Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach

We propose the use of robust optimization (RO) as a powerful methodology for multiperiod stochastic operations management problems. In particular, we study a two-echelon multiperiod supply chain problem, known as the retailer-supplier flexible commitment (RSFC) problem with uncertain demand that is only known to reside in some uncertainty set. We adopt a min-max criterion, whereby the cost function is minimized against the worst case demand occurrence. To solve the min-max RSFC problem we employ a recent extension of the RO method adapted to dynamic decision problems and known as the affinely adjustable robust counterpart (AARC) methodology. The AARC solution is tested by a large simulation study and found to provide excellent results.

[1]  H. Scarf.  THE OPTIMALITY OF (S,S) POLICIES IN THE DYNAMIC INVENTORY PROBLEM , 1959 .

[2]  C. C. Holt,et al.  Planning Production, Inventories, and Work Force. , 1962 .

[3]  Jr. Arthur F. Veinott.  The Status of Mathematical Inventory Theory , 1966 .

[4]  James P. Monahan.  A Quantity Discount Pricing Model to Increase Vendor Profits , 1984 .

[5]  P. Schweitzer,et al.  Generalized polynomial approximations in Markovian decision processes , 1985 .

[6]  Lawrence W. Robinson,et al.  Optimal and Approximate Policies in Multiperiod, Multilocation Inventory Models with Transshipments , 1990, Oper. Res..

[7]  Marshall L. Fisher,et al.  Reducing the Cost of Demand Uncertainty Through Accurate Response to Early Sales , 1996, Oper. Res..

[8]  Yunzeng Wang,et al.  Periodic review production models with variable capacity, random yield, and uncertain demand , 1996 .

[9]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[10]  Arkadi Nemirovski,et al.  Robust Truss Topology Design via Semidefinite Programming , 1997, SIAM J. Optim..

[11]  Ramesh Srinivasan,et al.  Design of component-supply contract with commitment-revision flexibility , 1997, IBM J. Res. Dev..

[12]  Ravi Anupindi,et al.  Analysis of supply contracts with total minimum commitment , 1997 .

[13]  K. Talluri,et al.  An Analysis of Bid-Price Controls for Network Revenue Management , 1998 .

[14]  Ravi Anupindi,et al.  Approximations for multiproduct contracts with stochastic demands and business volume discounts: single supplier case , 1998 .

[15]  Ravi Anupindi,et al.  Supply Contracts with Quantity Commitments and Stochastic Demand , 1999 .

[16]  William S. Lovejoy,et al.  Quantity Flexibility Contracts and Supply Chain Performance , 1999, Manuf. Serv. Oper. Manag..

[17]  Arkadi Nemirovski,et al.  Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions , 1999, SIAM J. Optim..

[18]  Arkadi Nemirovski,et al.  Robust solutions of Linear Programming problems contaminated with uncertain data , 2000, Math. Program..

[19]  Arkadi Nemirovski,et al.  Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions , 1999, SIAM Rev..

[20]  G. Gallego,et al.  Perishable Asset Revenue Management with Markovian Time Dependent Demand Intensities , 2000 .

[21]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[22]  Marshall L. Fisher,et al.  Ending Inventory Valuation in Multiperiod Production Scheduling , 2001, Manag. Sci..

[23]  Dmitry Krass,et al.  Analysis of supply contracts with minimum total order quantity commitments and non-stationary demands , 2001, Eur. J. Oper. Res..

[24]  Arkadi Nemirovski,et al.  Robust optimization – methodology and applications , 2002, Math. Program..

[25]  A. Ben-Tal,et al.  Adjustable robust solutions of uncertain linear programs , 2004, Math. Program..

[26]  Vineet Padmanabhan,et al.  Comments on "Information Distortion in a Supply Chain: The Bullwhip Effect" , 1997, Manag. Sci..

[27]  Dimitris Bertsimas,et al.  A Robust Optimization Approach to Supply Chain Management , 2004, IPCO.

[28]  Jean-Philippe Vial,et al.  A practical implementation of stochastic programming: an application to the evaluation of option contracts in supply chains , 2004, Autom..

[29]  Garud Iyengar,et al.  Robust Dynamic Programming , 2005, Math. Oper. Res..