**Analytic Hierarchy Process Applied to Supply Chain Management**

sion model, based on AHP, in the transport sector, concerning the reconfiguration of the railway infrastructure of the seaport of Trieste is presented in **Chapter 6**. In **Chapter 7** au‐ thors propose a novel approach to ensure safety in emergency conditions in industrial plants considering the presence of dangerous equipment and human errors. The proposed idea aims to integrate the Human Reliability Analysis (HRA) and the Failure Mode and Ef‐

The topic is extended in **Chapter 8** where the authors develop a perceived comprehensive disaster Risk Index in three Chilean Cities. In **Chapter 9** we shift our attention to identify stakeholders' decision criteria using a meta-heuristic approach and AHP. **Chapter 10** presents an analysis on evaluation of growth simulators for forest management in terms of functionality and software structure using AHP. The problem of measuring closeness in weighted environments (decision-making environments) is developed in **Chapter 11**. The relevance of this article is related to having a dependable cardinal measure of distance in weighted environments. **Chapter 12** provides an AHP Method with BOCR Merits to Ana‐ lyze the Outcomes of Business Electricity Sustainability. Finally, **Chapter 13** addresses how AHP model developed for contractor selection can be implemented on the computer to get

This book is intended to be a useful resource for anyone who deals with decision making problems. Furthermore, we hope that this book will provide useful resources, techniques

As editors of this book, we would like to thank the authors who accepted to contribute with their invaluable research as well as the referees who reviewed these papers for their effort, time and invaluable suggestions. Our special thanks to Ms. Ana Pantar, Publishing Process Manager, for

**Fabio De Felice**

Cassino, Italy

PA, USA

**Thomas L. Saaty**

**Antonella Petrillo**

Naples, Italy

University of Pittsburgh,

University of Naples Parthenope,

University of Cassino and Southern Lazi,

fects Analysis (FMEA).

VIII Preface

the right ratings using some existing computer software.

and methods for further research on Analytic Hierarchy Process.

her precious support and her team for this opportunity to serve as guest editors.

Valerio Antonio Pamplona Salomon, Claudemir Leif Tramarico and Fernando Augusto Silva Marins

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64022

#### **Abstract**

Resource allocation (RA) and supplier selection (SS) are two major decision problems regarding supply chain management (SCM). A supply chain manager may solve these problems by considering a single criterion, for instance, costs, customer satisfaction, or delivery time. Applying analytic hierarchy process (AHP), the supply chain manager may combine such criteria to enhance a compromised solution. This chapter presents AHP applications to solve two real SCM problems faced by Brazilian companies: one problem regarding the RA in the automotive industry and another one to SS in a chemical corporation.

**Keywords:** analytic hierarchy process, ranking reversal, resource allocation, supplier selection, supply chain management

### **1. Introduction**

Supply chain is the "global network used to deliver products and services from raw materials to end customers through an engineered flow of information, physical distribution, and cash" [1]. Therefore, many decision problems make up the supply chain management (SCM). Resource allocation (RA) and supplier selection (SS) are two major decision problems regarding SCM. A supply chain manager may solve these problems by considering a single criterion, for in‐ stance, costs, customer satisfaction, or delivery time. Applying Analytic Hierarchy Process (AHP), the supply chain manager may combine such criteria to enhance a compromised solution.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Foundations of AHP came back from the 1970s [2]. Originally, AHP consisted in hierarchy structuring, relative measurement (pairwise comparisons between criteria and between alternatives), and distributive synthesis (priorities are normalized, i.e., they sum equal to one).

One great advance in AHP practice is the "absolute measurement", also known as "ratings" [3]. In absolute measurement, alternatives are compared with standard levels, instead of pairwise compared. Relative measurement has been most applied than ratings, even with software packages including ratings [4, 5]. Since in relative measurement alternatives must be pairwise compared, their number must be less than or equal to nine, that is, "seven, plus or minus two" [6]. In absolute measurement there is no bound for the set of alternatives. Another advantage from using ratings is the opportunity to avoid biases. With alternatives being compared with each other, two by two (relative measurement), some historical trends could be kept in mind. Comparing alternatives with a standard (absolute measurement) seems to provide a less partial or unbiased measurement.

Another advance for original AHP comes with the "ideal synthesis" [7]. With ideal synthesis, priorities are not normally distributed. That is, the sum of priority vectors components will not be equal to one. In this mode, the highest priority regarding each criterion will be equal to one. Normalizing priorities creates a dependency among priorities. However, if an old alternative is deleted or if a new one is inserted normalized priorities can lead to illegitimate changes in the rank of alternatives, known as rank reversal (RR). RR was firstly associated with AHP in preliminary studies by Professor Valerie Belton at University of Cambridge [8].

This chapter presents AHP applications to solve SCM problems. Two real cases from Brazilian companies are presented, one case regarding to RA in the automotive industry and another one to SS in a chemical corporation. In both cases, AHP was applied with absolute measure‐ ment. However, in the first case, the normal synthesis was adopted; in the second case, ideal synthesis was applied. The first conclusion from these cases is that for RA, normal synthesis maybe proper than ideal synthesis; conversely, for SS, ideal synthesis maybe more indicated.

### **2. Ranking reversal and synthesis mode**

To illustrate the concept of RR, let us consider a decision of project selection by a company. The decision criteria are Benefits (B), Opportunities (O) and Risks (R). After pairwise comparisons, the priorities for the criteria (B, O and R) are, respectively, 73%, 19%, and 8%. Project X will be the selected one, due its highest overall priority (**Table 1**).


**Table 1.** Priorities for Projects X, Y, and Z (normal synthesis).

Let us now consider that the supplier responsible for Project Z unexpectedly discontinues its operations. So, this alternative must be deleted of the decision. Then, surprisingly, overall priority of Project Y becomes higher than Project X's (**Table 2**).


