Analysing the factors that influence the Pareto frontier of a bi‐objective supply chain design problem

• Author: Sebastián Lozano,Belarmino Adenso‐Díaz,Antonio Palacio
• DOI: http://doi.org/10.1111/itor.12493
• Published date: 01 November 2018
• Date: 01 November 2018

Intl. Trans. in Op. Res. 25 (2018) 1717–1738

DOI: 10.1111/itor.12493

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Analysing the factors that influence the Pareto frontier

of a bi-objective supply chain design problem

Antonio Palacioa, Belarmino Adenso-D´

ıazaand Sebasti´

an Lozanob

aDepartment of Industrial Engineering, University of Oviedo, Oviedo, Spain

bDepartment of Industrial Management, University of Seville,Seville, Spain

E-mail: palacioantonio.uo@uniovi.es [Palacio]; adenso@uniovi.es [Adenso-D´

ıaz]; slozano@us.es [Lozano]

Received 19 December 2016; receivedin revised form 6 October 2017; accepted 9 November 2017

Abstract

In this paper a bi-objective multi-product model for the design of a production/distribution supply chain

logistic networkwith four echelons is considered. The proposed optimization model minimizes the total cost of

the network(including the fixed cost to open facilities and the transportation costs between them) and the total

CO2emissions. Fivefactors (network size, product complexity,cost variability, CO2emissions generationand

over-capacity) are considered for the experimental framework. The problem is solved using the ε-constraint

method and the resulting Pareto frontiers (PF) are characterized using five newmetrics specifically developed

for analysinghow those factors affect the resulting optimal configurations. The resultsshow that over-capacity

and product complexity are the two most influential factors regarding the characteristics of the PF, and that

their effects are in the same direction: more complexity and capacity mean a wider set of optimaalternatives,

some close to the ideal point, and in general with a smaller number of links used.

Keywords:logistics network design; bi-criteria optimization; Pareto frontier; cost minimization; emissions minimization;

product complexity

1. Introduction

A supply chain logistic network can be described as a graph where the nodes represent suppliers,

producers/manufacturers, distribution centres, warehouses and customers; and the set of arcs

represent the transportation links between these facilities. Although there are other nodes that

can be considered when designing a supply chain logistic network (e.g. recyclingcentres, assemblers,

recovery plants), those four echelons are those traditionally taken into account when analysing

supply networks (Sabri and Beamon, 2000).

During the last decades the study of logistic networks has grown notably with many works

studying different kinds of problems related to supply chains. Note that most of these studies only

consider a single objective function, usually cost (Mangiaracina et al., 2015). However, this may be

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies

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1718 A. Palacio et al. / Intl. Trans. in Op. Res.25 (2018) 1717–1738

Fig. 1. Number of references (period 2000–2015) dealing with multiobjective supply chain network design (all of them

include in addition cost/profit optimization; forinstance, dealing with sustainability, time, and cost/profit,three papers

were found; dealing with time and cost/profit, 12 paperswere found). [Colour figure can be viewed at

wileyonlinelibrary.com]

insufficient today due to the increasein the complexity of the management of supply chains in recent

decades, with an increase in competition, lead times reduction, operational risk, environmental

constraints, etc. Hence, considering multiple objectives simultaneously when designing logistics

structures is a field that represents a more realistic view of the current situation.

This research effort in designing better multiobjective logistics networks is expanding this field

and involves different approaches. They can be divided into different groups according to their

research objectives,the corresponding decisions in the design process and the corresponding solution

methodologies.

Regarding the first dimension, there are many different objectives that have been studied simul-

taneously in multiobjective optimization problems; revenue, sustainability, lead times, service level,

financial criteria and production-related objectives are the most popular. Profit-related objectives

are included in almost every piece of research because minimization of costs (or maximization of

profit) is generally considered as the first key objective. The rest of the objectives can be found

in combination with the cost minimization objective, depending on the particular interest of the

company or researcher, with sustainability, lead time and service level (i.e. percentage demand ful-

filled) as the most popular. Figure 1 provides a summary of the number of references dealing with

multiobjective approaches to logistic network design.

The second dimension, namely the decisions to be made in a logistic network design process, is

another important aspect when dealing with a multiobjective problem.The most common decisions

in a logistic network are the facilities’ locations and the transportation flows. There are some

cases where this problem is extended to include capacity decisions both for the facilities and the

transportation links, or routing (Lopes et al., 2013). Other decisions in multiobjective logistic

networks that are frequently studied are the number of products manufactured, the inventory levels

of the facilities and the uncertainty level (Mangiaracina et al., 2015).

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies