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The traveling purchaser problem with stochastic prices: Exact and approximate algorithms

Listed author(s):
  • Kang, Seungmo
  • Ouyang, Yanfeng
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    The paper formulates an extension of the traveling purchaser problem where multiple types of commodities are sold at spatially distributed locations with stochastic prices (each following a known probability distribution). A purchaser's goal is to find the optimal routing and purchasing strategies that minimize the expected total travel and purchasing costs needed to purchase one unit of each commodity. The purchaser reveals the actual commodity price at a seller upon arrival, and then either purchases the commodity at the offered price, or rejects the price and visits a next seller. In this paper, we propose an exact solution algorithm based on dynamic programming, an iterative approximate algorithm that yields bounds for the minimum total expected cost, and a greedy heuristic for fast solutions to large-scale applications. We analyze the characteristics of the problem and test the computational performance of the proposed algorithms. The numerical results show that the approximate and heuristic algorithms yield near-optimum strategies and very good estimates of the minimum total cost.

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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 209 (2011)
    Issue (Month): 3 (March)
    Pages: 265-272

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    Handle: RePEc:eee:ejores:v:209:y:2011:i:3:p:265-272
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    1. Leipala, Timo, 1978. "On the solutions of stochastic traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 2(4), pages 291-297, July.
    2. Bianchi, Leonora & Campbell, Ann Melissa, 2007. "Extension of the 2-p-opt and 1-shift algorithms to the heterogeneous probabilistic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 131-144, January.
    3. Liu, Yu-Hsin, 2008. "Diversified local search strategy under scatter search framework for the probabilistic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 332-346, December.
    4. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    5. Singh, Kashi N. & van Oudheusden, Dirk L., 1997. "A branch and bound algorithm for the traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 97(3), pages 571-579, March.
    6. Renaud, Jacques & Boctor, Fayez F., 1998. "An efficient composite heuristic for the symmetric generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 108(3), pages 571-584, August.
    7. Golden, Bruce & Levy, Larry & Dahl, Roy, 1981. "Two generalizations of the traveling salesman problem," Omega, Elsevier, vol. 9(4), pages 439-441.
    8. Bertsimas, Dimitris & Howell, Louis H., 1993. "Further results on the probabilistic traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 65(1), pages 68-95, February.
    9. Snyder, Lawrence V. & Daskin, Mark S., 2006. "A random-key genetic algorithm for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 174(1), pages 38-53, October.
    10. Jason D. Papastavrou & Srikanth Rajagopalan & Anton J. Kleywegt, 1996. "The Dynamic and Stochastic Knapsack Problem with Deadlines," Management Science, INFORMS, vol. 42(12), pages 1706-1718, December.
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