chapter 4 a case study of banana in...

51
89 CHAPTER 4 A CASE STUDY OF BANANA IN INDIA This chapter offers solutions for a selection of post-harvest technologies, optimal route selection including risk identification and risk assessment for a case study of the banana supply chain in India. This work was initiated by interview and discussion with banana growers, traders, commission agents, wholesalers, and faculty members and Researchers from Tamil Nadu Agriculture University. Risk issues and risk factors were obtained through interview and discussion. Causal Loop Diagram, a tool from systems dynamics was developed after interview and discussion. The Fuzzy Delphi Technique Method (FDM) was used in order to obtain values of elementary risk factors. The Analytic Hierarchy Process (AHP) was applied for selecting the most appropriate post-harvest technology alternative. Dynamic Programming was used for analysis of optimal routes of the banana supply chain. Finally, the multistage fuzzy goal programming approach was employed to deal with uncertainty in price, quality attributes, and operation costs of post harvest technological practices in order to achieve the maximum profit and the most reasonable risk in profit loss. 4.1 ANALYSIS OF RISK FACTORS INFLUENCING PRICE FLUCTUATION IN THE SUPPLY CHAIN Likelihood of an uncertainty event occurring can be referred to as risk. Risk magnitude must be measured to evaluate possibility of the uncertainty event. The term risk is the preference in quantitative analysis

Upload: others

Post on 24-Mar-2020

11 views

Category:

Documents


1 download

TRANSCRIPT

89

CHAPTER 4

A CASE STUDY OF BANANA IN INDIA

This chapter offers solutions for a selection of post-harvest

technologies, optimal route selection including risk identification and risk

assessment for a case study of the banana supply chain in India. This work

was initiated by interview and discussion with banana growers, traders,

commission agents, wholesalers, and faculty members and Researchers from

Tamil Nadu Agriculture University. Risk issues and risk factors were

obtained through interview and discussion. Causal Loop Diagram, a tool from

systems dynamics was developed after interview and discussion. The Fuzzy

Delphi Technique Method (FDM) was used in order to obtain values of

elementary risk factors. The Analytic Hierarchy Process (AHP) was applied

for selecting the most appropriate post-harvest technology alternative.

Dynamic Programming was used for analysis of optimal routes of the banana

supply chain. Finally, the multistage fuzzy goal programming approach was

employed to deal with uncertainty in price, quality attributes, and operation

costs of post harvest technological practices in order to achieve the maximum

profit and the most reasonable risk in profit loss.

4.1 ANALYSIS OF RISK FACTORS INFLUENCING PRICE

FLUCTUATION IN THE SUPPLY CHAIN

Likelihood of an uncertainty event occurring can be referred to as

�risk�. Risk magnitude must be measured to evaluate possibility of the

uncertainty event. The term �risk� is the preference in quantitative analysis

90

(rather than uncertainty). In the next section, risk identification will be

discussed.

4.1.1 Risk Identification and Risk Assessment

Based on the rapid agricultural supply chain risk assessment

guideline reported by World Bank (Jaffee 2013), an agricultural supply chain

may be subjected to or experience multiple risks, with farmers and firms

facing risks from different sources. All possible risk issues were discussed

through interview and discussion in order to get a list of all possible major

risk issues, followed by elementary risks, risk factors and elementary risk

factors. Quantification of weight for risk issues, elementary risk factor value

and effectiveness weight for method responding to risk was done by using

Fuzzy Delphi Method. A Causal Loop Diagram was applied to show

mechanisms of elementary factors influencing risk value. A Conceptual

Model for Risk Identification and the Risk Assessment Process is shown in

Figure 4.1.

91

Figure 4.1 Conceptual Model for Risk Identification and Risk

Assessment Process

4.1.2 Price Fluctuation and Elementary Risk Factors

Risk management includes activities to identify, analyze and

respond to risk. Risk identification reviews the uncertainties in a supply chain

and lists the consequent risks. Risk identification produces a list of the risks

that are likely to affect the supply chain and hence the broader organization.

The general procedure for risk identification follows:

(1) Define the overall supply chain process

(2) Divide this into a series of distinct, related operations

(3) Systematically consider the details of each operation

(4) Identify the risks in each operation and their main features

(5) Describe the most significant risks in a register.

5. Define Rule for model: Knowledge base in food technology, agribusiness, and agro-industry

6. Application of Fuzzy Inference System (FIS)

7. Risk Value for Sustainability

3. Elementary Risk Factors and value of Elementary Risk Factors

1. Interview and Discussion with experts

4. Risk Profile: Risk Issues: Elementary Risk, Risk Factor, Elementary risk, and method to respond to risk

4. Development of Causal Loop Diagram

2. Application of Fuzzy Delphi Methods

92

Handling Awareness

Storage time Season

Post-Harvest Treatment

Risk event Magnitude

Consequence of Risk Poor Appearance

For the actual identification of risk in step 4, tools like analyses of

historical data, brainstorming, cause-and-effect analyses, fault trees, process

mapping, likelihood�impact matrices and scenario planning and the Delphi

method are generally used (Water 2007). At the first phase of the risk

management process in this work, the main risks of the fresh produce supply

chain were identified based on interviews carried out with experts involved in

the systems, academia and related research institutes. Then the cause-and-

effect diagram was developed.

