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Production and Operations Management 2025

Maximizing Profit and Minimizing Waste with Buy-x-Get-y-Free Promotion Policies During Clearance Sales

Fang Liu1; Arvind Sainathan2

1 Durham University · 2 NEOMA Business School

open access

Abstract

Maximizing profit and minimizing waste (leftover inventory) can be two conflicting objectives during clearance sales. B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>x</mml:mi> </mml:math> G <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>y</mml:mi> </mml:math> policies (buy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>x</mml:mi> </mml:math> units at full price and get <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>y</mml:mi> </mml:math> units free) are popular promotion policies for achieving these objectives. We consider four scenarios depending on whether customers are homogeneous/heterogeneous in their valuations and whether the retailer’s objective is to maximize profit/minimize waste. In each scenario, we characterize the structure of the optimal promotion policy (OPP). We categorize the two kinds of OPPs based on the retailer’s objective as profit-based and clearance-based OPPs. If customers are homogeneous, we show that B1G <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>y</mml:mi> </mml:math> policies are always optimal. However, if they are heterogeneous, B1G <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>y</mml:mi> </mml:math> policies may not maximize profit, resulting in a complex structure for profit-based OPPs. Therefore, we focus on B1G0, B1G1, and B2G1 policies due to their prevalence among retailers. We then derive how both kinds of OPPs change with quantity. We explain the impact of quantity using the ideas of bundling effect and differentiation effect . We perform a numerical study to examine (i) the impact of the two kinds of OPPs on profit and waste, and (ii) the impact of demand uncertainty. Finally, we discuss how our results apply to several practical instances.

DOI
10.1177/10591478251323794
Sources
openalex

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