INTRODUCTION
One of the major objectives of effective purchasing is to select the suppliers that would be best for the company and the consumers. The selected suppliers should provide a high degree of customer service in terms of on-time delivery, quality, price, and service after the sales. Some suppliers may offer low prices but the quality may be poor. Some suppliers may have good on-time delivery performance record but they may have a bad record in terms of the service after the sales. There are so many other criteria that need to be analyzed as well as the trade-offs among those criteria prior to selecting the most suitable supplier. This paper develops a sophisticated and unique but still easy to apply algorithm that analyzes these trade-offs and selects the optimum supplier. If one supplier can't meet all the demand the algorithm determines the optimum quantities to buy from other supplier(s).
The already existing traditional techniques use various methods such as decision analysis, factor rating, and even linear programming, but none of the previous research combines these various techniques in a unique and comprehensive manner to generate an optimal rather than sub optimal solution.
METHODOLOGY
The first major step in the algorithm is to find the expected prices offered by suppliers under uncertainty that involves probabilities by using
Sadik Çökelez is Associate Professor, California State University, Dominguez
Hills, School of Management, Carson, CA 90747.
Journal of Customer Service in Marketing & Management, Vol. 3(3) 1997
© 1997 by The Haworth Press, Inc. All rights reserved.
7
AÇIKLAMA: Bu makaleyi bu bilimsel dergiye eskiden gönderdiğim tarihte doçent olmam itibarı ile yukarıdaki dip notta "Associate Professor" ibaresi bulunmaktadır. Ama makalemin yayınlandığı aynı yıl içinde Profesörlüğe(Full
Professor) terfi etmiştim. Mini proje ile ilgili daha önce web sitesine postaladığım bilimsel makalemin California'ya ya gelmeden yayınlandığı daha eski tarihte ise Michigan' da ki
Oakland University'de yardımcı doçenttim; o nedenle o makaledeki üniversite ismi değişik gözüküyor.

8 Journal of Customer Service in Marketing & Management a decision analysis. These expected prices are converted to indices by using a common base.
The second major step is to find the on-time delivery performances of the suppliers under uncertainty that involves probabilities by conducting a decision analysis. The expected on-time delivery percentages are converted to indices by using a common base.
The third major step is to determine the defective rates for each supplier to assess the quality and to convert these to indices with a common base.
The fourth major step is to conduct a factor rating analysis by scoring and weighing various subjective factors pertinent to suppliers. These weighted scores are eventually converted to indices with a common base. The fifth major step is to multiply the above-mentioned indices by the corresponding weights and sum them for each supplier to get the value index for each supplier.
The sixth major step is to determine the transportation costs and transportation cost indices; these numbers constitute the objective function coefficients of the minimization part of the linear program discussed in the next step whereas the value indices mentioned in the previous step constitute the objective function coefficients of the maximization part of the linear program.
The final step is to formulate the complete linear program with all the relevant constraints and solve it on the computer using a simple and very userfriendly computer software called LINDO (Linear Interactive Discrete
Optimizer).
The full methodology including the minor steps are outlined below:
1. a. Find the expected price for each supplier under uncertainty by using decision analysis with probabilities. Expected price for supplier i is denoted by p i
.
b. Determine the lowest p i
and divide this lowest p i
by every p i to get the price index for each supplier. This is a case of inverse proportionality as the most desirable supplier would be the one offering the lowest price.
2. a. Find the expected on-time performance for each supplier under uncertainty by using decision analysis with probabilities. Expected on-time delivery percentage of each supplier is denoted by o i
.
b. Determine the highest o i and divide every o i by this highest o i to get the on-time delivery index for each supplier. This is a case of direct proportionality because the higher the on-time delivery the better the supplier is.

