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Analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices

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  • Konur, Dinçer
  • Toptal, Ayşegül

Abstract

In this study, we analyze the replenishment decision of a buyer with the objective of maximizing total expected profits. The buyer faces stepwise freight costs in inbound transportation and a hybrid wholesale price schedule given by a combination of all-units discounts with economies and diseconomies of scale. This general cost structure enables the model and the proposed solution to be also used for the supplier selection of a buyer under the single sourcing assumption. We show that the buyer's replenishment problem reduces to finding and comparing the solutions of the following two subproblems: (i) a replenishment problem involving wholesale prices given by an all-units discount schedule with economies of scale and a lower bound on the replenishment quantity, and (ii) a replenishment problem involving wholesale prices given by an all-units discount schedule with diseconomies of scale and an upper bound on the replenishment quantity. We propose solution methods for these two subproblems, each of which stands alone as practical problems, and utilize these methods to optimally solve the buyer's replenishment problem.

Suggested Citation

  • Konur, Dinçer & Toptal, Ayşegül, 2012. "Analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices," International Journal of Production Economics, Elsevier, vol. 140(1), pages 521-529.
    • Handle: RePEc:eee:proeco:v:140:y:2012:i:1:p:521-529
    DOI: 10.1016/j.ijpe.2012.07.003
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    Cited by:

    1. Schaefer, Brian & Konur, Dinçer, 2015. "Economic and environmental considerations in a continuous review inventory control system with integrated transportation decisions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 142-165.
    2. Saravanan Venkatachalam & Arunachalam Narayanan, 2016. "Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost," International Journal of Production Research, Taylor & Francis Journals, vol. 54(14), pages 4087-4103, July.
    3. Dinçer Konur & Joseph Geunes, 2019. "Integrated districting, fleet composition, and inventory planning for a multi-retailer distribution system," Annals of Operations Research, Springer, vol. 273(1), pages 527-559, February.
    4. Andrew Manikas & Michael Godfrey, 2018. "A Spreadsheet Approach For Incorporating Actual Motor Carrier Freight Rates And External Environmental Costs In A Newsvendor Model," International Journal of Management and Marketing Research, The Institute for Business and Finance Research, vol. 11(1), pages 55-72.
    5. Konur, Dinçer, 2014. "Carbon constrained integrated inventory control and truckload transportation with heterogeneous freight trucks," International Journal of Production Economics, Elsevier, vol. 153(C), pages 268-279.

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