international journal of mechanical engineering and technology (ijmet...

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 1, January- April (2012), © IAEME

46

SUPPLIER SELECTION: A GOAL PROGRAMMING APPROACH

Rajesh Singh*,S.K.Sharma**Peeyush Pandey***

*Corresponding author and Research Scholar, Department of Mechanical Engineering,

IT-BHU, Varanasi (U.P.) INDIA [[email protected]]

** Professor & Ex. Head, Department of Mechanical Engineering, IT-BHU, Varanasi

(U.P.) INDIA [[email protected]]

***M.Tech student, Department of Mechanical Engineering, IT-BHU, Varanasi(U.P.)

INDIA[[email protected]]

ABSTRACT

Supply chain has added new dimension to business strategies. Now the competition is not

between independent organizations working for their own benefit, it is between networks

of interconnected and interdependent organizations seeking mutual benefits. Supply chain

performance depends on successful delivery of quality products and services to end

customers at competitive price with good service level. To achieve this, the company

should maintain strategic fit between its supply chain strategy and its competitive strategy.

Decision making in the field of supply chain management has become more complex due

to a large number of alternatives, multiple and sometimes conflicting goals and an

increasing turbulent environment. Some of the problems associated with supply chain

management have been effectively handled by some of the analytical techniques – Goal

programming (GP) etc.

Some of the problems associated with supply chain management have been affectively

handled by some of the analytical techniques namely goal programming (GP). The main

emphasis in this paper is on outlining Goal Programming methodologies and reporting

computational experience. This technique is found to be more effective in dealing with

problems involving multiple objectives with conflicting criteria.

Key Words: Mutual, conflicting, turbulent, computational.

INTERNATIONAL JOURNAL OF MECHANICAL

ENGINEERING AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)

ISSN 0976 – 6359 (Online)

Volume 3, Issue 1, January- April (2012), pp. 46-63

© IAEME: www.iaeme.com/ijmet.html

Journal Impact Factor (2011) - 1.2083 (Calculated by GISI)

www.jifactor.com

IJMET

© I A E M E



47

1.0 INTRODUCTION

The economic and competitive pressures have made it imperative for organizations to

focus on supply chain to reduce costs and improve operating efficiencies in supply chain

network. The thrust of global economy drives the organizations to improve process, parts

and labour, virtually anywhere in the world and get the desired combination of low cost

and high quality.

Market outcome from innovation can be studied from different lenses. The industrial

organizational approach of market characterization according to the degree of competitive

pressure and the consequent modeling of firm behavior often using sophisticated game

theoretic tools, while permitting mathematical modeling, has shifted the ground away from

an intuitive understanding of markets. The earlier visual framework in supply chain, of

market demand and supply along price and quantity dimensions, has given way to

powerful mathematical models which though intellectually satisfying has led policy

makers and managers groping for more intuitive and less theoretical analyses to which

they can relate to at a practical level.[]

In such supply chains, the owner of each entity attempts to maximize its benefit. Focus on

individual links of the supply chain invariably leads to inefficient and high cost

product/service delivery system. In the process, such a supply chain looses to supply chain

that is customer focused where the individual links orient their business processes and

decisions to ensure least cost delivery of products/services to the ultimate customer.

Goal Programming is a branch of multi objective optimization, which in turn is a branch of

multi- criteria decision analysis (MCDA), also known as multiple criteria decision making

(MCDM). It can be thought of as an extension of linear programming that allows

simultaneous satisfaction of several conflicting objectives while obtaining a solution that is

optimal with respect to the decision maker’s specification of goal priorities. In the typical

real world situation, goals set by the decision makers are achievable only at the expense of

other goals, which are often incompatible. Since it may be impossible for a decision maker

to meet all the decided goals, he / she attempts to find a solution that comes as close as

possible to reaching all goals. Thus there is a need to establish a hierarchy of importance

among these incompatible goals. This hierarchy ensures that before the less important

goals are considered, the more important goals must be satisfied. The hierarchy can be

established by providing either ordinal or cardinal ranking of the goals in terms of their

importance to the organization.[2]

2.0 LITERATURE REVIEW

In the last two decades, both academicians as well as practitioners have shown keen

interest on the subject supply chain management (SCM). Globalization of market,

increased competition, reducing gap between products in terms of quality and performance

are compelling the academicians and industry to rethink about how to manage business

operations more efficiently and effectively. Since, scope for improvement within the



48

organization is decreasing; the academicians and captains of industry are looking for newer

alternatives of integrating the business activities beyond the organization’s boundary.

More specifically, they are trying to align and coordinate the business processes and

activities of the channel members to improve the overall performance and effectiveness of

supply chain. As a result, producer, vendor and buyer have started aligning their operations

to make the business more focused. The alignment and integration lead to deliver more

value and satisfaction to the customer for the same price. This makes the supply chain

more competitive. In the process, the channel partners increase their market share and

profit.

In the management (strategy) on the other hand, there is a vast array of relatively simple

and intuitive models in supply chain network for both managers and consultants to choose

from. Most of these supply chain models provide insights to the manager which help in

crafting a strategic plan consistent with the desired aims.

Supply Chain Management is an approach to dealing with suppliers and not only

purchasing but also a comprehensive approach to develop maximum value from the supply

chain. Leading companies determine the right supply chain strategy and often develop a

logistics management for organization to ensure effective warehousing and distribution

network to fulfill customer’s requirement.

3.0 GOAL PROGRAMMING

In cardinal ranking cases, importance of parameters or weights are assigned to the given

goals. Then all of them are expressed in a composite objective function: the problem is

solved as a single- objective problem. In these types of problems determining the weights

is the most important concern. This approach of goal programming is called Non

preemptive Goal Programming. This method can be used if all the goals are defined using

some common units for example, in terms of money units. If the goals are not

commensurable, normalization procedure is needed in this case. The most intuitive and

simplest way for normalizing the goals is to express them in percentages rather than in

absolute values.

Goal programming is multi objective programming technique. it can thought of as an

extension of linear programming that allows simultaneous satisfaction of several

conflicting objectives while obtaining a solution that is optimal with respect to the decision

makers specification of goal priorities.

In the typical real world situation, goals set by the decision maker are achievable only that

the expense of other goals, which are often incompatible. Since it may be impossible for a

decision maker to meet all of the decided goals, he/she attempts to find a solution that

comes as close as possible to reaching all goals. Thus, there is a need to establish a

hierarchy of importance among these incompatible goals. This hierarchy ensures that

before the less important goals are considered, the more important goals must be satisfied.

The hierarchy can be established by providing either ordinal or cardinal ranking of the

goals in terms of their importance to the organization. In cardinal ranking cases, important



49

parameters or weight are assigned to given goals. Then, all of them are expressed in a

composite objective function; the problem is solved as a single objective problem. In these

types of problem, determining the weights is the most important concern. This approach of

goal programming is called No preemptive Goal programming. This method can be used if

all the goals are defined using some common units. If the goals are not commensurable,

normalization procedure is needed in this case. The most intuitive and simplest way for

normalization procedure is needed in this case. The most intuitive and simplest way for

normalizing the goals is to express them in percentages rather than in absolute values.

Ordinal ranking to express ranking of the goals in order of priority, Known as preemptive

priorities. This method is named as Preemptive goal programming. In this approach, the

most important goal which is in priority one is satisfied using the standard linear

programming after that the second priority level is considered then the third and so on.[2]

3.1 Methodology The methodology used in Goal Programming comprises modeling phase and solution

phase. The steps of the methodology are summarized as follows.

3.2 Modeling Phase:

This phase focuses on following points.

• Define vendors supply chain selection criteria,

• Collect necessary data,

• Calculate performance measures,

• Identify main and sub goals,

• Determine target values for the goals

• Express the notation used in the mathematical model,

• List the assumptions,

• Formulate the goals,

• Formulate constraints,

3.3 Solution Phase Once the modeling phase requirements are ensured the decision maker has to focus on

solving the model.

