**3. AHP applied to SCM in an automobile plant**

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

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

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

**City Round 1 Round 2 Round 3**

Madrid 29.8% 30.5% 32.6%

Rio de Janeiro 27.7% 48.4% 67.4%

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

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

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

Tokyo 23.4% 21.1%

Gore presidency [10].

Chicago 19.1%

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

is adopted for presidential elections.

other methods which not allow RR.

is adopted.

Olympics.

Supply chain is a network of supplier-customer companies connected by information and production flows, among other flows. For instance, a supply chain for an automobile produc‐ tion, beyond the car maker, or car assembler, may include auto parts manufacturers (Tiers 1 and 2 Suppliers), raw material providers, logistics providers, car dealers, and, as end customer, the car owner (**Figure 1**).

**Figure 1.** Automobile supply chain.

Let us consider a Brazilian manufacturer of vehicle frames, also known as chassis. This manufacturer has four plants (two in Brazil, one in Mexico, and a new one in Argentina) to closer supply its customers. These plants act as Tier 1 Suppliers for major car assemblers. In all these plants, the multiple source policy is adopted. That is, purchased items are provided eventually by more than one supplier. This policy has the main advantages of supplier competition and operational flexibility [11].

Blanking is the main process in the chassis production. Blank dies are specialized tools purchased in large lots to attend annual demands. The decision making is decentralized: buyers from each plant select suppliers for local requirements. Due to multiple supplier policy, a lot is often distributed in more than one supplier. Then, this is a resource allocation (RA) problem.

Suppliers are usually selected for a lot considering two main attributes: payment conditions and supplier loading. Usually, suppliers offering best payment conditions are selected. However, if a supplier has too many orders, then this supplier will be sidestepped. The distribution of a lot among suppliers is all done by a single buyer.

In one of the Brazilian plants, the Production Manager decides to apply the AHP, considering his team expertise to a new purchase of blank dies. The production management team, composed of three engineers, including the Production Manager, listed twelve more attributes desired for a supplier:


**Figure 2.** Hierarchy of attributes to prioritize suppliers of blank dies.


In one of the Brazilian plants, the Production Manager decides to apply the AHP, considering his team expertise to a new purchase of blank dies. The production management team, composed of three engineers, including the Production Manager, listed twelve more attributes

**•** Flexibility, based on the supplier's skills to change product specifications or lot size in orders.

**•** Certification of the management system, according to international standard.

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

**•** Post-sales costs, differently charged by suppliers for post-sales support.

desired for a supplier:

**•** Capability, that is, supplier's know-how.

**•** Quality, based on engineering tolerance. **•** Reliability, based on expected lifetime.

**•** Sub-suppliers, that is, suppliers of the supplier.

**•** Price truthful (does the die worth the charged price?).

**Figure 2.** Hierarchy of attributes to prioritize suppliers of blank dies.

**•** Services, post-sale technical support provided by suppliers.

**•** Reaction, that is, supplier's speed to incorporate these changes.

The fourteen attributes (the new twelve plus the old two) were grouped based on the Benefits-Opportunities-Costs-Risks (BOCR) model [12], resulting in a hierarchy for the set of attributes (**Figure 2**).

The Production Manager decided that each major aspect of BOCR should equally contribute for the decision. Therefore, the overall priorities for Benefits, Opportunities, Costs, and Risks were set in 25% each. Every member of the production management team made pairwise comparisons between attributes inside the aspects (**Table 7**).


**Table 7.** Pairwise comparisons for attributes on benefits according to one member of production management team.

Comparisons made by every engineer were individually aggregated, by geometrical mean, since they are willing their preferences for the same organization [13]. This procedure results in an aggregated comparisons matrix (**Table 8**).


**Table 8.** Pairwise comparisons for attributes on benefits aggregated to all member of production management team.

The local priorities for all attributes can be obtained normalizing the right eigenvector for the aggregated comparison matrices. The overall priorities for the attributes are obtained weighting local priorities by 25% (**Table 9**).



