Joint inventory control across products with supply uncertainty and responsive pricing

We study sourcing and responsive pricing decisions of a firm with two correlated products and price-dependent demand when supply capacities for these two products are uncertain. Cross-price effects exist between the two products, which means that the demand of each product depends on the prices of both products. First, we apply the tool of convexity and some recent results to establish the convexity of the value-to-go function during each period; then we use KKT conditions and some structural properties given by convexity to derive structural results of the optimal order policy for these two correlated products in a periodic review setting. Contrary to the classical “base-stock” policy derived in the literature for single product or multiple products without uncertain supply capacity, we show that the optimal order policy in our inventory control problem is complicated and it follows the “order-up-to” structural property only under some conditions. Numerical studies are carried out to present the structural properties of the optimal order policy and show the effect of the complementarity or substitutability on the profits.

[1]  Paul H. Zipkin.  On the Structure of Lost-Sales Inventory Models , 2008, Oper. Res..

[2]  Pinar Keskinocak,et al.  Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions , 2003, IEEE Engineering Management Review.

[3]  Brigitte Maier,et al.  Supermodularity And Complementarity , 2016 .

[4]  David Simchi-Levi,et al.  Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case , 2004, Math. Oper. Res..

[5]  Christopher S. Tang,et al.  Responsive pricing under supply uncertainty , 2007, Eur. J. Oper. Res..

[6]  David Simchi-Levi,et al.  Coordinating inventory control and pricing strategies: The continuous review model , 2006, Oper. Res. Lett..

[7]  Jinxing Xie,et al.  Inventory management for dual sales channels with inventory-level-dependent demand , 2015, J. Oper. Res. Soc..

[8]  U. W. Thonemann,et al.  Coordination of pricing and inventory control across products , 2009 .

[9]  Qi Feng,et al.  Integrating Dynamic Pricing and Replenishment Decisions Under Supply Capacity Uncertainty , 2010, Manag. Sci..

[10]  T. Morton,et al.  A periodic review, production planning model with uncertain capacity and uncertain demand—optimality of extended myopic policies , 1994 .

[11]  採編典藏組.  Society for Industrial and Applied Mathematics(SIAM) , 2008 .

[12]  Emmett J. Lodree,et al.  An insurance risk management framework for disaster relief and supply chain disruption inventory planning , 2008, J. Oper. Res. Soc..

[13]  Izak Duenyas,et al.  Dynamic Pricing of Substitutable Products in the Presence of Capacity Flexibility , 2012, Manuf. Serv. Oper. Manag..

[14]  Kazuo Murota,et al.  Discrete convex analysis , 1998, Math. Program..

[15]  S. Sethi,et al.  Supply Diversification with Responsive Pricing , 2011 .

[16]  K. Kogan,et al.  Optimal policies for inventory usage, production and pricing of fashion goods over a selling season , 2006, J. Oper. Res. Soc..

[17]  Claudio Barbieri da Cunha,et al.  The logic of logistics: theory, algorithms and applications for logistics management , 1999 .

[18]  Lijun Ma,et al.  Loss-averse newsvendor problem with supply risk , 2016, J. Oper. Res. Soc..

[19]  T. M. Whitin.  Inventory Control and Price Theory , 1955 .

[20]  Izak Duenyas,et al.  Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity , 2005, Oper. Res..

[21]  Woonghee Tim Huh,et al.  (s, S) Optimality in Joint Inventory-Pricing Control: An Alternate Approach , 2008, Oper. Res..

[22]  Xin Chen,et al.  Technical Note - Preservation of Supermodularity in Parametric Optimization Problems with Nonlattice Structures , 2013, Oper. Res..

[23]  Panos Kouvelis,et al.  Responsive Pricing Newsvendor Networks with Discretionary Commonality , 2017 .

[24]  Xiangyu Gao,et al.  Preservation of Structural Properties in Optimization with Decisions Truncated by Random Variables and Its Applications , 2018, Oper. Res..

[25]  D. Simchi-Levi,et al.  Coordination of Pricing and Inventory Decisions: A Survey and Classification , 2004 .

[26]  Dogan A. Serel,et al.  Optimal resource acquisition policy for a newsvendor under supply risk , 2014, J. Oper. Res. Soc..

[27]  Awi Federgruen,et al.  Combined Pricing and Inventory Control Under Uncertainty , 1999, Oper. Res..

[28]  Christopher S. Tang,et al.  Strategic Approaches for Mitigating Supply Chain Risks , 2012 .

[29]  Jiri Chod,et al.  Resource Flexibility with Responsive Pricing , 2005, Oper. Res..

[30]  Jan A. Van Mieghem,et al.  Price Versus Production Postponement: Capacity and Competition , 1999 .

[31]  C. Yano,et al.  Coordinated Pricing and Production/Procurement Decisions: A Review , 2005 .

[32]  S. Gilbert.  Coordination of Pricing and Multiple-Period Production Across Multiple Constant Priced Goods , 2000 .

[33]  Xin Chen,et al.  Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case , 2004, Oper. Res..

[34]  Youhua Chen,et al.  TECHNICAL NOTE---A Computational Approach for Optimal Joint Inventory-Pricing Control in an Infinite-Horizon Periodic-Review System , 2011 .

[35]  Xiangyu Gao,et al.  A new approach to two-location joint inventory and transshipment control via L♮-convexity , 2015, Oper. Res. Lett..

[36]  Bill Canis,et al.  The Motor Vehicle Supply Chain: Effects of the Japanese Earthquake and Tsunami , 2011 .

[37]  L. Joseph Thomas.  Technical Note - Price and Production Decisions with Random Demand , 1974, Oper. Res..