3.4 Solving the model

In solving non preemptive goal programming problems, a value for each goal is specified

and deviational variables are introduced and the objective function is expressed as an

overall function to be minimized. This is done when all the goals are considered to be of

equal importance. However, differential weights may be given to the various goals in

accordance with their significance. For a particular priority sequence of objectives to be

achieved, consider the first priority objective function and related constraints; solve the

problem as extended linear programming problem using LINGO software. Then consider

next priority objective function and include earlier objective function as constraint with

target value as its right hand side constant along with initially declared constraints. Like

this proceed with next priority objectives function solving with including earlier objective

functions as constraints with initially declared constraints.



50

In method of difference, instead of trying to maximize or minimize the objective criterion

directly as in linear programming, set of constraints are to be maximized. In this the

objective function contains primarily the deviational variables that represent each goal or

sub goal. The deviational variable is represented in two dimensions in the objective

function, a positive and a negative from each sub goal/ or constraint. Then the objective

function becomes the minimization of weighted sum of all the deviation between the

targets and their aspiration levels, based on the relative importance or priority assigned to

them. In order to satisfy the minimization type of goal, the positive deviations from target

levels should be minimized and in case of maximization type of goal, the negative

deviations should be minimized.[3]

3.5 RESULTS AND INTERPRETATION

After each alternative model was solved, the resulting order quantities assigned to each

selected vendor were obtained. Each alternative model can be evaluated.

3.6 Computational experience with Goal Programming

A goal programming approach has been applied in decision problems which include

multiple objectives and conflicting criteria for selecting an alternative from a known set of

alternatives. The study focuses on assessing supply chain of vendors through goal

programming using changing goal priorities.

4.0 GOAL PROGRAMMINNG USING CHANGING GOAL PRIORITIES-CASE

STUDY

The vendor selection process has undergone significant changes during the past twenty

years. These include quality guide lines, improved reliability, reduced product costs and

increased technical capabilities. A supply chain selection of vendors is a multi objective

problem involving both quantitative and qualitative criteria. Over the years a number of

quantitative approaches have been applied to supplier selection problems. Although the

goal programming (GP) has previously been implemented in supplier selection problems,

in this paper a comprehensive application of GP with software tool for a real situation case

is presented along with changing goal priorities to choose the best supply chain of vendors

with optimum cost.[4] This model was solved on LINGO optimization software by

utilizing the sequential goal programming solution method. A vendor selection problem

has been formulated as a changing goal priorities integer goal programming. This selection

problem includes seven primary goals: minimizing the amount of units rejected, number of

lots rejected, mount of units delivered late, amount of lots delivered late, and maximize the

multiplication of the order quantity with the past landed cost index , multiplication of the

order quantity with capacity utilization ratio, Multiplication of order quantity with measure

of past business . This paper also includes comparison of conventional model with new

comprehensive approach of goal programming. The proposed approach has the capability



51

to handle realistic situation in a changing goal environment by using lingo software tool

and provides a better decision tool for selection.[5]

One of the important areas of purchasing research that has significant practical implication

is evaluation and selection of Vendors. Several researches have addressed the strategic

importance of the Vender evaluation process. These studies have mainly emphasized the

impact of the selection decision of vendors on the various functional areas of business

from procurement to production and delivery of the product to the end customer. Vendors

having reliable supply chain are considered as the best intangible asset of any organization.

Hence both new and established vendors are coming for critical review of their plant

capacity, financial condition and performance, particularly in today’s dynamic situation.

The materials executives have to follow a selective policy and chose only those vendors

that are suitable to their needs. A true measurement of in effective purchasing department

is obtained by the quality of a reliable vendors selected for supplying goods and services.

The purchaser’s primary interest lies in getting for his company, the best value of money

from his vendors. This implies that he should be in opposition to asses and rate their

vendors performance against what is expected from an ideal suppliers in the prevailing

socio-political and economical environment. The absolute standard is difficult to define

with any degree of exactness, but mathematical models are available to evaluate the

performance of vendors.

Many companies purchase many of items from many of suppliers. Purchased materials

accents for 30 to 60 percent of sales and more than 50 percent of the cost of goods sold in

most manufacturing firms. In today’s competitive operating environment it is impossible to

successfully produce low-cost, high quality products without satisfactory suppliers.