(a) Poor appearance prediction

(b) Change price down prediction

Figure 4.2 Relationship between the risk input factors, risk magnitude

and consequences

Appearance Season

Production Quantity

Risk event Magnitude

Consequence of Risk Change Price Down

93

4.1.3 Application of Fuzzy Theory for Risk Identification

Fuzzy set theory, (Zadeh 1965) was developed for solving

problems in various areas in which observations and judgments are

subjective, vague and imprecise. A fuzzy inference system (FIS) is to

determine the degree to which the inputs belong to each of the appropriate

fuzzy sets through their membership functions. The input is always a crisp

numerical value limited to the universe of discourse of the input variable and

the result of fuzzification is a fuzzy degree of membership. The problem of

constructing a membership function is that capturing the meaning of the

linguistic terms employed in a particular application adequately and assigning

the meanings of associated operations to the linguistic terms. The scenario

involves a specific knowledge domain of interest. For this case, fifteen

experts were interviewed to elicit the knowledge of interest and to express the

knowledge in some operational form of a required type. The magnitude of

risk events is usually affected by some risk factors which are determined

through the recognized cause and effect feedback loops. In

Figure 4.2, it is shown that the magnitude of a poor appearance risk event has

been affected by four risk input factors. The experts are asked to provide three

estimates of a specific value by determining the minimum (ai), the most

plausible (bi), and the maximum estimated value (ci). The estimates are

presented in the form of triangular fuzzy numbers (ai, bi, ci), where

i = 1, 2, .., nth expert.

The consolidation of input factors are done using the fuzzy Delphi

technique. The final consolidated fuzzy numbers will act as inputs to the

fuzzy control system to determine the magnitude of risk events in the later

stage (Kaufmann and Gupta 1988; Kunsch and Springael 2008). The values of

input factors affecting risks are proposed by different experts as triangular

fuzzy numbers (TFN) based on their subjective judgments. The Fuzzy Delphi

94

technique was employed to consolidate the TFNs provided by the experts.

The magnitude of risk is assessed by the fuzzy control system (fuzzy logic

if�then rules) based on the values of input factors. The fuzzy logic if�then

rule performs approximate reasoning with imprecise or vague dependencies

and commands. The fuzzy control systems consist of three major components

(Zimmermann, 2001): fuzzification module, Inference and Defuzzification.

The first step is to define all possible risks that are considered by

identified experts in the systems from both members involved in the supply

chain (including farmers, commission agent, brokers, traders, commission

agents in the banana supply chain) and people who are not involved in the

supply chain but work in business related to the banana supply chain

(including, market analyst, faculty members from universities, and scientists

from research institutes). The Fuzzy Delphi technique was employed in the

first stage to define important risk through steps; important risk magnitude

value was found with respect to major risk factors as shown in Table 4.1.

Price fluctuation was selected for study in the further step since it is

the most important risk recommended by experts. Table 4.2 describes

indentified possible elementary factors evaluated by experts through a

questionnaire with respect to price fluctuation.

95

Table 4.1 Some of risks in banana chain in Tamil Nadu

No. Risk Risk respect to Risk Characteristic

1 Price Fluctuation Risk

Farmers

/Retail Supplier

Market price changes from the prediction of commitment/contract

2 Demand Risk Farmers/

Brokers/

Traders

Demand suddenly decline from prediction shortly

3 Production Loss Risk

Farmers/ Harvested product is down grade, rejected, which is not marketable

4 Competition Risk Farmers/ Brokers/

Traders/Retail Supplier

The emergence of substitute (Mango, Sweet lime, Apple, Grape) result in market competition

5 Cost Risk

Farmers / Retail Supplier

Over input investment in pre-harvest treatment, or cost of product may rise due to management neglectance

6 Quality Risk Farmers/Brokers/

Traders/

Commission agent

Appearance, size, shape are not satisfied and product can be rejected or down grade

7 Investment Implementation Risk

Farmers/ Brokers/ Traders

The member may not fulfill the investment by contract/commitment

8 Information Sharing Risk

Brokers/Traders/ Commission agent

Information sharing may result in the loss of business secret of members

9 Worst Weather Condition Risk

Farmers Various normal and abnormal calamities

96

Table 4.1 (Continued)

No. Risk Risk respect to Risk Characteristic

10 Season Risk Farmers/broker/ traders/ Commission agent

Change of monsoon period and rainfall may result in loss of production

11 Commitment/Contract Failure

Farmers/broker/ traders/Commission agent

At the stage of ripening, a farmer cannot find the satisfactory broker to purchase his product at the harvest stage

12 Trust risk Farmers / Brokers/ Traders/Commission agent

The distrust between members involved in the chain in increasing the transaction cost

