Carton Set Optimization in E‐commerce Warehouses: A Case Study

• Date: 01 September 2020
• Published date: 01 September 2020
• Author: Ehsan Ardjmand,Manjeet Singh
• DOI: http://doi.org/10.1111/jbl.12255

Carton Set Optimization in E-commerce Warehouses: A Case

Study

Manjeet Singh

1

, and Ehsan Ardjmand

2

1

DHL Supply Chain

2

Ohio University

In this study, a three-stage methodology for carton set optimization in e-commerce warehouses is proposed and evaluated on three DHL Sup-

ply Chain warehouses. The methodology includes order cubing, carton grouping, and optimal carton set selection. A modified largest area

fits first algorithm for order cubing is proposed. For optimal carton set selection, a genetic algorithm with a novel crossover strategy is intro-

duced. The results show that the proposed carton set optimization approach can improve the shipping cost and carton utilization by 7% and

7.8%, and considerably improve the carbon footprint of the operations, even when the number of carton types is not changed.

Keywords: carton optimization; E-commerce; largest area fits first; order cubing; optimal carton set selection

INTRODUCTION

With the increased technological capabilities and Internet pene-

tration rates, e-commerce businesses have experienced substantial

sales growth in recent years. On a global scale and led by Asian

markets, e-commerce sales has soared from $1.336 trillion in

2014 to $3.535 trillion in 2019, and is expected to grow into

$6.542 trillion by 2023 (Statista, 2020). Only in 2019, seasonally

adjusted retail e-commerce sales in the United States have

increased by 4.2 percent from the first quarter to the second

quarter (Department of Commerce, 2019).

While offering enormous benefits, e-commerce growth has

also initiated various managerial challenges at strategic, tactical,

and operational levels of retailers’supply chains. To deal with a

significant annual expansion, supply chain managers need to

improve their strategic and tactical decisions regarding supply

chain issues such as topological design, outsourcing, supplier

selection, transportation, and warehousing (Ganeshan et al.,

1999). At an operational level, e-commerce order profiles are

highly complex and challenging to manage. E-commerce orders

are usually small in size, have irregular arrival patterns, are sea-

sonally distributed, and are expected to be fulfilled with a high

service level (Zhu et al., 2014; Leung et al., 2018; Ardjmand

et al., 2018b).

Realizing the importance of operational decisions in the e-

commerce supply chain and their financial implications, research-

ers have developed a large body of literature on this subject,

spanning from warehouse operations (Valle et al., 2017; Scholz

et al., 2017; Ardjmand et al., 2018b, 2019) to transportation

(Toth and Vigo, 2002) and shelf space optimization (Eroglu

et al., 2018). Despite the existence of an extensive operations lit-

erature, there seems to be a gap between the theory and practice

of supply chain operational issues in terms of the problems

investigated and the methodologies utilized. One such problem is

the carton set optimization, which is concerned with specifying a

set of cartons along with their dimensions in order to minimize

the total shipping cost of orders given a particular demand pat-

tern. The carton set optimization problem is highly relevant and

directly impacts the operational costs of warehouses and the

environmental footprint of e-commerce supply chains by reduc-

ing the number of generated cartons and hence reducing the last

mile delivery trips.

With significant growth in e-commerce, one consequence of

the increased number of parcel deliveries has been the change in

the pricing model. The model has drifted away from a per-carton

or total weight of the carton shipped pricing to one that highly

depends on the utilization of cartons. Starting in 2007, along

with a new pricing model, the newly introduced "Dimensional

Weight" concept began to play a significant role in pricing parcel

shipments. Dimensional weight (also known as "Volumetric

Weight") depends on the length, width, and height of a parcel

and is calculated as

DimWeightðlbÞ¼lengthðinÞweightðinÞheightðinÞ

αin3

lb

 (1)

where αwhich depends on the contract between the given com-

pany and their shipper(s). When introduced, dimensional weight

was merely used to penalize those shipping packages over three

cubic feet. However, in May 2014, parcel shippers announced

expanding the application of dimensional weight ratings to all

shipments starting in 2015. After 2015, the shipping cost on all

parcels is determined by the greater of its actual weight and

dimensional weight. Thus, shipping cost for parcel kis calculated

as

CostðkÞ¼MaxfPriceðDimWeightðkÞÞ,PriceðWeightðkÞÞg (2)

where Price is a pricing function. When considering this new

pricing model, parcels with lower densities and lower fill rate

would be charged, based on dimensional weight, more than the

same size parcels with higher densities and fill rate. In the

absence of dimensional weight considerations, warehouses may

not find it necessary to focus on optimizing the carton size or

minimizing void space (empty space in a carton) for order

Corresponding author:

Ehsan Ardjmand, Department of Analytics and Information Systems,

College of Business, Ohio University, Athens, Ohio, USA; email:

ardjmand@ohio.edu

Journal of Business Logistics, 2020, 41(3): 222–235 doi: 10.1111/jbl.12255

© 2020 Council of Supply Chain Management Professionals