## Supplier Selection Problem: Ranking of Suppliers

In real world, sourcing executives generally have a large pool of suppliers to select from. In terms of leveraging analytics, the supplier selection process at a high level looks like:

The problem of ranking suppliers (pre-qualification) represents a class of multiple criteria optimization problems that deal with the ranking of a finite number of alternatives, where each alternative is measured by several conflicting criteria. Below, I will be sharing several multiple criteria ranking approaches for the supplier ranking problem, namely, the pre-qualification of suppliers.

In the pre-qualification process, which is generally the Phase I, readily available qualitative and quantitative data are collected for the various suppliers. This data can be obtained from trade journals, internet and past transactions to name a few sources. Once this data is gathered, these suppliers are evaluated using multiple criteria ranking methods. The decision maker (DM) then selects a portion of suppliers for extensive evaluation in Phase II.

## Examples of criteria:

The sourcing professional will determine the criteria based on the unique sourcing objectives but based on my experience, below are some criteria that can be used:

## Suggested Analytical Methods

Each method has advantages and limitations and a sourcing professional will need to collaborate closely with their Data Scientists to evaluate which methods will suit their unique needs. Suggested methods that we will touch upon are below. I will explain them at a very high level in this article and will follow-up with detailed articles describing each of these in detail in separate articles.:

- LP Metric method
- Rating method
- Borda Count
- Pairwise comparison of criteria
- Analytical Hierarchy process

### Lp Metric Method

In Mathematics, Lp represents distance between two vectors x and y. In the context of supplier ranking, the ranking of suppliers is done by calculating the Lp metric between the Ideal solution and each vector representing the supplier’s rating for the criteria. The ideal solution represents the best values possible for each criterion from the initial list of suppliers. Since no supplier will have the best values for all criteria, the ideal solution is an artificial target that can’t be met. The Lp metric approach computes the distance of each supplier’s attributes from the ideal solution and ranks the supplier’s based on that distance- The Smaller the better.

### Rating (Scoring) method

Rating is one of the simplest and most widely used ranking methods under conflicting criteria. In this method, first an appropriate rating scale is agreed to. The scale should be clearly understood by the deciision maker (DM) to be used properly.

Next, using the selected scale, you need to provide a rating for each criteria. Same rating can be given to more than one criteria. The ratings are then normalized to determine the weights of the criteria.

### Borda Count

This method, named after Jean Charles de Borda, a French Physicist, follows the following logic:

* Step 1:* Let us say we have n criteria. In this step, the n criteria are ranked 1 (most important) to n (least important):

Criterion ranked 1 gets n points, 2 nd rank gets n-1 points, and the last place criterion gets 1 point.

* Step 2:* Calculate the sum of all the points = n(n+1)/2

Then calculate the weight for each criterion as shown below:

Criterion ranked 1 = n/s

Criterion ranked 2 = n-1/s

Using this approach, calculate a total weight for each supplier based on all criterion

### Pairwise comparison of criteria

When there are many criteria, it will be difficult to rank order them precisely. In practice, pair-wise comparison of criteria is used to facilitate the criteria ranking required by the Borda count. Here, the decision maker is asked to give relative importance between two criteria Ci and Cj, whether Ci is preffered to Cj, Cj is preferred to Ci or both are equally important.

When there are n criteria, decision maker has to respond to n(n-1)/2 pair wise comparisons. Based on the decision maker’s response, the criteria rankings and their weights can be computed using the following three steps:

* Step 1:* Construct a pairwise comparison matrix. As an example, if there are five criteria A,B,C,D and E, the matrix will look something like this (1 indicates that the criteria is more preferred)

* Step 2*: Compute the row sums for the matrix

* Step 3:* Rank the criteria based on row sums and compute their weights. Ex: If for Row A, Row Sum = 5 and the total of Row sums for all rows = 15, then Wa = 5/15

Note: Scaling criteria values

One drawback of the ranking methods discussed so far is that they use criteria weights that require the criteria values to be scaled properly (we assume that they are already scaled). In practice, supplier criteria may be measured in different units. Some criteria value may be very large while others may be small. If the criteria values are not scaled properly, the criteria with large magnitudes would simply dominate the final rankings, independent of the assigned weights.

### Analytics Hierarchy Process

The Analytics Hierarchy process is a multi criteria decision making method for ranking alternatives. Using AHP, you can assess not only quantitative but various qualitative factors as well, such as financial stability, trust level etc. in the supplier selection process. The buyer establishes a set of evaluation criteria and AHP uses these criteria to rank the different suppliers. Basic principles of AHP are:

- Design a hierarchy – Top vertex is the main objective and bottom vertices are the alternatives. Intermediate vertices are criteria/subcriteria (which are more and more aggregated as you go up in the hierarchy),
- At each level of the hierarchy, a paired comparison of the vertices criteria/sub-criteria is performed from the point of view of their contribution weights to each of the higher level vertices that they are linked to.
- Uses both rating AND comparison method.
- Uses pairwise comparison of alternatives with respect to each criteria and gets a numerical score for each alternative on every criteria.
- Computes total weighted score for each alternative and ranks the alternatives accordingly.

Based on my research