13 Political risk Farmers/Brokers/

Traders

Government policy may interrupt market, production and distribution mechanism

14 Communication risk

Farmers/Brokers/

Traders

Miscommunication may result in loss benefit to competitor

15 Time risk Farmers/Brokers/

Traders

Change of time to obtain

information and get produce may

result to loss in profit

16 Technology risk Farmers/Brokers/

Traders

Implementation of technology

may result in loss in profit

17 Diseases Farmers Diseases may result in loss in

quality and production quantity

97

Table 4.2 Possible factor variable affecting to price fluctuation

No Elementary Risk Risk Characteristic

1 Production quantity

Production quantity is over market demand

2 Reference demand Demand from previous years

3 Season Temperature and Product Substitute products, and peak production

4 Poor appearance Physical damage, over ripen shape, dissatisfied size

5 Storage time Banana storage time before arriving to wholesale market

6 Productive area Commercial production area

7 Productivity per area

Yield, production output per area

8 Transportation time

Time that banana is delivered from orchard to wholesale market

9 Transportation cost

Cost incurs during production planning and operation

10 Reference price Average price from previous years

11 Retail store numbers

Number of retail outlet

12 Export market Demand share for export market

13 Opportunistic behavior

This risk arises because of the potential opportunity

14 Population Region population will relate to domestic consumption

15 Interest rate Interest rate announced by bank and offered by commission agent

98

Table 4.2 (Continued)

No Elementary Risk Risk Characteristic

16 Food safety

awareness

Food Hygiene

17 Truck load Quantity of bananas per truck

18 Handling

Awareness

Methods and handling operations are being

done carefully

19 Pre-Harvest

Treatment

spray schedule to control fungal infection and

insect infestation etc.

20 Post- Harvest

Treatment

Handling, de-latexing, grading, washing,

cooling, packing, etc

4.1.4 Application of the Causal Loop Diagram for Analysis of Price

Fluctuation

From elementary risk factors influencing price fluctuation given in

Table 4.2, as well as information obtained from discussion with experts,

important magnitude 5.0 and cut=0.40 are selected elementary factors. If

the value of important magnitude is equal or greater than 5.0 with is less

than 0.40, then the elementary will not be selected in which pre-harvest

treatment is an example as show in Figure 4.3. When the value of center of

area for important magnitude is equal or greater than 5.0 and is equal or

greater than 0.40, then the elementary will be selected. Figure 4.3 illustrates

this condition in which post-harvest is not selected.

99

Figure 4.3 Pre-Harvest Treatment: x 0.4, x 5.0 : X is not selected

and eliminated from Causal-Loop Diagram

Figure 4.4 Post-Harvest Treatment x 0.4, x 5.0 : X is selected

and used for Causal-Loop Diagram

This is to select the important elementary risk factors to construct

the Causal-Loop diagram. An elementary risk factor is selected if important

impact magnitude is greater than 50% (important magnitude > 5.0). The

elementary risk factor meeting the criteria are: production quantity, reference

demand, season, poor appearance, storage time, and productive area,

productivity per area, reference price, retail store numbers, export market,

handling awareness and post- harvest treatment.

100

Twelve screened elementary factors obtained from Table 4.2 were

included as input variables in the Causal-Loop diagram in Figure 4.5.

Prob of Price decline

-

Storage time

Prob of poorapparience

-

Season

share for exportmarket

Qunaity Demand+

Retail outletnumbers

share forprocessing unnit

Productivity per area

Productive area

Production quantity

+

+

Production costper unit

Reference price

Target price

+

Price

Reference quantitydemand

Fresh banana share formodern reatailers

+

Referenceproduction quantity

Return+

+

+

-Expectec production

cost per unit

+

Minimum referencedomestic demand

Change in demand

+

Time to change indemand

-

adjust price downdelay

adjust price updelay

Change price down

Time to formexpections

Expected demand byWhole-Saler

-

++

Target revenue

+

+

Effect price ondemand

-

+

+

+

+

Demand elasticity

Expected profitper unit

+

Post-harvestTreatment

Handlingawareness

Apparience

+

+

-+

Change in price

Aadjust reference pricedelay

-

+

Delay to adjustreference production

-

Figure 4.5 Causal-Loop Diagram for Price Fluctuation Mechanism

101

The Causal Loop Diagram as a tool of dynamics approach was

presented to verify screened elementary factors and explain price fluctuation

dynamics from the case study.

The causal loop diagram was developed, which includes all systems

significant variables and the regulating feedbacks, is exhibited in Figure 4.5.

The increase of return from banana price will encourage banana

growers to increase their production area and the production area directly

increase production quantity and higher return but at the same time, when

production area is increased, probability of price decline will be also

increased. However, when higher production quantity is disclosed to

commission agents and production quantity data will be taken to account for

estimating quantity demand. Higher production quantity will increase

reference quantity demand while actual quantity demand from different

markets will be quantified by commission agents. If total quantity demand

from different markets is higher than reference quantity demand, price tends

to be increased, but if total quantity demand from different markets is lower

than reference quantity demand, price is prone to decline. The increase of

delay time between point of time that commission agents perceive production

quantity information and point of time that fruits are being sold will decrease

difference between reference quantity demand and total quantity demand from

different markets.

From total quantity demand from different markets, wholesalers

will markup price based on their expected profit by comparing with their

operation cost, while banana growers will markup their price based on their

expected profit by comparing with their agriculture production cost.

Commission agents will play the major role for difference between price

quantified by farmers and price quantified by wholesalers in very limited

102

short time. When time to perceive information between reference price and

total quantity demand is increased, change in price will be decreased. If

banana growers can understand demand and perceive wholesale�s price in

early and wholesalers and retailers markets can understand reference

production quantity, there is very helpful because more benefit will contribute

to farmers, wholesalers, retailer, and customers, instead of contributing to

commission agent at the most at present.