Selection decisions of vendors are complicated by the fact that various criteria must be

considered in the decision making process. Quality, Delivery, cost, capacity and past

business are known as the most crucial criteria. Frequently, the relevant criteria are in

conflict. For example, the suppliers with the lowest price may not have the vest quality or

delivery performance of the various suppliers under consideration. The firm must analyze

the tradeoffs among the relevant criteria when making decision regarding selection of

vendors. Consequently, it can be said that the assessing supply chain of vendors. Through

goal programming, is often an inherently multi-objective one. In this chapter, an integrated

goal programming model is presented in order to solve supply chain selection of a vendor

of a manufacturing company. [6]

4.1 Case Study Description The study has been conducted in an petroleum company which produces more than 10

varieties of products. As per the company policy the actual name of the company is not

mentioned. The company manages all of the business operation using SAP R/3, which is

an Enterprise Resource planning system. The company requires many kinds of material

and finished components in large amounts. There are many suppliers willing to supply to

such an organization. This is to say for a specific item. Different alternative suppliers are

available from abroad domestic and International markets. From this point of view it can

be ascertained that management and evaluation of all these suppliers is very hard,

complex, and comprehensive task. This study considers one final product which requires



52

four items such as raw material or finished products and each item being supplied by four

different vendors and hence this study focuses on selection of vendors.

Problems that are faced by the company in the procurement and production are as

follows:

• Lateness of the materials that are ordered.

• Rejection of the lots that are not meeting the

quality levels.

• Specification set by the company.

• Appearance of low quality or broken parts in

production.

In order to overcome these problems, the management believes that the necessity of an

effective vendor evaluation and selection system is of great importance. Company’s most

important goal is to establish a vendor selection system based on tangible criteria and thus

want to use the output of this system for supplier selection and order allocation decision.

Performing such a system also allows management to reduce the supplier base. The

company desires to determine the best suppliers for each material and allocate order

among them. [7]

4.2 The Proposed approach

This study showed an application of the goal programming to solve a multi- item multiple

sourcing vendor selection problems. Such a model can be useful for future order allocation

decision while benefiting from past performance data. The integrated model includes two

basic objectives in a preemptive structure to address these consideration quality, delivery,

cost, capacity, and amount of past business. The methodology used in this study comprises

modeling and solution phases, sequentially. Therefore the steps of the methodology are

summarized as follows.

4.3 Vendor selection criteria

In order to determine preference for the company about the supplier selection criteria three

meetings were organized with participation of the purchasing specialists. According to

these meeting seven important criteria were defined to address quality, delivery, cost,

productivity, and previous business consideration.[8] The main and sub criteria are shown

in Table 4.1



53

4.4 DATA COLLECTION

Performance data of the suppliers such as quantity of units received, quantity of unit

rejected, No. of lots received, No. of lots received, No. of lots rejected, No. of unites

delivered late, No. of lots delivered late, Minimum past landed cost, Average past landed

cost, Percentage of coal used, Particulate Emission(PE) of smoke in Kg/Ton, Content of

SO2 in smoke in percentage, Content of CO in smoke in percentage, Yearly capacity of the

suppliers are collected.

The problem premises considered as stated earlier as companies single final product which

requires four items such as raw materials or finished products and each items to be

supplied by four different vendors and each of the vendors can supply any of the items.

The company wants to order total of 1,00,000 units of each item all four suppliers put

together. Vendor supply capacity constraints to our company are also collected and are as

follows.

• Vendor-4 can supply item no-2, a maximum of 30.000 no- of units



• The planning period is two year

4.5 Calculation of the performance measures

The data collected earlier are used to calculate the performance measures as per the

following formulas are shown in table 4.3

URP = Unit rejected

Unit received

LRP = Lots rejected

Lots received

UDLP = Unit delivered late

Unit received



54

LDLP = Lots delivered late

Lots received

PLCI = Min.previous landed cost

Avg. previous landed cost

PUR = Unit received

Yearly Productivity of the supplier

MPE = Unit received from the relevant supplier

Total quantity received from all suppliers

MPS = Number of times price changed of lots

Total number of lots

FSPU= Coal used/Yr*Percentage of coal used*PE

100*Yearly Productivity for item i

FSO2= FSPU*Percentage of SO2 in smoke

100

FCO= FSPU*Percentage of CO in smoke

100

Performance table for the year 2009 is shown in the in the Appendix 1 and the

coefficient collected same way for the year 2010.