**Table 9.** Overall priorities of attributes for suppliers of blank dies.

The production management team prioritized six potential suppliers with ratings, that is, relative measurement, by consensus. They prioritized the suppliers rating them in a 0–1 linear scale (**Table 10**). For Certification (A2), the priority value was binary: 1, when the supplier had a certified management system, or 0, otherwise.


**Table 10.** Rated suppliers of blank dies.

S5 was the most expensive supplier (A9 = 0.3) and S6 was the cheapest one (A9 = 1). However, S6 will be not be selected, since it was relatively overloaded (A14 = 0.5). Usually, a buyer makes this decision. Sometimes, buyers make unpredictable decisions for production management.

Then, Production Manager decides to go on with AHP application. Next step is normalizing priorities for each attribute. Then, normalized priorities need to be weighted by criteria


priorities (**Table 9**). This way, a decision matrix brings local priorities for each aspect (BOCR) and overall priorities (**Table 11**).

**Table 11.** Local and overall priorities for suppliers of blank dies.

**Attribute Overall priority**

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

Capability (A1) 7% Certification (A2) 1% Quality (A3) 4% Reliability (A4) 8% Services (A5) 5% Flexibility (A6) 6% Reaction (A7) 13% Sub-suppliers (A8) 6% Payment conditions (A9) 17% Price truthfulness (A10) 4% Post-sale costs (A11) 4% No-access (A12) 2% Historical delays (A13) 5% Supplying load (A14) 18%

**Table 9.** Overall priorities of attributes for suppliers of blank dies.

a certified management system, or 0, otherwise.

**Table 10.** Rated suppliers of blank dies.

The production management team prioritized six potential suppliers with ratings, that is, relative measurement, by consensus. They prioritized the suppliers rating them in a 0–1 linear scale (**Table 10**). For Certification (A2), the priority value was binary: 1, when the supplier had

**Supplier A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14** S1 0.8 1 0.7 0.8 0.8 0.8 0.9 0.9 0.6 0.6 0.7 0.8 0.9 0.9 S2 0.7 0 0.8 0.7 0.8 0.9 0.7 0.8 0.7 0.8 0.8 0.8 0.7 0.8 S3 1 1 0.9 0.9 0.9 0.7 1 1 0.5 0.5 0.7 0.7 0.7 0.9 S4 0.8 0 0.9 0.9 0.8 0.9 0.8 0.8 0.8 0.9 0.8 0.9 0.9 0.8 S5 0.7 1 0.8 0.85 0.9 0.8 0.6 0.8 0.3 0.3 0.8 0.9 0.8 0.7 S6 0.5 0 0.6 0.6 0.6 0.5 0.2 0.6 1 1 0.5 0.2 0.5 0.5

S5 was the most expensive supplier (A9 = 0.3) and S6 was the cheapest one (A9 = 1). However, S6 will be not be selected, since it was relatively overloaded (A14 = 0.5). Usually, a buyer makes this decision. Sometimes, buyers make unpredictable decisions for production management.

Then, Production Manager decides to go on with AHP application. Next step is normalizing priorities for each attribute. Then, normalized priorities need to be weighted by criteria Production Manager decided to delete Suppliers 5 and 6 for the next supplying of blank dies. Then, the lot will be equally divided in four suppliers (S1–S4). The overall priorities for suppliers will change from (18.0%, 17.0%, 18.3%, 18.6%, 14.7%, 13.3%) to (25%, 25%, 25%, 25%). This is not a case of ranking reversal. If S5 and S6 were deleted in **Tables 10** and **11**, overall priorities will be (25.0%, 23.7%, 25.3%, 26.0%). Therefore, AHP application supported the Production Manager decision.

Production Manager, finally, communicates the decision to procurement management. The new role for buyers will be only to contact suppliers and purchase the blank dies. After all, production will be the user of the blank dies in their processes, not the buyers. No contest emerged, and the company was confident that select suppliers not only based in costs and risks, but also considering benefits and opportunities would be a better decision.