Apart from quantity demand, post-harvest treatment, storage time,

and seasons are also will increase to price change. If post-harvest treatment

and storage time are not handled accordingly for respective seasons,

probability of poor appearance of banana attribute will be increased that make

price can be prone to decline.

4.2 SELECTION OF THE POST-HARVEST TECHNOLOGY

Innovation in computer technology and information help to manage

the whole chain (Tijskens et al 2001). The increasing importance of

information for the successive enabler in a food supply chain of events has a

number of severe practical and managerial consequences (economics of scale

and scope). The coordination of all enabler in the chain helps in achieving the

following:

(1) Increase the efficiency of material and information resources;

reduce risk of safety and quality,

(2) Decrease the production life cycle,

(3) Decrease the obtaining and retaining of that information

throughout the chain (Transaction cost),

103

(4) Decrease the cost and number of replacing a commodity by

different enablers in the chain (packaging cost and

environment benefit),

(5) Reduce the stock level by one enabler (based on production

information by the successor actor),

(6) Decide the optimal location in the chain for increase quality

(7) Increase profit, motivation for cooperation within the supply

chain, asking for complex innovations, not only from inside

the food supply chain (Commercial organization and

technological influence) but also from outside the chain (e.g.

social, legal, political and commodity influence). These issues

are very different in nature and their impact is shown in

Table 4.3.

Acceptance of a product by the consumer is the ultimate aim of the

supply chain. Managing and optimizing the supply chain ensures that the

consumer in the near future goes on purchasing their foods from that

particular chain. Within purchase decision, a number of factors play an

important role. It would be a great advantage to managing fresh produce

quality if the shelf life of a product could be accurately predicted. In practice,

the variability which is inherent in fresh fruits and vegetables makes this very

difficult. With the growth in economy, information technology and industrial

development, cross cultural customers are increasing day by day. This effect

changes consumers� behavior in India. People are more aware of quality of

living and are willing to pay more for better quality.

104

Table 4.3 Related Issues of fresh produce purchasing

Related Issues Details

The intrinsic quality of the product and the attributes that are connected to quality

Product- related issue

Safety of the commodity e.g. microbial infection, radiation, health

Availability of comparable product on the local Market

Market -related issue

Confidence in the enterprise with respect to quality, applied technology, and information

Cost of purchase of the commodity

Price reduction

Economics-related issue

Sale promotion

Is the commodity ethically acceptable? e.g. child labor

Social issues within the boundaries of the social commodity

Is the technology applied acceptable e.g. genetic modifications, organic production?

Does the commodity cause some social issues?

Does the commodity fulfill consumer�s expectation?

Psychological issue

Is the information about the product, its contents, and its production and processing adequate and reliable? (advertising and labeling)

Source: Tijskens et al (2001)

Despite the broad range of post-harvest technologies used to

maintain quality and extend shelf-life of fresh fruits and vegetables in several

countries through the world, application of those technologies is still limited

in some countries in Asia. Moreover, it is very complex when enablers try to

select the appropriate technology. Once the handling and post-harvest

technological methods are implemented, one can link the value between

105

technological contribution and products� attributes. However, several enablers

in the fresh produce chain might hold multiple values, or mixed values,

including: growers, commission agents, wholesalers, retailers and end-

customers. To get products as expected, enablers may not always be

motivated exclusively by one technology�s contribution value; many actors

can hold multiple values, and the degree of belonging to each value may

differ. Chain designers need to understand why actors in the chain apply or

do not apply handling and post-harvest technology in a fresh produce

distribution system. In order to deliver the fresh product to a destination with

the highest possible quality, post-harvest handling is a very important factor

to be considered and taken into account in the supply chain model (since

quality attributes are always influenced by post-harvest treatment and any

partner in agro-industrial supply chain cannot avoid risk of this nature). When

there is application of innovative technology without consideration of

economic perspective, actors may face risk of reduced profit due to the high

quality and high price with less demand.

For an assessment of incomplete information, FDM is useful in

many situations; experts� judgments cannot be properly reflected in

quantitative terms. For this case study, FDM is used along with AHP. This

approach can consider all of the goals (tangible or intangible) dealing with the

selection of post-harvest strategies

4.2.1 Alternative Technology Strategies

There are six alternative post-harvest technology strategies

considered for illustrating the proposed selection method. Note that the

proposed approach has the flexibility to consider as many strategies as

needed. Six post-harvest technologies including pre-cooling technology,

pre-storage treatment, refrigerated storage technology, control atmosphere

106

storage, packing, and future trend technology are considered. Possible

techniques for each technology are shown in Table 4.4.