4.6 Identification of the goals

The main objective considered is a composite goal which includes seven different sub

goals to address the predefined vender supply chain performance criteria, and minimizes

the weighted sum of all the deviation between the targets and their aspiration levels for all

materials.

4.7 Determination of the Target values

For each objective it is necessary to determine the target value to be satisfied on the basis

of each criterion. These values demonstrate the expected performance levels from the

vendor selection and must be determined by the company. Normally, the ideal values of

the measures are the maximum values that could be possible for them. For example, this

value is zero for the URP, while it is 1.0 for the PLCI. To do that, an interview was made

with the managers for determination of the target values, and they expressed each of the



55

performance targets as a weighted average of the best two suppliers, which is calculated by

the following equation for each material:

Target value = 0.70*Measure of the best supplier +0.30* Measure of the second best

vendor.

On the other hand, it can be found out the target landed cost for given material by

putting the last landed costs of the best two suppliers into the above formulation instead of

the performance measures.

4.71 Notation Nations used in the model are given as follows.

Decision Variables

QOijt : Quantity ordered from supplier i for item j

on year t.

X ij : Binary integer variable (1 if supplier i is

selected for item j; 0, otherwise)

4.72 Parameter and constants

i: 1,…, I (supplier)

j: 1,….J (item)

t: 1,…,T (year)

URP ij : Percentage of units rejected for item

j from supplier i.

LRP ij : Percentage of lost rejected for item j from

supplier i.

UDLPij : Percentage of units delivered late for item

j from supplier i.

LDLPij : Percentage of units rejected for item j

from supplier i.

PLCIij : Past landed cost index for item j of

supplier i.

PUR ij : Capacity utilization ratio of supplier I for

item j.

MPEij : measure of past business for item j from

supplier i

MPSij : measure of price stability for item j from

supplier i

LLCij : last landed cost for item j of supplier i

FSPUij : fraction of smoke in percentage per unit

for item j from supplier i

FSO2ij : fraction of SO2 in percentage per unit


FCOij : fraction of CO in percentage per unit


TURPj : target percentage value of the URP

from item j.

TLRPj : target percentage value of the LRP



56

from item j.

TUDLPj : target percentage value of the UDLP

from item j.

TLDLPj : target percentage value of the LDLP

from item j.

TPLCIj : target percentage value of the PLCI

from item j.

TPURj : target percentage value of the PUR

from item j.

TMPEj : target percentage value of the MPE

from item j.

TMPSj : target percentage value of the MPS

from item j.

TLCIj : target landed cost for itemj.

TFSPUj : target percentage value of the FSPU

from item j

TFSO2j : target percentage value of the FSO2

from item j

TFCOj : target percentage value of the FCO

from item j

NURPjt : negative deviation from TURPj on year t.

PURPjt : positive deviation from TURPj on year t.

NLRPjt : negative deviation from TLRPj on year t.

PLRPjt : positive deviation from TLRPj on year t.

NUDLPjt : negative deviation from TUDLPj on year t.

PUDLPjt : positive deviation from TUDLPj on year t.

NLDLPjt : negative deviation from TLDLPj on year t.

PLDLPjt : positive deviation from TLDLPj on year t.

NPLCI jt: negative deviation from TPCLIj on year t.

PPLCIjt : positive deviation from TPLCIj on year t.

NPURjt : negative deviation from TPURj on year t.

PPURjt : positive deviation from TPURj on year t.

NMPEjt : negative deviation from TMPEj on year t.



57

PMPEjt : positive deviation from TMPEj on year t.

NMPSjt : negative deviation from TMPSj on year t.

PMPSjt : positive deviation from TMPSj on year t.

NLCjt : negative deviation from TLCj on year t.

PLCjt : positive deviation from TLCj on year t.

PFSPUjt : positive deviation from TFSPUj on year t.

NFSPUjt : negative deviation from TFSPUj on year t.

