{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T06:05:43Z","timestamp":1768457143193,"version":"3.49.0"},"reference-count":63,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,13]],"date-time":"2021-02-13T00:00:00Z","timestamp":1613174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education in Poland under the programme &quot;Regional Initiative of Excellence&quot; 2019 - 2022","award":["project number 015\/RID\/2018\/19, total funding amount 10,721,040,00 PLN."],"award-info":[{"award-number":["project number 015\/RID\/2018\/19, total funding amount 10,721,040,00 PLN."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Shelf space on which products are exhibited is a scarce resource in the retail environment. Retailers regularly make decisions related to allocating products to their outlets\u2019 limited shelf space. The aim of the paper was to develop a practical shelf space allocation model offering the possibility of horizontal and vertical product grouping, representing an item (product) with facings, capping, and nesting, with the objective of maximizing the retailer\u2019s profit. Because real category-management problems address a lot of retailer\u2019s rules, we expanded the basic shelf space allocation model, using shelf constraints, product constraints, multi-shelves constraints, and category constraints. To solve the problem, we proposed two adjustable methods that allowed us to achieve good results within a short time interval. The validity of algorithms was estimated, using the CPLEX solver and illustrated with example problems. Experiments were performed on data generated on the basis of real retail values. To estimate the performance of the proposed approach, 45 cases were tested. Among them, the proposed approach found solutions in 34 cases, while CPLEX found solutions only in 23 cases. The profit ratio of the proposed approach is, on average, 94.57%, with minimal and maximal values of 86.80% and 99.84%, accordingly.<\/jats:p>","DOI":"10.3390\/sym13020314","type":"journal-article","created":{"date-parts":[[2021,2,14]],"date-time":"2021-02-14T05:54:49Z","timestamp":1613282089000},"page":"314","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Heuristic Approach to Shelf Space Allocation Decision Support Including Facings, Capping, and Nesting"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1808-6020","authenticated-orcid":false,"given":"Kateryna","family":"Czerniachowska","sequence":"first","affiliation":[{"name":"Department of Process Management, Wroclaw University of Economics and Business, 53-345 Wroclaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3832-8154","authenticated-orcid":false,"given":"Marcin","family":"Hernes","sequence":"additional","affiliation":[{"name":"Department of Process Management, Wroclaw University of Economics and Business, 53-345 Wroclaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1287\/mnsc.1030.0165","article-title":"Metaheuristics with Local Search Techniques for Retail Shelf-Space Optimization","volume":"50","author":"Lim","year":"2004","journal-title":"Manag. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0925-5273(98)00134-0","article-title":"Study on shelf space allocation and management","volume":"60\u201361","author":"Yang","year":"1999","journal-title":"Int. J. Prod. Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.ejor.2006.07.004","article-title":"Goal programming model for grocery shelf space allocation","volume":"181","author":"Reyes","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"H\u00fcbner, A. (2011). Retail Category Management: Decision Support Systems for Assortment, Shelf Space, Inventory and Price Planning, Springer.","DOI":"10.1007\/978-3-642-22477-5"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0377-2217(99)00448-8","article-title":"Efficient algorithm to allocate shelf space","volume":"131","author":"Yang","year":"2001","journal-title":"Eur. J. Oper. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0022-4359(94)90002-7","article-title":"Shelf management and space elasticity","volume":"70","author":"Hoch","year":"1994","journal-title":"J. Retail."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1108\/09590551111109094","article-title":"Heuristics for retail shelf space allocation problem with linear profit function","volume":"29","author":"Gajjar","year":"2011","journal-title":"Int. J. Retail Distrib. Manag."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Frontoni, E., Contigiani, M., and Ribighini, G. (2014, January 10\u201312). A heuristic approach to evaluate occurrences of products for the planogram maintenance. Proceedings of the MESA 2014\u201410th IEEE\/ASME International Conference on Mechatronic and Embedded Systems and Applications, Senigallia, Italy.","DOI":"10.1109\/MESA.2014.6935615"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s10479-008-0497-9","article-title":"A model and case study for efficient shelf usage and assortment analysis","volume":"180","author":"Fadiloglu","year":"2010","journal-title":"Ann. Oper. Res."