Table 4.4 Post-harvest Technologies for maintaining the quality of

fresh produce

Technologies Possible techniques Room and forced air cooling Hydro-cooling Icing

Pre-cooling

Vacuum cooling Surface coating and wraps Curing of root and tuber Dehydration (Curing of bulb crops)

Pre-storage

Chemical control of fungi and bacteria pathogens Sprouting suppressants for root, tubers and bulb crops Post-harvest chemical treatment to reduce disorderPre-storage

Irradiation Control of humidity Control of ethylene Refrigerated storage Control of chilling injuring and low temperature sweetening

Control atmosphere storage

Control atmosphere (CA) storage

Conventional packs Coat with Shrink Film Packing Modified atmosphere packing (MAP) Minimally processed products and MAP Replacements for post-harvest chemicals Increased emphasis on the health aspects of fresh

Future trends

Genetically modified (GM) fruits and vegetables

107

4.2.2 Criteria for Selecting Post-Harvest Technology

Post-harvest technology strategy has impact on quality attributes of

the product reaching the customer (Aked 2002). However, when a customer

at a retailer is searching to buy the product, not only quality issue must be

considered but also Marketing issues as well as economic issues taken in to

account to make a decision. Considered in paper including three related issues

namely product, marketing and economics issues are considered in this work.

Their details are shown in Tables 4.5-4.7.

Table 4.5 Criteria for product’s quality attributes

Criteria Measurement

Color as per species and ripe state Appearance

External and internal defect

Firmness Texture

Other textural factor (e.g. mealiness)

Taste components

Aroma component

Flavor

Sensory evaluation

Table 4.6 Marketing criteria

Criteria Measurement

Availability Availability of expected and comparable product in the local market

Confidence Confidence on the enterprise with respect to quality, applied technology, and information

108

Table 4.7 Economic criteria

Criteria Measurement

Cost Setting and operation cost

Price Price reduction, flexibility in price setting mechanism

Promotion Sale promotion, attraction of product for sale

promotion

From survey and discussion, social issues and psychological issues

did not play significant role in the Indian agricultural business.

4.2.3 Methodology for Selecting Post-Harvest Technology

The conceptual model of the proposed method for selecting

post-harvest technology is shown in Figure 4.6.

Figure 4.6 Conceptual model for selecting post-harvest technology

Identification of Post-harvest technology strategies

Identification of the decision criteria

Construct the hierarchy scheme

Construct Pairwise comparisons using fuzzy Delphi method

Defuzzification

Utilize AHP method to find best post-harvest technology

109

Firstly, the alternative technology strategies are specified (those

which are chosen to be performed). Then, the enablers, both in private and

government sectors involved in the chain are interviewed. Moreover interview

and discussion were performed with experts in academia who are in touch

with agribusiness. Post-harvest technological goals was defined and the

hierarchy scheme was constructed. FDM is used to obtain data from field

work for the pairwise comparisons. Using the Centriod Method, fuzzy

numbers associated with the pairwise comparisons is transformed to crisp

values. Finally, by applying AHP approach, the optimum post-harvest

technology strategy is selected.

The AHP is a decision-aid that can provide the decision maker

(DM) with relevant information to assist the DM in choosing the "optimum"

alternative or to rank a set of alternatives. The hierarchy scheme of the

proposed AHP is shown in Figure 4.7.

4.2.4 Consolidation of Experts’ Input: Fuzzy Delphi Method

The values of input factors are not normally known with certainty.

When DM considers input criteria to select post-harvest technology, owing to

the imprecise and uncertain pairwise rating of these factors and a general lack

of data for their probabilistic quantification, fuzzy logic is implemented. The

values of the input factors are determined based on the experience and

subjective judgment of experts involved in the post-harvest chain. Fuzzy logic

is an analytical approach that allows for multiple membership of sets and

different levels of belonging to any one set. The FDM consists of the

following steps (Kaufmann and Gupta, 1988; Shaheen et al 2007):

Step 1: �n� number of experts provide the estimates of input factors

in the form of triangular fuzzy numbers Ai = (ai, bi, ci). Triangular

110

membership function is shown in equation (4.1). In Delphi technique highly

qualified experts must be interviewed to give their opinions regarding a

specific issue. The minimum number of experts required in Delphi technique

has been reported as 12 persons (Kaufmann and Gupta, 1988). Each expert

may give his/her best estimate on the amount of input factor based on his/her

experience as a triangular fuzzy number. For this purpose, the experts are

asked to provide three estimates of a specific value by determining the

minimum, the most plausible, and the maximum estimate. The estimates are

presented in the form of triangular fuzzy numbers:

0 , x a(x a) /(b a), a x b , a x b

f (x)(c x) / (c b), b x c , b x c0 , c x

(4.1)

Step 2: The estimates are averaged. For each expert, the deviation

from the average is calculated as shown below:

ave ave ave ave i i iF (a b c ) 1/ n a , b , c (4.2)

i iave i a a , i i i

1F A b 1/ n, c cn (4.3)

where Fave = fuzzy average; and (aave bave cave) = first, second and third

elements of the fuzzy number, respectively.

Step 3: The deviations in the estimates are sent back to the experts

for revision. Each expert provides a new triangular fuzzy number. Steps 1�3

are repeated until two successive averages become reasonably close based on

the decision maker�s stopping criterion as described in step 4 (Shaheen et al

2007).

111

Step 4: This is the step for defuzzification. It transforms the

resulting fuzzy values from expert�s judgement into a crisp value. The centre

of area method (Z*) as the function shown in (4.4) is utilized for

defuzzification (Zimmermann 2001)

(4.4)

4.2.5 Numerical Illustration

Defuzzified values obtained from step 4.2 are applied for pairwise

comparison in the AHP approach. In pairwise comparison for technology,

first technology being compared can contribute to the objective over the

second technology. A five point scale used in this study is shown in Table 4.8.