PFSO2jt : positive deviation from TFSO2j on year t.

NFSO2jt : negative deviation from TFSO2j on year t.

PFCOjt : positive deviation from TFCOj on year t.

NFCOjt : negative deviation from TFCOj on year t.

WURP : Weight assigned to the URP goal.

WLRP : Weight assigned to the POLR goal..

WUDLP : Weight assigned to the UDLP goal.

WLDLP : Weight assigned to the LDLP. goal.

WPLCI : Weight assigned to the PLCI. goal.

WPUR : Weight assigned to the PUR goal.

WMPE : Weight assigned to the MPE goal.

WMPS : Weight assigned to the MPS goal

WFSPU : Weight assigned to the FSPU goal

WFSO2 : Weight assigned to the FSO2 goal

WFCO : Weight assigned to the FCO goal



58

NOS : Number of suppliers to be selected

RQjt : Required quantity for item/on year t.

AYCij : average yearly capacity of supplier i

for item. j.

MABij : Minimum amount of business to be

given to supplier i for item. j.

4.73 Assumptions

Some assumptions made while mathematical model of the problem was being developed

are as follows:

• The planning period two year.

• The material requirements and average yearly

capacities of the suppliers are constant during the planning period.

• It is assumed that the early deliveries do not affect the landed costs.

• There is no budget constraint to obtain the order.

4.8 Formulation of the Goals The first objective function aims to minimize the weighted sum of all the deviations occurred from

the differences between the desired and achieved levels of the sub goals. Because all performance

measures and target values was measured in percentages, there is no need for normalization of the

goals. The sub goals were formulated as soft constraints in the model, as shown below:

Sub Goal 1 : minimize the amount of units rejected II I I I

∑ URPij *QO ijt +NURP jt – PURP jt i=1

I = TURP j * ∑ QO ijt i=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 2 : minimize the numbers of lots rejected. I

∑ LRPij *QO ijt + NLRP jt – PLRP jt

i=1

I

= TURP j * ∑ QOijt

i=1 for j=1, …., J: and t = 1,..., T.

Sub Goal 3: minimize the amounts of units delivered late. I

∑ UDLPij *QO ijt + NUDLP jt – PUDLP jt i=1

I = TUDLP j * ∑ QOijt

i=1 for j=1, …., J: and t = 1,..., T.



59

Sub Goal 4: minimize the amounts of lots delivered late. I ∑ LDLPij *QO ijt + NLDLP jt – PLDLP jt i=1

I = TLDLP j * ∑ QOijt I=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 5: maximize the multiplication of the order quantity and the past landed cost index. I

∑ PLCIij *QO ijt + NPLCI jt – PPLCI jt

i=1

I

= TPLCI j * ∑ QOijt i=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 6: maximize the multiplication of the order quantity and the capacity utilization ratio. I ∑ PURij *QO ijt + NPUR jt – PPUR jt i=1

I = TPUR j * ∑ QOijt i=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 7: maximize the multiplication of the order quantity and the measure of past business. I ∑ MPE ij *QO ijt + NMPE jt – PMPE jt

i=1

I

= TMPE j * ∑ QOijt i=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 8 : minimize the multiplication of the order quantity and the measure of past business. I

∑ MPS ij *QO ijt + NMPS jt – PMPS jt i=1

I

= TMPS j * ∑ QOijt i=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 9 : minimize the multiplication of the order quantity and the fraction of smoke per unit. I

∑ FSPU ij *QO ijt + NFSPU jt – PFSPU jt

i=1

I



60

= TFSPU j * ∑ QOijt

i=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 10 : minimize the multiplication of the order quantity and the fraction of SO2 per unit. I

∑ FSO2 ij *QO ijt + NFSO2 jt – PFSO2 jt i=1

I

= TFSO2 j * ∑ QOijt i=1

for j=1, …., J: and t = 1,..., T.

Sub Goal 11 : minimize the multiplication of the order quantity and the fraction of CO per unit. I

∑ FCO ij *QO ijt + NFCO jt – PFCO jt i=1

I = TFCO j * ∑ QOijt

i=1

for j=1, …., J: and t = 1,..., T.

