The assortment problem: A survey

The assortment or catalog problem involves determining which of the possible set of sizes or qualities of some product should be stocked when it is not possible or desirable to stock all of them and substitution in one direction (larger for smaller or higher-quality for lower-quality) is possible at some cost. We review the work published on this topic over the last 50 years.

[1]  Ram Akella,et al.  Single-Period Multiproduct Inventory Models with Substitution , 1999, Oper. Res..

[2]  K. Littlewood..  Special Issue Papers: Forecasting and control of passenger bookings , 2005 .

[3]  Narendra Agrawal,et al.  Management of Multi-Item Retail Inventory Systems with Demand Substitution , 2000, Oper. Res..

[4]  Barrie M. Baker.  A spreadsheet modelling approach to the assortment problem , 1999, Eur. J. Oper. Res..

[5]  Peter Tryfos,et al.  An Integer Programming Approach to the Apparel Sizing Problem , 1986 .

[6]  Jeffrey I. McGill,et al.  Airline Seat Allocation with Multiple Nested Fare Classes , 1993, Oper. Res..

[7]  Peter Tryfos,et al.  Technical Note - On the Optimal Choice of Sizes , 1985, Oper. Res..

[8]  M. L. Chambers,et al.  The Cutting Stock Problem in the Flat Glass Industry - Selection of Stock Sizes , 1976 .

[9]  E. Page,et al.  A Note on a Two-dimensional Dynamic Programming Problem , 1975 .

[10]  Wieslaw Sadowski,et al.  A Few Remarks on the Assortment Problem , 1959 .

[11]  Douglas R Shier.  Mathematical models for selecting catalogs of standard-sized items , 1978 .

[12]  Nils Boysen,et al.  Jena Research Papers in Business and Economics A general solution framework for component commonality problems , 2008 .

[13]  M. L. Wolfson.  Selecting the Best Lengths to Stock , 1965 .

[14]  D. W. Pentico,et al.  The Assortment Problem with Probabilistic Demands , 1974 .

[15]  K. Talluri,et al.  The Theory and Practice of Revenue Management , 2004 .

[16]  Jr. Charles R. Frank,et al.  A Note on the Assortment Problem , 1965 .

[17]  David W. Pentico,et al.  The assortment problem with dynamic deterministic demands and stationary stocking-substitution policies , 2008 .

[18]  Genaro J. Gutierrez,et al.  Effect of increasing component commonality on service level and holding cost , 1992 .

[19]  Yehuda Bassok,et al.  Random Yield and Random Demand in a Production System with Downward Substitution , 1999, Oper. Res..

[20]  Garrett J. van Ryzin,et al.  Stocking Retail Assortments Under Dynamic Consumer Substitution , 2001, Oper. Res..

[21]  Renwick E. Curry,et al.  Optimal Airline Seat Allocation with Fare Classes Nested by Origins and Destinations , 1990, Transp. Sci..

[22]  Peter Paul Belobaba,et al.  Air travel demand and airline seat inventory management , 1987 .

[23]  P. K. Agrawal.  Determining stock-sheet-sizes to minimise trim loss , 1993 .

[24]  G. F. Newell.  Dispatching Policies for a Transportation Route , 1971 .

[25]  Z. Drezner,et al.  An EOQ Model with Substitutions Between Products , 1995 .

[26]  Ulrich Wilhelm Thonemann,et al.  Optimal Commonality in Component Design , 2000, Oper. Res..

[27]  Zvi Drezner,et al.  Deterministic hierarchical substitution inventory models , 2000, J. Oper. Res. Soc..

[28]  Haldun Süral,et al.  Multidimensional assortment problem with an application , 1999, Networks.

[29]  Richard D. Wollmer,et al.  An Airline Seat Management Model for a Single Leg Route When Lower Fare Classes Book First , 1992, Oper. Res..

[30]  David W. Pentico,et al.  The Assortment Problem with Nonlinear Cost Functions , 1976, Oper. Res..

[31]  Lawrence W. Robinson,et al.  Optimal and Approximate Control Policies for Airline Booking with Sequential Nonmonotonic Fare Classes , 1995, Oper. Res..

[32]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[33]  Guillermo Gallego,et al.  Semiconductor inventory management with multiple grade parts and downgrading , 2006 .

[34]  David W. Pentico,et al.  The Discrete Two-Dimensional Assortment Problem , 1988, Oper. Res..

[35]  Jayashankar M. Swaminathan,et al.  Multi-product inventory planning with downward substitution, stochastic demand and setup costs , 2004 .

[36]  Friedrich Hanssmann.  Determination of Optimal Capacities of Service for Facilities with a Linear Measure of Inefficiency , 1957 .

[37]  David P. Rutenberg,et al.  Design Commonality to Reduce Multi-Item Inventory: Optimal Depth of a Product Line , 1971, Oper. Res..

[38]  R. Phillips,et al.  Pricing and Revenue Optimization , 2005 .

[39]  A. I. Hinxman.  The trim-loss and assortment problems: A survey , 1980 .

[40]  James E. Ward,et al.  A parts selection model with one-way substitution , 1994 .

[41]  Peter Belobaba,et al.  OR Practice - Application of a Probabilistic Decision Model to Airline Seat Inventory Control , 1989, Oper. Res..

[42]  R. Bellman.  Dynamic programming. , 1957, Science.

[43]  C. Bongers.  Optimal Size Selection in Standardization: A Case Study , 1982 .