Table 4.8 Five point scale rating

Scale Explanation

1 Both technologies contribute equally to the objective

2 Moderate importance, slightly favor one technology over the other

3 Strong importance, strongly favor one over the other:

4 Very strong importance, strongly favor one over the other

5 Extremely importance, the first technology is extremely relevant to

contribute to object than the other.

An algorithm is presented based on the proposed approach for the

selection of post-harvest technology to be performed specifically with the

112

banana supply chain in South India. It is assumed that the availability of each

post-harvest technology is constant. The algorithm is presented in five steps:

Step 1:

The criteria considered for selecting the best post-harvest

technology in banana supply chain are listed below:

(1) Appearance: Color as Per Ripe Stage (CR)

(2) Appearance: Defect as per Skin Area (DS)

(3) Texture: Firmness (FS)

(4) Flavor : Taste and Aroma (TA)

(5) Availability of Product and Comparable Product (AC)

(6) Confidence on business firm (CF)

(7) Setting and Operation Cost (CP)

(8) Sale Price Reduction (PR)

(9) Price Promotion (SP)

The post-harvest-technologies considered in our case study are:

(1) Pre-cooling (PC)

(2) Pre-storage Treatment (PS)

(3) Refrigerated Storage: Control of Ethylene (CE)

(4) Control Atmosphere Storage (CA)

(5) Modified Atmosphere Packing (MA)

(6) Minimally Processed Products (MP)

113

Step 2:

Based on the objective, criteria and alternative identified in step1,

hierarchy scheme for AHP is formed and is shown in Figure 4.7.

Figure 4.7 The hierarchy scheme

Commission agents and wholesalers in the banana business chain in

Bangalore and Chennai markets, faculty members from Tamil Nadu

Agricultural University and officials from government agencies are defined as

experts to estimate importance degrees of decision criteria. Worst cases,

general cases, and best cases are assumed to make experts estimated

minimum important values (a), most plausible important value (b), and

maximum important value (c) for each pairwise comparison from nine

criteria.

The information received through interviews conducted with

banana commission agents, wholesalers, and academic experts is used to build

fuzzy membership functions for each pairwise comparison showed in

Table A1.1 in Appendix 1.

CR FS AC TA CF

PC PS CE MA CA MP

CP SP PR DS

The Most Appropriate Post- Harvest Technology

114

These values are in turn used to build pairwise comparison matrices

of criteria. The initial fuzzy values obtained are defuzzified to crisp numbers

through equation (4.4) using MATLAB software. Outputs of these

computations of crisp values are shown in Table A1.2 of Appendix 1. Then,

the crisp valued obtained from MATLAB is converted into a rating score as

shown in Table A1.3 of Appendix 1. The eigenvectors derived in this step

reflect the weights associated for each criterion. These details are presented

in Table 4.9.

Table 4.9 Decision criteria: pairwise comparison

Product Market Economics

Criteria CR DS FS TA AC CF CP PR SP Priority Rank

CR 0.125 0.117 0.155 0.122 0.102 0.167 0.216 0.123 0.069 0.1328 3

DS 0.104 0.097 0.127 0.134 0.089 0.146 0.081 0.079 0.066 0.1026 6

FS 0.075 0.071 0.093 0.117 0.116 0.146 0.081 0.069 0.082 0.0944 7

TA 0.092 0.065 0.071 0.090 0.116 0.067 0.102 0.100 0.082 0.0871 9

AC 0.175 0.156 0.130 0.110 0.143 0.167 0.093 0.174 0.189 0.1485 1

CF 0.058 0.052 0.084 0.104 0.067 0.078 0.095 0.138 0.126 0.0891 8

CP 0.075 0.156 0.077 0.113 0.200 0.106 0.130 0.133 0.137 0.1253 2

PR 0.113 0.136 0.149 0.098 0.091 0.062 0.108 0.110 0.151 0.1131 4

SP 0.183 0.149 0.115 0.110 0.076 0.062 0.095 0.074 0.101 0.1073 5

Step 4: The comparison of post-harvest technologies under each

criterion is carried out. Technological pairwise comparisons with respect to

each criteria are shown in Appendix 2. The eigenvectors derived from this

step are presented in Table 4.10 along with weights obtained for each

criterion.

115

Table 4.10 Post-harvest technological comparison with respect to each

criterion

Criteria CR DS FS TA AC CF CP PR SP

Priority 0.1328 0.1026 0.0944 0.0871 0.1485 0.0891 0.1253 0.1131 0.1073

PC 0.0997 0.0726 0.0792 0.1646 0.0664 0.0580 0.2656 0.2627 0.0730

PS 0.0696 0.0564 0.1163 0.1134 0.1269 0.3396 0.3158 0.3223 0.2807

CE 0.1421 0.0956 0.1389 0.0994 0.0850 0.0771 0.1532 0.1876 0.2096

CA 0.2531 0.1692 0.2017 0.2143 0.1669 0.1141 0.1505 0.1119 0.0979

MA 0.3828 0.3419 0.3881 0.3307 0.2426 0.1781 0.0663 0.0620 0.1456

MP 0.0528 0.2643 0.0759 0.0776 0.3121 0.2331 0.0520 0.0535 0.1932

The responses received from commission agents, wholesalers and

experts of academia are checked for consistency. These details are presented

below.