Sadik Çökelez 9
3. a. Determine the defective rates in the shipments sent by each supplier and denote them by d i
.
b. Determine the lowest d i
and divide this lowest d i by every d i
to get the quality index for each supplier. This is a case of inverse proportionality because the lower the defective case the higher the quality.
4. a. Analyze the subjective factors relevant to supplier selection, assign each factor a weight, and score each factor for each supplier and use factor rating techniques to get the weighted scores for all the suppliers. Weighted subjective scores are denoted by s i
.
b. Determine the highest s i
and divide every s i
by this highest s i
to get the subjective score index for each supplier. This is a case of direct proportionality because the higher the subjective score the more desirable the supplier is.
5. Multiply every p i
, o i,
, d i
, and s i
by their corresponding weights and sum them up for each i and denote them by v i for each supplier. That is, the overall value of each supplier in terms of price, on-time delivery, quality, and subjective aspects is denoted by v i
. The higher the v i
the better the supplier is.
6. Determine t ij where t ij
is the transportation cost from supplier i to the warehouse j of the buying company. Determine the lowest t ij
and divide this lowest t ij
by every t ij
to get transportation cost in dices, It ij
. This is a case of inverse proportionality because the
lower the transportation cost the better it is.
7. Formulate the supplier selection optimization linear program by using the above-mentioned v i
values and It ij values as the objective function coefficients of the linear program; we want to maximize the supplier values and minimize the transportation costs. Minimizing a linear program with t ij
as objective function coefficients is the same as maximizing a linear program with It ij
as objective function coefficients. Since we are trying to maximize the supplier values with v i
values it is essential to make conversion to It ij
so that we can deal with a single integrated maximization objective. It is also possible to prioritize the goals of the purchasing company by assigning the appropriate weight
(W v
) to supplier value criterion and the appropriate weight (W
It
) to the transportation criterion in the objective function of the linear program. Later, add all the relevant constraints such as capacity and demand constraints.
Finally, solve this linear program by using the LINDO (Linear
Interactive Discrete Optimizer) package to select the best supplier that would result in optimum customer service.

10 Journal of Customer Service in Marketing & Management
If one supplier can't meet all the demand, the linear program finds the optimum quantities to purchase from each supplier.
A NUMERICAL EXAMPLE
Suppose that we have three potential suppliers and we aim for the optimal selection. Let us assume that the following data are pertinent to the three suppliers in question:
PRICE TABLE
High Demand (s
1
) Medium Demand (s
2
) Low Demand (s
3
)
Supplier 1 $18 $21 $26
Supplier 2 $20 $21 $22
Supplier 3 $19 $20 $23
P (s
1
) = 0.3 P(s
2
) = 0.5 P(s
3
) = 0.2
Different suppliers have different price/discount strategies as indicated in the table and the probability for different levels of demand can easily be obtained by analyzing past data.
Step 1a
The expected prices (p i
) are computed as follows:
p
1
= 0.3(18) + 0.5(21) + 0.2(26) = 21.1 for Supplier 1.
p
2
= 0.3(20) + 0.5(21) + 0.2(22) = 20.9 for Supplier 2.
p
3
= 0.3(19) + 0.5(20) + 0.2(23) = 20.3 for Supplier 3.
Step 1b
The lowest price, p
3
, is 20.3. This figure is divided by every p i
:
The price index for Supplier 1, Ip
1
= 20.3/21.1 = 0.9621.
The price index for Supplier 2, Ip
2
= 20.3/20.9 = 0.9713.
The price index for Supplier 3, Ip
3
= 20.3/20.3 = 1.0000.
Suppose that the following are the on-time delivery related data for the next step, Step 2:

Sadik Çökelez 11
ON-TIME DELIVERY PERCENTAGES
High Demand (s
1
) Medium Demand (s
2
) Low Demand (s
3
)
Supplier 1 100% 95% 90%
Supplier 2 90% 95% 100%
Supplier 3 85% 88% 95%
P(s
1
) = 0.3 P(s
2
) = 0.5 P(s
3
) = 0.2
(Note: Supplier 2 and Supplier 3 have increasing on-time delivery percentages in the case of lower demand which is typically the case as it is easier to meet lower demand. Supplier 1, on the other hand, shows a surprisingly reversed pattern; such a case is possible if Supplier 1 doesn't care much for medium or small orders but takes large orders very seriously.)
Step 2a
The decision analysis yields the following results: o
1
= 0.3(100) + 0.5(95) + 0.2(90) = 95.5 for Supplier 1.
o
2
= 0.3(90) + 0.5(95) + 0.2(100) = 94.5 for Supplier 2.
o
3
= 0.3(85) + 0.5(88) + 0.2(95) = 88.5 for Supplier 3.
Step 2b
The highest o i
is 95.5. The on-time delivery index is obtained by dividing every o i
by this highest figure:
The on-time delivery index for Supplier 1, Io
1
= 95.5/95.5 = 1.0000.
The on-time delivery index for Supplier 2, Io
2
= 94.5/95.5 = 0.9895.
The on-time delivery index for Supplier 3, Io
3
= 88.5/95.5 = 0.9267.
Step 3a
Let us assume that the inspection data showed the following defective rates in the shipments for each supplier:
DEFECTIVE RATES
Supplier 1
Supplier 2
Supplier 3
4%
5%
5%
Step 3b
The lowest d i
is 4%. The defective rate index is obtained by dividing this figure by every defective rate:

