On Integral Policies in Deterministic and Stochastic Distribution Systems

Yang Bo (), Milind Dawande (), Ganesh Janakiraman () and S. Thomas McCormick ()
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Yang Bo: Department of Decision Sciences and Managerial Economics, CUHK Business School, The Chinese University of Hong Kong, Shatin, Hong Kong
Milind Dawande: Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080
Ganesh Janakiraman: Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080
S. Thomas McCormick: Sauder School of Business, The University of British Columbia, Vancouver, British Columbia V6T 1Z2

Operations Research, 2017, vol. 65, issue 3, 703-711

Abstract: The “integrality” question for dynamic optimization models of inventory control asks if there exists an integral optimal policy, given integral initial inventory levels, capacities, and demand realizations. One practical implication of this question lies in whether or not full-truckload (FTL) shipping is optimal if customer demand is in integral number of truckloads. In this paper, we investigate the integrality question in single-product, multiechelon distribution systems and show that integrality holds under deterministic demand but fails to hold under stochastic demand. In distribution systems with stochastic demand, less-than-truckload (LTL) shipping can be significantly cheaper than the cost of the optimal FTL shipping policy, even in the presence of economies of scale. For instance, this occurs in settings where shipping costs are expected to increase in the future and/or inventories are more expensive to hold upstream than downstream. In such situations, our results highlight the importance of strategically positioning inventory: LTL shipments can offer a more balanced allocation of inventory across the distribution network, leading to benefits that can exceed the savings from FTL shipments due to economies of scale. However, when the cost parameters are fairly constant across time and inventory holding costs are not significantly higher upstream than downstream, then the difference between the costs of optimal FTL and optimal LTL shipping is provably marginal.

Keywords: integrality; inventory models; distribution systems (search for similar items in EconPapers)
Date: 2017
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