In order to estimate relative weight of the criteria in pairwise

comparative matrix A, priority of criteria is compared by computing eigen

values and eigenvectors as

maxA.W .W (4.5)

where w is eigenvector of matrix A; max is largest eigenvalue of matrix A.

Consistency is achieved by examining reliability of judgement in

pairwise comparison. Consistency Ratio (CR) and Consistency Index (CI) are

defined as

max nCIn 1

(4.6)

116

CICRRI

(4.7)

where n is number being comparing in the matrix, and RI is random

consistency index. RI depends on number of criteria being compared as

shown in Table 4.11.

Table 4.11 Random Consistency Index

Number of criteria (n) 6 7 8 9 Random Consistency Index (RI) 1.25 1.32 1.40 1.45

As shown in Table 4.11, from the nine criteria pairwise

comparison, RI is 1.45, and on the another hand, from the six alternative

technological pairwise comparison RI is 1.25. Using equation (4.5), (4.6),

(4.7) and RI from Table 4.12, CRs are compared and are shown in

Table 4.12.

Table 4.12 Consistency Ratio of pairwise comparison

Respect to n CI RI CR

9 Criteria Product, Marketing, Economics

9 9.372 0.047 1.45 0.032

6 Technologies Color attribute 6 6.244 0.049 1.25 0.039

6 Technologies Defect attribute 6 6.223 0.045 1.25 0.036

6 Technologies Firmness attribute 6 6.414 0.083 1.25 0.066

6 Technologies Flavor (Aroma and Taste) 6 6.348 0.070 1.25 0.055

6 Technologies Availability 6 6.303 0.061 1.25 0.048

6 Technologies Confidence 6 6.165 0.033 1.25 0.026

6 Technologies Cost 6 6.520 0.104 1.25 0.083

6 Technologies Price Reduction 6 6.183 0.037 1.25 0.029

6 Technologies Sale Promotion 6 6.361 0.072 1.25 0.058

117

All CRs obtained are shown in Table 4.1.2. Since all the CR is less

than 0.1, so the pairwise comparison is found to be consistent.

Through the FDM and AHP applications, the ranking of alternative

technologies to be advised for implementing in the banana supply chain are

shown with final priority (weight) in Table 4.13.

Table 4.13 Post-harvest Technology Ranking with respect to all criteria

Final Priority Rank

PC: Pre-cooling 0.128 6

PS: Pre-storage treatment 0.191 2

CE: Control of Ethylene 0.133 5

CA: Control Atmosphere Storage 0.166 3

MA: Modified Atmosphere

Packing 0.234 1

MP: Minimally Processing 0.149 4

As shown in Table 4.13, modified atmosphere packing technology

is the most significant with an overall priority of 0.234 followed by pre-

storage treatment technology with a priority of 0.191, controlled atmosphere

storage technology with priority of 0.1656, minimally process technology

with priority of 0.1485, control of ethylene with a priority of 0.1328 and pre-

cooling technology with a priority of 0.1284.

118

4.3 APPLICATION OF FUZZY LOGIC AND DYNAMIC

PROGRAMMING FOR SELECTING OPTIMAL ROUTES

A player in a particular stage of the chain can perform one or more

actions of handling, processing, transportation and storage in order to control

the quality state. The Dynamic Programming (DP) approach applied to the

banana case study is presented in this session. Notations used in DP is

presented below:

cs : Quality state of color development attribute, determined by

handling or operation conditions and throughput time.

ds : Decision with respect to handling which affect color

development at state cs .

dx : Decision with respect to handling or operation which affect the

defect development state ds .

sk = (cs,ds): The product state at each of stage k (k = 0, �, n), s0 is the initial

state and sn is the final state sk = (cs, ds) : The product state at

each of stage k (k = 0, �, n), s0 is the initial state and is the

final state.

xka(cx,dx): A group of possible decisions with respect to alternative a

(a = 1, 2, �, m) of handling or operation from stage k-1 to stage

k which affect to color development state cx and defect

development state dx .

pk[(s)]k-1,xka): possible price from action xka for product from stage k-1 to

stage k.

119

ck[(sk-1.xka): possible cost from action xka for product from stage k-1 to stage

k.

: for decision xka, transformation Tk is the change from

quality state Sk-1 to quality sate Sk. The effect of action xka on

the quality state Sk-1, leading to a new quality state Sk. This

process of a decision leading to a new quality state is repeated

until the target state is reached with maximum profit.

Yk-1 s1(k-1)) = max{(p1(k-1) (s1(k-1) x1ka) � c1(k-1) (S1(k-1.)x1ka))

+[(y1k(T)]1k(s)]1 (k-1), x1ka))} (4.8)

Function yk(Sk) provides possible profit occurring from the optimal

route from state Sk at stage k to the end of the chain. For all possible

decisions, the resulting state Sk-1 and corresponding yk(Sk) value is determined

to price product and cost of operation decisions xk. Then, the maximum profit

is calculated for all possible decisions. Recursively, the function

yk(k=n, n-1,�, 0) is calculated until the initial state s0 is reached. The

underlying profits for the transfer from one state to another are summed.