As can be seen, there exist some conflicts among the above goal due to the different optimization

structures. The first four of sub goals are expressed in a minimization form, and they aim at

minimizing the order quantity as far as possible. However, the succeeding three goals, which are to

be maximized, try to maximize the order quantity. Therefore, in order to satisfy the first four goals

the positive deviations from the target levels should be minimized, while the negative deviations

should be minimized for the last three goals. Under these considerations the objective function

taken the following form: J I J I

Min {WURP*∑ ∑ PURPjt + WLRP*∑ ∑ PLRPjt+ j=1 i=1 j=1 i=1

J I J I WUDLP* ∑ ∑ PUDLPji + WLDLP* ∑ ∑ PLDLPji j=1 i=1 j=1 i=1

J I J I

+ WPLCI*∑ ∑ NPLCIjt + WPUR* ∑ ∑ NPURji + j=1 i=1 j=1 i=1

J I J I

WMPE ∑ ∑ NMPEji + WMOPS ∑ ∑ PMPSjt } j=1 i=1 j=1 i=1

4.9 Formulation of the constraints

4.91 Demand Constraints:

the sum of the assigned order quantities to the selected suppliers should not be less then the

required quantity by the company. J

∑ QOij + QOijt >= RQjt j=1

for j=1 ,…….j and t=1,…….,T



61

4.92 Capacity Constraint:- The quantity ordered from the selected supplier should be equal or

less than its average yearly capacity.

QOijt <= AYCijt * Xij

for i= 1,-----------I; j=1,--------J and t= 1,------T

5.0 GENERATION OF ALTERNATIVE ACHIEVEMENT FUNCTION

The first task for the formulation of the achievement function is to give priority to each of

the objectives. However, it is possible to generate different sets of priorities. Changes in

the priority ranking in the achievement function can have a major impact on the optimal

solution. By recording the priority ranking, the management can make tradeoff decisions

and decide which solution to select as ‘best’ therefore instead of using only one priority

scheme, all alternative priority- ranking structures were used to provide alternative

solutions to the management. The problem was solved separately for these alternatives.

6.0 SOLUTION OF THE MODEL

In this research, the Industrial LINGO software was used to solve model. LINGO is known

as mathematical programming language, and allows users to solve linear and also

nonlinear models. The sequential goal programming solution method was utilized in this

software to get the optimum results for different achievement function. If the model is

solved against the target values determined by the company, some of the undesirable

deviations are found out s higher than Zero, so the related goals are not satisfied. It means

that selected supply chain cannot meet the targets of the company. In order to overcome

this matter, necessary modifications must be actualized on the targets, In this study, they

were implemented by increasing the target value by the value of positive deviation

obtained in the maximization goals, and by decreasing the target value by the value of

negative deviation for maximization goals. After the first priority objective was satisfied,

the second priority objective was added into the model.

7.0 RESULT

For each of the priority of goals, the resulting optimum order quantities assigned to each

vendor are calculated using method of Goal Programming and are shown in Table 4.5.



62

8.0 CONCLUSION

A goal programming method was developed for vendor selection of a manufacturing

company. The described model determines the best vendor for each material, and also

simultaneously allocates purchase orders among them with consideration of conflicting

objectives. It is observed that when company follows goal priority-1, order has to be

placed on Vendor-2 and Vendor-4. When the company implements goal priority -2, or goal

priority-3, order has to be placed both on vendor -1 and Vendor-4. Finally when the

company adopts goal priority-4, order has to be placed on Vendor-1.Hence the

management of company can choose appropriate vendors. The performance measures or

criteria used to evaluate vendor’s supply chain are tangible, and calculated according to the

proper formulations developed in the modeling phase. Vendor selection decision affects

both responsiveness and efficiency of supply chain. Vendors with lower price may not

have the best quality or delivery performance. The company must analyze the trade off

among the relevant criteria when making decision regarding selection.

9.0 REFERENCE

1. Badri. M.A., Davis, D.L., Davis, D. (1995). "Decision support models for the location of

firms in industrial sites", International Journal of Operations & Production Management, Vol.

15, No.1, pp. 50-62.