},{"key":"ref_10","first-page":"99","article-title":"Retail shelf space allocation analysis using system dynamics approach","volume":"9","author":"Jajja","year":"2013","journal-title":"J. Qual. Technol. Manag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.omega.2016.07.001","article-title":"A shelf-space optimization model when demand is stochastic and space-elastic","volume":"68","author":"Schaal","year":"2017","journal-title":"Omega"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.ejor.2017.01.039","article-title":"An integrated assortment and shelf-space optimization model with demand substitution and space-elasticity effects","volume":"261","author":"Schaal","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","first-page":"100","article-title":"Center of Orientation: Effect of Vertical and Horizontal Shelf Space Product Position","volume":"36","author":"Valenzuela","year":"2009","journal-title":"ACR N. Am. Adv."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.jretai.2006.08.009","article-title":"Adding consumer behavior insights to category management: Improving item placement decisions","volume":"82","author":"Desrochers","year":"2006","journal-title":"J. Retail."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1287\/opre.22.1.13","article-title":"Mathematical Model for Simultaneously Determining the Optimal Brand-Collection and Display-Area Allocation","volume":"22","author":"Anderson","year":"1974","journal-title":"Oper. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/0377-2217(79)90030-4","article-title":"Product selection and space allocation in supermarkets","volume":"3","author":"Hansen","year":"1979","journal-title":"Eur. J. Oper. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1287\/mnsc.27.7.822","article-title":"A Model for Optimizing Retail Space Allocations","volume":"27","author":"Corstjens","year":"1981","journal-title":"Manag. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1057\/jors.1986.69","article-title":"A dynamic programming approach for product selection and supermarket shelf-space allocation","volume":"37","author":"Zufryden","year":"1986","journal-title":"J. Oper. Res. Soc."},{"key":"ref_19","first-page":"153","article-title":"Vanden Asymmetric cannibalism in retail assortments","volume":"65","author":"Bultez","year":"1989","journal-title":"J. Retail."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1111\/j.1540-5915.1994.tb01848.x","article-title":"A Model for Determining Retail Product Category Assortment and Shelf Space Allocation","volume":"25","author":"Borin","year":"1994","journal-title":"Decis. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/0022-4359(95)90005-5","article-title":"A sensitivity analysis of retailer shelf management models","volume":"71","author":"Borin","year":"1995","journal-title":"J. Retail."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/S0022-4359(99)80086-4","article-title":"An inventory-theoretic approach to product assortment and shelf-space allocation","volume":"74","author":"Urban","year":"1998","journal-title":"J. Retail."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1016\/S0305-0548(00)00035-6","article-title":"A fast algorithm for assortment optimization problems","volume":"28","author":"Li","year":"2001","journal-title":"Comput. Oper. Res."},{"key":"ref_24","unstructured":"Moholkar, M., and Sanjeev, S. (2001, January 27\u201329). A Genetic Algorithm Based Approach to Unequal Capacity Scheduling in Complex Retail Environments. Proceedings of the ORSI International Conference, Ahmedabad, India."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/S0377-2217(01)00021-2","article-title":"The impact of product substitution on retail merchandising","volume":"135","author":"Rajaram","year":"2001","journal-title":"Eur. J. Oper. Res."},{"key":"ref_26","unstructured":"Rodrigues, B., Lim, A., and Qian, Z. (2002, January 9\u201311). A Heuristic for Shelf Space Decision Support in the Retail Industry. Proceedings of the American Conference on Information Systems AMCIS 2002 Proceedings, Dallas, TX, USA."},{"key":"ref_27","first-page":"87","article-title":"An investigation of automated planograms using a simulated annealing based hyper-heuristic","volume":"32","author":"Bai","year":"2005","journal-title":"Oper. Res. Comput. Sci. Interfaces Ser."