**Table 2.** Priorities for Projects X and Y (normal synthesis).

Foundations of AHP came back from the 1970s [2]. Originally, AHP consisted in hierarchy structuring, relative measurement (pairwise comparisons between criteria and between alternatives), and distributive synthesis (priorities are normalized, i.e., they sum equal to one).

2 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

One great advance in AHP practice is the "absolute measurement", also known as "ratings" [3]. In absolute measurement, alternatives are compared with standard levels, instead of pairwise compared. Relative measurement has been most applied than ratings, even with software packages including ratings [4, 5]. Since in relative measurement alternatives must be pairwise compared, their number must be less than or equal to nine, that is, "seven, plus or minus two" [6]. In absolute measurement there is no bound for the set of alternatives. Another advantage from using ratings is the opportunity to avoid biases. With alternatives being compared with each other, two by two (relative measurement), some historical trends could be kept in mind. Comparing alternatives with a standard (absolute measurement) seems to

Another advance for original AHP comes with the "ideal synthesis" [7]. With ideal synthesis, priorities are not normally distributed. That is, the sum of priority vectors components will not be equal to one. In this mode, the highest priority regarding each criterion will be equal to one. Normalizing priorities creates a dependency among priorities. However, if an old alternative is deleted or if a new one is inserted normalized priorities can lead to illegitimate changes in the rank of alternatives, known as rank reversal (RR). RR was firstly associated with AHP in preliminary studies by Professor Valerie Belton at University of Cambridge [8].

This chapter presents AHP applications to solve SCM problems. Two real cases from Brazilian companies are presented, one case regarding to RA in the automotive industry and another one to SS in a chemical corporation. In both cases, AHP was applied with absolute measure‐ ment. However, in the first case, the normal synthesis was adopted; in the second case, ideal synthesis was applied. The first conclusion from these cases is that for RA, normal synthesis maybe proper than ideal synthesis; conversely, for SS, ideal synthesis maybe more indicated.

To illustrate the concept of RR, let us consider a decision of project selection by a company. The decision criteria are Benefits (B), Opportunities (O) and Risks (R). After pairwise comparisons, the priorities for the criteria (B, O and R) are, respectively, 73%, 19%, and 8%.

**Project Benefits (73%) Opportunities (19%) Risks (8%) Overall** X 0.540 0.185 0.149 0.442 Y 0.348 0.659 0.691 0.434 Z 0.112 0.156 0.160 0.124

Project X will be the selected one, due its highest overall priority (**Table 1**).

provide a less partial or unbiased measurement.

**2. Ranking reversal and synthesis mode**

**Table 1.** Priorities for Projects X, Y, and Z (normal synthesis).

With the same set of criteria and alternatives, but with ideal synthesis, overall priority of Project X will be higher than Project Y's, considering Project Z (**Table 3**), or not (**Table 4**).


**Table 3.** Priorities for Projects X, Y, and Z (ideal synthesis).


**Table 4.** Priorities for Projects X and Y (ideal synthesis).

As presented in **Tables 1**–**4**, when one alternative is pulled out from the decision, ideal synthesis preserves ranks; conversely, normal synthesis reverses ranks. RR also may occur when new alternatives are inserted, or even when the set of criteria is changed. Matter of fact, absolute measurement and ideal synthesis always preserve ranks [9]. However, it is important to note that RR can be legitimate. That is, RR has already occurred. Two examples of real world decisions with RR are the United States Presidential Election, in 2000, and the Election of Host City of the 2016 Summer Olympics, in 2009.

The United States Presidential Election, in 2000, was quite controversial. The main contesters were Al Gore, George W. Bush, and Ralph Nader (**Table 5**).


**Table 5.** United States presidential election 2000.

Bush won with 271 electoral votes against 266 votes for Gore. It was the only fourth time, in 54 presidential elections, that the electoral vote winner failed to win also by popular vote. However, this is not an RR situation, because the set of alternatives was unchanged. An RR could have happened if Nader had quit. That is, most of Nader's popular votes could go to Gore, in a case of Nader deletion from **Table 5**. For this reason, Nader was accused of spoil the Gore presidency [10].

During the 121st International Olympic Committee Session, Rio de Janeiro was selected as the host city of the 2016 Summer Olympics. Chicago, Madrid, and Tokyo were the other applicant cities (**Table 6**). On the first round, Madrid had more votes, Rio was the second, Tokyo was the third, and Chicago, with fewer votes, was eliminated. From the second round, Rio had more votes, then, an RR occurred, and, for the first time, South America will host the Summer Olympics.


**Table 6.** Votes for host city of Summer Olympics 2016.

Depending on the type of measurement and synthesis, ranks can be preserved or reversed with AHP. Nevertheless, the main discussion is the legitimacy of RR for the decision. For instance, RR may be avoided for a president election. After all, it is not only a pair of persons (the nominee for president and the running mate) who are being elected. With the candidate, also his ideas, political orientation (conservationist or reformist, etc.), and a whole party is being selected for a four-year term. For this reason, in countries like Brazil, a two round election is adopted for presidential elections.

In another instance, for the selection of the host city for a major event, RR can be acceptable. At first, it may sound strange: X is preferred among X, Y and Z, but Y is preferred between X and Y. What happened? Who preferred Z also preferred Y than Z. In this case, RR will be legitimate. Since, AHP is a method that allows RR, its application than will be proper than other methods which not allow RR.

In Sections 3 and 4, two SCM problems are presented. For the first one, RR will not be a problem: the normal synthesis is adopted. In the second case, RR must be avoided: the ideal synthesis is adopted.
