[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86453-en":3,"doc-seo-86453-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86453,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Optimizing ARDL Models for Retail Sales Forecasting and Fair Pricing","Pricing food products to balance profitability with consumer welfare drives a core retail challenge. Dynamic pricing often increases revenue while neglecting consumer fairness, motivating a framework that embeds fairness constraints into retail sales forecasting. The approach models total retail trade sales using a log–log Autoregressive Distributed Lag (ARDL) specification, treats the product-price coefficient as sales elasticity, and maximizes forecast sales subject to CPI-anchored price bounds. It is solved via Linear Programming (LP) and Simulated Annealing (SA), benchmarked against common forecasting baselines, and clarified by CPI-deflated re-specification.","arXiv :2607 .09956v 1 [ cs .LG] 10 Jul 2026  \nOPTIMIZING ARDL MODELS FOR RETAIL SALES FORECASTING  \nAND FAIR PRICING  \nSujay Uday Rittikar  \nDepartment of Applied Computer Science  \nThe University of Winnipeg  \nWinnipeg, MB, Canada  \n[rittikar-s@webmail.uwinnipeg.ca](rittikar-s@webmail.uwinnipeg.ca)  \n[suj00rit20@gmail.com](suj00rit20@gmail.com)  \nJuly 14, 2026  \nABSTRACT  \nPricing food products to balance profitability with consumer welfare is a central challenge for retailers.  \nDynamic pricing is widely used to maximize revenue, yet most pricing models optimize business objectives while overlooking consumer fairness. This paper studies the risk of consumer exploitation under dynamic food pricing in Canada and proposes a methodology that embeds fairness constraints directly into retail sales forecasting. We model total retail trade sales with a log–log Autoregressive Distributed Lag (ARDL) specification, in which the coefficient on a product price is a sales elasticity, and pose the pricing problem as maximizing forecast sales subject to price bounds anchored to the Consumer Price Index (CPI) . We solve this problem with both Linear Programming (LP) and Simulated Annealing (SA), under single-product and multi-product configurations. A key finding is that the fitted nominal elasticities are positive. As a result, an unconstrained sales-maximizer would push every price to its upper bound, and the CPI ceiling is the safeguard that prevents this. Simulated Annealing instead settles on conservative, interior prices that lower consumer cost while still meeting the sales target. We benchmark forecast accuracy against naive, seasonal-naive, ARIMA, and SARIMA baselines, and a CPI-deflated re-specification shows that the positive nominal elasticities are largely an inflation-driven artifact. The result is a transparent, fairness-aware pricing framework.  \nKeywords Retail Sales Forecasting · Autoregressive Distributed Lag · Consumer Fairness · Price Elasticity · Linear Programming · Simulated Annealing · Metaheuristics  \n1 Introduction  \nRetail food prices are adjusted based on factors affecting a business’s revenue and sales, with dynamic pricing being a common strategy to optimize profits. This involves varying prices over time or across customer segments to maximize their revenue. While effective, dynamic pricing raises concerns about fairness [1] . Many consumers are unaware of complex pricing strategies, leading to perceptions of unfairness [2, 3] . Balancing price optimization with fairness is essential. However, price optimization often relies on behavioral biases rather than genuine differences in consumer valuations [4], which can lead to unethical practices when businesses prioritize profit over fairness [5] . Personalized pricing can increase efficiency but may trigger backlash if price differences are linked to protected characteristics like gender or race, making it difficult to distinguish between legitimate preferences and unfair discrimination.  \nRetailers often adjust prices based on historical trends to boost sales and enhance profitability, which highlights the challenge of time-series forecasting. This process involves predicting retail sales while accounting for price fluctuations over time [6] . With the advancement of machine learning, various statistical time-series forecasting models have emerged, one of the most prominent being the Autoregressive Distributed Lag (ARDL) model. ARDL incorporates exogenous variables to make predictions, making it particularly effective for long-term forecasting [7] . The model has been widely applied in addressing economic problems such as analyzing trade openness and economic growth  \nA PREPRINT-JULY 14, 2026  \n[8] . To optimize the performance of machine learning models and align their sales forecasts closely with actual retail sales, various strategies are employed. A common one is to combine multiple forecasting models: the large-scale M5 retail forecasting competition found ","cbCaihAHV4UzRR1J","https://ap.wps.com/l/cbCaihAHV4UzRR1J","pdf",555781,3,1,12,"English","en",105,"# Introduction\n## Dynamic pricing and fairness concerns\n## Time-series forecasting and ARDL motivation","[{\"question\":\"How does the paper incorporate consumer fairness into retail pricing?\",\"answer\":\"It formulates the pricing problem as maximizing forecast sales while imposing price bounds anchored to the Consumer Price Index (CPI). This embeds fairness constraints directly into the forecasting-driven pricing decision.\"},{\"question\":\"What role does the ARDL model play in the method?\",\"answer\":\"The paper models total retail trade sales with a log–log ARDL specification where the coefficient on product price is interpreted as sales elasticity, linking pricing to forecasted demand.\"},{\"question\":\"Why can unconstrained sales maximization lead to unfair outcomes?\",\"answer\":\"With positive fitted nominal elasticities, an unconstrained optimizer would raise every price to its upper bound. The CPI ceiling is described as the safeguard that prevents pushing prices too high.\"}]",1784211829,30,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"optimizing-ardl-models-for-retail-sales-forecasting-and-fair-pricing","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/optimizing-ardl-models-for-retail-sales-forecasting-and-fair-pricing/86453/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the paper incorporate consumer fairness into retail pricing?","Question",{"text":75,"@type":76},"It formulates the pricing problem as maximizing forecast sales while imposing price bounds anchored to the Consumer Price Index (CPI). This embeds fairness constraints directly into the forecasting-driven pricing decision.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What role does the ARDL model play in the method?",{"text":80,"@type":76},"The paper models total retail trade sales with a log–log ARDL specification where the coefficient on product price is interpreted as sales elasticity, linking pricing to forecasted demand.",{"name":82,"@type":73,"acceptedAnswer":83},"Why can unconstrained sales maximization lead to unfair outcomes?",{"text":84,"@type":76},"With positive fitted nominal elasticities, an unconstrained optimizer would raise every price to its upper bound. 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