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.ijpe.2004.07.003","article-title":"A model for shelf space allocation and inventory control considering location and inventory level effects on demand","volume":"97","author":"Hwang","year":"2005","journal-title":"Int. J. Prod. Econ."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Esparcia-Alcazar, A.I., Lluch-Revert, L., Sharman, K.C., Albarracin-Guillem, J.M., and Palmer-Gato, M.E. (2006, January 8\u201312). Towards an evolutionary tool for the allocation of supermarket shelf space. Proceedings of the Eighth Annual Conference on Genetic and Evolutionary Computation, GECCO 2006, Proceedings, Seattle, WA, USA.","DOI":"10.1145\/1143997.1144269"},{"key":"ref_30","unstructured":"Esparcia-Al\u0107azar, A.I., Lluch-Revert, L., Sharman, K., Albarrac\u00edn-Guillem, J.M., and Palmer-Gato, M.E. (2006, January 16\u201321). An Evolutionary Algorithm for the Product to Shelf Allocation Problem. Proceedings of the IEEE Congress on Evolutionary Computation (CEC), Vancouver, BC, Canada."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1287\/opre.1070.0409","article-title":"Demand estimation and assortment optimization under substitution: Methodology and application","volume":"55","author":"Fisher","year":"2007","journal-title":"Oper. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.ejor.2006.12.067","article-title":"Retail replenishment models with display-space elastic demand","volume":"186","author":"Abbott","year":"2008","journal-title":"Eur. J. Oper. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1287\/ijoc.1070.0219","article-title":"A model for fresh produce shelf-space allocation and inventory management with freshness-condition-dependent demand","volume":"20","author":"Bai","year":"2008","journal-title":"INFORMS J. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Esparcia-Alc\u00e1zar, A.I., Mart\u00ednez-Garc\u00eda, A.I., Albarrac\u00edn-Guillem, J.M., Palmer-Gato, M.E., Merelo, J.J., Sharman, K.C., and Alfaro-Cid, E. (2008). A multiobjective evolutionary algorithm for the linear shelf space allocation problem. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer.","DOI":"10.1007\/978-3-540-87700-4_99"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1287\/mksc.1080.0365","article-title":"Interaction between shelf layout and marketing effectiveness and its impact on optimizing shelf arrangements","volume":"27","author":"Fok","year":"2008","journal-title":"Mark. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/j.cie.2008.09.012","article-title":"A genetic algorithm approach to an integrated problem of shelf space design and item allocation","volume":"56","author":"Hwang","year":"2009","journal-title":"Comput. Ind. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Landa-Silva, D., Marikar, F., and Le, K. (2009, January 9\u201312). Heuristic approach for automated shelf space allocation. Proceedings of the ACM Symposium on Applied Computing (SAC), Honolulu, HI, USA.","DOI":"10.1145\/1529282.1529482"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s10479-008-0455-6","article-title":"A piecewise linearization for retail shelf space allocation problem and a local search heuristic","volume":"179","author":"Gajjar","year":"2010","journal-title":"Ann. Oper. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.jretai.2010.01.004","article-title":"Retail Shelf Allocation: A Comparative Analysis of Heuristic and Meta-Heuristic Approaches","volume":"86","author":"Hansen","year":"2010","journal-title":"J. Retail."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.jretai.2010.02.006","article-title":"Retailer Dynamic Pricing and Ordering Decisions: Category Management versus Brand-by-Brand Approaches","volume":"86","author":"Hall","year":"2010","journal-title":"J. Retail."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.jretai.2010.02.008","article-title":"Joint Optimization of Product Price, Display Orientation and Shelf-Space Allocation in Retail Category Management","volume":"86","author":"Murray","year":"2010","journal-title":"J. Retail."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s10479-008-0450-y","article-title":"The location and allocation of products and product families on retail shelves","volume":"179","author":"Russell","year":"2010","journal-title":"Ann. Oper. Res."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ozcan, T., and Esnaf, S. (2011, January 5\u20138). A heuristic approach based on artificial bee colony algorithm for retail shelf space optimization. Proceedings of the2011 IEEE Congress on Evolutionary Computation (CEC), New Orleans, LA, USA.","DOI":"10.1109\/CEC.2011.5949604"},{"key":"ref_44","first-page":"446","article-title":"Retail space design considering revenue and adjacencies using a racetrack aisle network","volume":"44","author":"Yapicioglu","year":"2012","journal-title":"IIE Trans. Inst. Ind. Eng."