12 Journal of Customer Service in Marketing & Management
The defective rate index for Supplier 1, Id
1
= 4/4 = 1.0000.
The defective rate index for Supplier 2, Id
2
= 4/5 = 0.8000.
The defective rate index for Supplier 3, Id
3
= 4/5 = 0.8000.
Step 4a
Now, let's suppose the following are the weights for each factor and scores of the subjective factors for each supplier:
WEIGHT SCORES OUT OF 100
Supplier 1 Supplier 2 Supplier 3
Technical and
Manufacturing Strength 0.10 75 92 91
Distribution Strength 0.10 85 98 96
Financial Strength 0.10 80 98 98
Management Practices 0.10 80 95 90
Ethical Practices 0.15 85 96 95
Social Responsibility 0.10 75 94 95
Environmental
Responsibility 0.10 80 98 98
Potential for
Long-term Loyalty 0.10 85 97 95
Service After Sales 0.15 75 96 95
1.00
The weighted subjective score for Supplier 1, i.e., s
1
is:
0.10(75) + 0.10(85) + 0.10(80) + 0.10(80) + 0.15(85) + 0.10(75)
+0.10(80) + 0.10(85) + 0.15(75) = 80.00.
The weighted subjective score for Supplier 2, i.e., s
2
is:
0.10(92) + 0.10(98) + 0.10(98) + 0.10(95) + 0.15(96) + 0.10(94)
+0.10(98) + 0.10(97) + 0.15(97) = 96.00.
The weighted subjective score for Supplier 3, i.e., s
3
is:
0.10(91) + 0.10(96) + 0.10(98) + 0.10(90) + 0.15(95) + 0.10(95)
+0.10(98) + 0.10(95) + 0.15(95) = 94.80.
Step 4b
The highest s i
is 96.00. The subjective score index is obtained by dividing every s i
by this highest figure:

Sadik Çökelez
The subjective score index for Supplier 1, Is
1
= 80.00/96.00 = 0.8333.
The subjective score index for Supplier 2, Is
2
= 96.00/96.00 = 1.0000.
The subjective score index for Supplier 3, Is
3
= 94.80/96.00 = 0.9875
Step5
Suppose that the purchasing manager assigns the following weights to various indices:
WEIGHT
Price Index 0.25
Delivery Index 0.25
Quality Index 0.30*
Subjective Value Index 0.20
1.00
Then the final overall value scores (v;) would be computed as follows:
The overall value of Supplier 1, v
1 is:
0.25(0.9621) + 0.25(1.0000) + 0.30(1.0000) + 0.20(0.8333) = 0.9572.
The overall value of Supplier 2, v
2
is:
0.25(0.9713) + 0.25(0.9895) + 0.30(0.8000) + 0.20(1.0000) = 0.9302.
The overall value of Supplier 3, v
3
is:
0.25(1.0000) + 0.25(0.9267) + 0.30(0.8000) + 0.20(0.9875) = 0.9192.
*Note: In some cases where quality problems may cause serious safety hazards, we will have to aim for close to 100% quality; in such cases we should forget about the price or on-time delivery and attach a weight of 1.00 to the quality index.
Step 6
Suppose that this is a big company with centrally coordinated purchasing with four different purchasing locations where the shipments must be made with the following unit transportation costs from supply centers to purchasing centers:
Purchasing Purchasing Purchasing Purchasing
Center 1 Center 2 Center 3 Center 4
Supplier 1
Supplier 2 4
5 6
3
5
4
8
5
Supplier 3 6 8 8 9
13

14 Journal of Customer Service in Marketing & Management
The lowest transportation cost, t ij
, is 3. Therefore, if we divide 3 by every unit transportation cost ( t ij
) in the table we get the following transportation indices, I t ij
:
Purchasing Purchasing Purchasing Purchasing
Center 1 Center 2 Center 3 Center 4
Supplier 1 0.600 0.500 0.600 0.375
Supplier 2 0.750 1.000 0.750 0.600
Supplier 3 0.500 0.375 0.375 0.333
Step 7
In this step we use the v i
and It ij
parameters computed in the previous steps of this study to get the linear program of the form:
Max

W v v i x ij
+ W
It
It ij x ij i j s.t.

j x ij

s i
i=1,2,3,...,m
 x ij

d j
j=1,2,3,...,n
i
x ij

0 where
W v
= weight associated with supplier value criterion
W
It
= weight associated with transportation criterion v i
= value of supplier i
It iJ
= transportation index for shipment from supplier i to purchasing center j
x iJ
= optimum shipment quantities from supplier i to purchasing center j
s i
= supply capacity of supplier i
d
J
= demand of purchasing center j
Let's suppose that this purchasing company emphasizes the supplier value criterion, W v
, 10 times more than the transportation criterion,
W
It
W
It
.
Therefore, let W v
= 10 and
= 1. On the basis of this information, we have the following results:
For Supplier 1, W v
(v
1
) = 10(0.9642) = 9.642.
For Supplier 2, W v
(v
2
) = 10(0.9374) = 9.374.
For Supplier 3, W v
(v
3
) = 10(0.9192) = 9.192.
The W
It
(It iJ
) values would remain the same as It iJ
values because the weight associated with the transportation criterion,
W
It
, is equal to one.

