the vehicle capacity. The joint probability mass function of the demands of each customer is known. It is assumed that all products are stored together in the vehicle's single compartment. The policy that serves all customers with the minimum total expected cost is found by implementing a suitable dynamic programming algorithm. We prove that this policy has a specific threshold-type structure. Furthermore, we study a corresponding infinite-time horizon problem in which the service of the customers is not completed when the last customer has been serviced but it continues periodically with the same customer order. The demands of each customer for the products have the same distributions at different periods. The discounted cost optimal policy and the average-cost optimal policy have the same structure as the optimal policy in the finite-horizon problem. Numerical results are given that illustrate the structural results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 1 , January 2013 , pp. 1 - 23
Copyright
Copyright © Cambridge University Press 2013

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References

1.Bather, J. (2000). Decision theory: an introduction to dynamic programming and sequential decisions. Chichester: Wiley.Google Scholar
2.Clarke, G. & Wright, J.V. (1964). Scheduling of vehicles from a control depot to a number of delivery points. Operations Research 12: 568–581.CrossRefGoogle Scholar
3.Cordeau, J.-F., Laporte, G., Savelsbergh, M.W.P., & Vigo, D. (2007). Vehicle routing. In Barnhart, C. & Laporte, G. (eds.), Transportation, Handbook in Operations Research and Management Science, Vol. 14, Amsterdam: Elsevier, pp. 367–428.Google Scholar
4.Dantzig, G. & Ramser, R. (1959). The truck dispatching problem. Management Science 6: 80–91.CrossRefGoogle Scholar
5.Kyriakidis, E.G. & Dimitrakos, T.D. (2008). Single vehicle routing problem with a predefined customer sequence and stochastic continuous demands. Mathematical Scientist 33: 148–152.Google Scholar
6.Laporte, G. (1992). The vehicle routing problem: an overview of exact and approximate algorithms. European Journal of Operational Research 59: 345–358.CrossRefGoogle Scholar
7.Laporte, G. (2009). Fifty years of vehicle routing. Transportation Science 43: 408–416.CrossRefGoogle Scholar
8.Liong, C.Y., Wan Rosmanira, I., Khairuddin, O., & Zirour, M. (2008). Vehicle routing problem: models and solutions. Journal of Quality Measurement and Analysis 4: 205–218.Google Scholar
9.Pandelis, D.G., Kyriakidis, E.G., & Dimitrakos, T.D. (2012). Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands. European Journal of Operational Research 217: 324–332.CrossRefGoogle Scholar
10.Rembold, U., Blume, C., & Dillmann, R. (1985). Computer integrated manufacturing technology and systems. New York: Marcel Dekker.Google Scholar
11.Ross, S.M. (1992). Applied probability models with optimization applications. New York: Dover.Google Scholar
12.Secomandi, N. & Margot, F. (2009). Reoptimization approaches for the vehicle-routing problem with stochastic demands. Operations Research 57: 214–230.CrossRefGoogle Scholar
13.Simchi-Levi, D., Chen, X., & Bramel, J. (2005). The logic of logistics. Theory, algorithms and applications for logistics and supply chain management. New York: Springer.Google Scholar
14.Tatarakis, A. (2007). A class of single vehicle routing problems with predefined customer sequence and depot returns. Ph.D. thesis, Department of Financial and Management Engineering, University of the Aegean, Chios, Greece. Available from http://fidelity.fme.aegean.gr/deopsys/files/A.Tatarakis%PhD.pdf.Google Scholar
15.Tatarakis, A. & Minis, I. (2009). Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns. European Journal of Operational Research 197: 557–571.CrossRefGoogle Scholar
16.Tijms, H.C. (1994). Stochastic models: an algorithmic approach. New York: Wiley.Google Scholar
17.Toth, P. & Vigo, D. (Eds.) (2002). The vehicle routing problem. Philadelphia, PA: Siam.CrossRefGoogle Scholar
18.Tsirimpas, P., Tatarakis, A., Minis, I., & Kyriakidis, E.G. (2008). Single vehicle routing with a predefined customer sequence and multiple depot returns. European Journal of Operational Research 187: 483–495.CrossRefGoogle Scholar
19.Yang, W.-H., Mathur, K., & Ballou, R.H. (2000). Stochastic vehicle routing problem with restocking. Transportation Science 34: 99–112.CrossRefGoogle Scholar