2. Charnes, A., and W.W Cooper. (1977) Goal Programming and Multiple Objective

Optimizations. European Journal of operational Research. 1(1).39-54.

3. Ignizio, James. P. (1989) On the merits and demerits of integer goal programming. Journal of

the Operational Research Society. 40 (8). 781- 785.



63

4. Ellram, L.M. (1990), The supplier selection decision in strategic partnerships,. Journal of

Purchasing and Materials Management, Vol-26 (4), pp 8-14.

5. Ellram, L.M., (1991), A managerial guideline for the development and implementation of

purchasing partnerships, International Journal of Purchasing and Materials Management,

Summer, pp 2-16.

6. Korhonen, P. (1992) Multiple Criteria Decision Support: The State of Research and Future

Directions. Computers and Operations Research Vol. 19, No. 7, October 1992, pp. 549-551.

7. Lee, Sang. M. (1972). Goal Programming for Decision Analysis. Philadelphia: Auerback.

8. Lokesh vijayvargy (2008) effective vendor selection through goal programming using

changing goal priorities in supply chain, International Conference on Issues & Challenges in

supply chain management.

9. Sunil Chopra, Peter meindl. (2008). “Supply Chain Management Strategy, Planning, and

Operation.” Prentice Hall.

10. Verma, R. and Pullman, M. E. (1998). An Analysis Of The Supplier Selection Process,

Omega, International Journal of Management Science, Vol. 26 No. 6,p. 739-50.

APPENDIX 1

Table 4.5 Performance characteristics in year 2009

Vendor-1

URP LRP UDLP LDLP PLCI PUR MPE MPS FSPU FSO2 FCO

Item-1 0.0194 0.0000 0.0280 0.0000 0.9658 0.7200 0.2494 0.0200 0.0600 0.0180 0.0168

Item-2 0.0164 0.0000 0.0231 0.0400 0.9771 0.7317 0.2535 0.0200 0.0357 0.0093 0.0112

Item-3 0.0168 0.0000 0.0232 0.0000 0.9865 0.7280 0.2516 0.0087 0.0500 0.0225 0.0125

Item-4 0.0077 0.0000 0.0298 0.0000 1.0000 0.7297 0.2510 0.0115 0.0350 0.0098 0.0157

Vendor-2


Item-1 0.0124 0.0000 0.0459 0.0000 0.9496 0.7270 0.2518 0.0241 0.0790 0.0276 0.0197

Item-2 0.0095 0.0357 0.0335 0.0000 0.9286 0.6972 0.2416 0.0179 0.0383 0.0107 0.0126

Item-3 0.0119 0.0000 0.0190 0.0000 2.9799 0.7251 0.2505 0.0333 0.0457 0.0182 0.0123

Item-4 0.0097 0.0000 0.0208 0.0400 0.8991 0.7263 0.2515 0.0160 0.0272 0.0068 0.0116

Vendor-3


Item-1 0.0150 0.0000 0.0463 0.0417 0.9739 0.7267 0.2517 0.0167 0.0902 0.0333 0.0261

Item-2 0.0100 0.0417 0.0382 0.0417 0.9500 0.7269 0.2519 0.0160 0.0399 0.0119 0.0139

Item-3 0.0317 0.0417 0.0331 0.0000 0.9605 0.7251 0.2506 0.0125 0.0574 0.0218 0.0172

Item-4 0.0173 0.0400 0.0192 0.0400 0.9276 0.7263 0.2499 0.0080 0.0237 0.0054 0.0082

Vendor-4


Item-1 0.0126 0.0000 0.0192 0.000 0.9504 0.7136 0.2472 0.0208 0.0881 0.0281 0.0264

Item-2 0.0221 0.0417 0.0461 0.000 0.9344 0.7301 0.2530 0.0125 0.0367 0.0128 0.0128

Item-3 0.0153 0.0410 0.0157 0.040 0.9419 0.7155 0.2473 0.0164 0.0653 0.0215 0.0215

Item-4 0.0072 0.0000 0.0163 0.0417 0.9152 0.7198 0.2476 0.0042 0.0311 0.0054 0.0099

international journal of mechanical engineering and technology (ijmet...

Documents