},{"key":"ref_45","first-page":"77","article-title":"An approach to products placement in supermarkets using PrefixSpan algorithm","volume":"25","author":"Aloysius","year":"2013","journal-title":"J. King Saud Univ. Comput. Inf. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10288-012-0211-2","article-title":"A new model and a hyper-heuristic approach for two-dimensional shelf space allocation","volume":"11","author":"Bai","year":"2013","journal-title":"4OR"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Pinto, F., and Soares, C. (2013). Space allocation in the retail industry: A decision support system integrating evolutionary algorithms and regression models. Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Springer.","DOI":"10.1007\/978-3-642-40994-3_34"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.orl.2014.06.002","article-title":"Genetic algorithm with variable neighborhood search for the optimal allocation of goods in shop shelves","volume":"42","author":"Castelli","year":"2014","journal-title":"Oper. Res. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Chen, Y.K., Chiu, F.R., and Yang, C.J. (2014). An optimization model for product placement on product listing pages. Adv. Oper. Res.","DOI":"10.1155\/2014\/357693"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Erol, H., Bulkan, S., and Agaoglu, M. (2015). A Heuristic Approach for Shelf Space Allocation Problem. J. Mil. Inf. Sci., 4.","DOI":"10.17858\/jmisci.89213"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1111\/poms.12316","article-title":"Maximizing Revenue through Two-Dimensional Shelf-Space Allocation","volume":"24","author":"Geismar","year":"2015","journal-title":"Prod. Oper. Manag."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"149","DOI":"10.3233\/IDA-150775","article-title":"Combining regression models and metaheuristics to optimize space allocation in the retail industry","volume":"19","author":"Pinto","year":"2015","journal-title":"Intell. Data Anal."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1287\/inte.2016.0859","article-title":"Using analytics to enhance a food retailer\u2019s shelf-space management","volume":"46","author":"Silva","year":"2016","journal-title":"Interfaces"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.eswa.2016.01.043","article-title":"Formulation of customers\u2019 shopping path in shelf space planning: A simulation-optimization approach","volume":"55","author":"Ghazavi","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s10898-014-0238-3","article-title":"Optimizing assortment and pricing of multiple retail categories with cross-selling","volume":"66","author":"Ghoniem","year":"2016","journal-title":"J. Glob. Optim."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.ejor.2015.11.007","article-title":"An efficient algorithm for capacitated assortment planning with stochastic demand and substitution","volume":"250","author":"Kuhn","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.omega.2017.08.015","article-title":"When does cross-space elasticity matter in shelf-space planning? A decision analytics approach","volume":"80","author":"Schaal","year":"2018","journal-title":"Omega"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.omega.2017.10.006","article-title":"Integrated assortment planning and store-wide shelf space allocation: An optimization-based approach","volume":"81","author":"Flamand","year":"2018","journal-title":"Omega"},{"key":"ref_59","first-page":"1","article-title":"A new optimization model for market basket analysis with allocation considerations: A genetic algorithm solution approach","volume":"12","author":"Heydari","year":"2017","journal-title":"Manag. Mark."},{"key":"ref_60","first-page":"53529","article-title":"Floor Layout Optimization Using Genetic Algorithm","volume":"9","author":"Choubey","year":"2017","journal-title":"Int. J. Curr. Res."},{"key":"ref_61","first-page":"53529","article-title":"Profit maximizing through 3D shelf space allocation of 2D display orientation items with variable heights of the shelves","volume":"9","author":"Rabbani","year":"2018","journal-title":"OPSEARCH"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.ejor.2019.09.012","article-title":"A practical approach to the shelf-space allocation and replenishment problem with heterogeneously sized shelves","volume":"282","author":"Schaal","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"106420","DOI":"10.1016\/j.cie.2020.106420","article-title":"A reduced variable neighborhood search-based hyperheuristic for the shelf space allocation problem","volume":"143","author":"Yu","year":"2020","journal-title":"Comput. Ind. 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