Sadik Çökelez
15
Suppose we have the following demand and supply data:
Supplier
1
2
3
Capacity
40,000
38,000
35,000
Purchasing Center Demand
1
2
3
10,000
20,000
15,000
4 18,000
Then using the data immediately above as the right hand sides of the supply and demand constraints and the results of the detailed computations in the previous steps as the objective function coefficients we get the following linear program in expanded form for these specific data:
Max 9.572 x
11
+ 9.572x
12
+ 9.572x
13
+ 9.572x
14
+ 9.302 x
21
+ 9.302x
22
+ 9.302x
23
+ 9.302x
24
+ 9.192 x
31
+ 9.192x
32
+ 9.192x
33
+ 9.192x
34
+ 0.600 x
11
+ 0.500x
12
+ 0.600x
13
+ 0.375x
34
+ 0.750 x
21
+ 1.000x
22
+ 0.750x
23
+ 0.600x
24
+ 0.500 x
31
+ 0.375x
32
+ 0.375x
33
+ 0.333x
34 s.t.
x
11
+ x
12
+ x
13
+ x
14

40,000
x
21
+ x
22
+ x
23
+ x
24

38,000
x
31
+ x
32
+ x
33
+ x
34

35,000
x
11
+ x
21
+ x
31

10,000
x
12
+ x
22
+ x
32

20,000
x
13
+ x
23
+ x
33

15,000
x
14
+ x
24
+ x
34

18,000
Using LINDO (Linear Interactive Discrete Optimizer) computer software we get the following solution: x
11
= 10,000 x
12
= 0 x
13
= 15,000 x
14
= 0 x
21
= 0

16 Journal of Customer Service in Marketing & Management x
22
= 20,000 x
23
= 0 x
24
= 18,000 x
31
= 0 x
32
= 0 x
33
= 0 x
34
= 0
The computer solution shows that the company should choose Supplier 1 and
Supplier 2 and not Supplier 3 because all of the variables where the first subscript is 3 (denoting Supplier 3) have zero values. The computer output also shows the optimum quantities to ship from the chosen suppliers to various purchasing centers. For example, the value for x
11 above is 10,000 indicating that 10,000 units should be shipped from Supplier 1 to
Purchasing Center 1. The fact that x
1 2
is 0 indicates that nothing should be shipped from Supplier 1 to Purchasing Center 2. (A x
22
= 20,000 shows that
Purchasing Center 2 should meet its requirements from Supplier 2 rather than from Supplier 1). In a similar manner, a value of x
13
= 15,000 shows that
15,000 units should be shipped from Supplier 1 to Purchasing Center 3 and x
14
= 0 indicates that nothing should be shipped from Supplier 1 to
Purchasing Center 4. Nothing is shipped from Supplier 2 to Purchasing Center 1 or Purchasing Center 3 ( x
21
= 0 and x
23
= 0); 20,000 units are shipped to
Purchasing Center 2 and 18,000 units to Purchasing Center 4 from Supplier 2 (x
22
= 20,000 and x
24
= 18,000).
CONCLUSION
This paper contributes to the supplier selection decision that is one of the cornerstones of purchasing management by developing a methodology that uniquely modifies and combines the existing traditional techniques in an integrated manner. The model developed in this paper determines the best supplier by analyzing the subjective qualitative factors as well as quantitative factors and generates optimal results in regards to how much to ship from each supplier to each purchasing center. The above simple numerical example in the previous section illustrates the procedure.
One of the unique features of this model is its flexibility and adaptability and user-friendliness; for example, if a purchasing manager is interested only in the supplier value criterion he or she simply sets the weight parameter, W
It
, associated with the transportation criterion to zero in the objective function of linear program and the whole transportation segment

Sadik Çökelez is automatically deleted. On the other hand, if the minimizing of transportation costs is the only issue in a specific situation, simply set the weight parameter, W v
, associated with the supplier value criterion to zero and then the only remaining segment will be the transportation related part of the linear program.
This paper takes into account factors such as price, on-time delivery, quality, service after the sale, transportation costs and so on that are all very important in selection of the best suppliers by developing an original indexing procedure that would later generate the input parameters of the linear programming optimization model.
17
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