Finally, when the initial state is reached, the maximum profits of the supply

chain are known, and the consecutive routes of the postharvest supply chain

are obtained.

State variables are taken from the above approaches as basically

point valued (crisp) measures of conditions that exist at the beginning of any

phase of the solution. Above decision variables are also referred to as control

variables in which these variables are directly specified to obtain an optimal

solution at each stage (and in order to achieve maximum profit). The banana

supply chain can be optimized in such a way that the banana reaches the

120

retailers with its target ripeness, acceptable defect content and minimized risk

of quality loss. Practical uncertainties in both state values and decision

variables render them as fuzzy information in the nature of the fresh fruit

supply chain. It is hard to obtain reliable data and choose crisp mean values

for the DP approach.

There are two quality attributes that were studied: ripeness and

defect. For ripeness attributes, there are seven ripeness states classified by

color development as shown in Table 4.14. The quality state of bananas at

stage Sk is represented with value within range [1, 7]. The initial state of

bananas is dark green ck=0=1. The target state is a ripe banana at the retailer

according to the customer�s preference which is assumed to be ck=0=6. The

final state should not be below 6 because fruit will be stored for too long

before customer purchase and then additional storage cost for the retailer is

needed. The final quality state should not exceed 6 because fruit will be stored

for too little time before customer purchase. Sometimes bananas can reach an

over-ripened quality state before the product is sold. The quality (ripeness)

state of bananas during handling in the supply chain is shown in Table 4.14.

121

Table 4.14 Quality (ripeness) state of banana during handling in chain

Quality

StatePicture Description

1 Color is dark green. This shows bananas after harvesting.

2 Color is light green. The maturing process has begun

however there is still some time before they are ready to

eat.

3 Color is more yellow than green. The ripening has begun in

earnest and the fruit is now increasing its natural sugar

content. The flesh is changing from the chalky hardness of

under ripe fruit.

4 Color is yellow with green hint that familiar creamy texture

is developing now, and as the natural sugar content raises.

The fruit is getting ready for eating.

5 Color is all yellow with green tip on crown. The ripening

has begun in earnest and the fruit is now increasing its

natural sugar content. The flesh is changing from the

chalky hardness of under ripe fruit.

6 Color is all yellow. This is ready to eat The fruit is sweet

and creamy .

7 Color is yellow with brown �sugar spots� At the peak of

freshness now, and delicious to eat. The fruit is also

starting to soften as it ages heading towards its top sugar

content.

122

The decision variables are control variables that determine actions

to transfer products from stage k-1 to the stage k. All possible actions

(decision variables) are shown in Table 4.15.

Table 4.15 Action (decision) alternatives from stages k-1 to stage k

with alternative decision

Stage Decision Action at Stage k-1 to achieve next state at stage k

0 x11 Fruit bunch will be cut with de-handing.

x21 Fruit will be carried by truck, and kept in natural air. 1

x22 Fruit will be arranged in basket, carried by truck, and kept in cold storage.

x31 Fruit will be cleaned, and stored in natural air (no ripe aging).

x32 Fruit will be cleaned, ripen aged, and stored in natural air storage.

2

x33 Fruit will be cleaned, and ripen aged, and stored in controlled air storage.

x41 Fruit will be stored in natural air. 3

x42 Fruit will be stored in controlled air storage.

x51 Fruit will be carried by small truck without air control. 4

X52 Fruit will be delivered by small truck with air control.

At the second quality attribute, defects of banana with respect to

preference for product appearance, defects are classified using a 9-point

scale/rating. This type of evaluation is broadly followed in food science

research. The details are as shown in Table 4.16.

123

Table 4.16 Hedonic Scale for consumer acceptance testing

Scale Semantic Scaled Description

1 Dislike

extremely

Defect is found equal or more than 40 % of

whole fruit skin area per hand of banana.

2 Dislike Very

much

Defect is found equal or more than 30 % but

less than 40% of whole fruit skin area per hand

of banana.

3 Dislike

Moderately

Defect is found equal or more than 20 % but

less than 30% of whole fruit skin area per hand

of banana.

4 Dislike Slightly Defect is found equal or more than 10 % but

less than 20% of whole fruit skin area per hand

of banana.

5 Neither like nor

dislike

Defect is found equal or more than 5% but less

than 10% of total surface per hand of banana.

6 Like Slightly Defect is found equal or more than 3% but less

than 5% of whole fruit skin area per hand of

banana.

7 Like Moderately Defect is found equal or more than 2 % but

less than 3% of whole fruit skin area per hand

of banana.

8 Like very much Defect is found equal or more than 1 % but

less than 2% of whole fruit skin area per hand

of banana.

9 Like extremely Appearance is perfect, no defect

124

From Table 4.16, the defect development attribute state ds is

represented with value in range of 1 to 9. The initial state is 9 ([(d))]ka = 9),

while the target defect development state at the retailer according to the

customer�s acceptance should not be less than 5 (dka 5). As a classical

economic model, supply and demand have most impact on price. However,

with agricultural fresh commodities, several risk factors must be practically

accommodated in the model. Such a complicated model is rarely applicable

in real work. The value of the input factors to predict price is not normally

known with certainty. Moreover, the relationship between the values of the

input factors and the magnitude of risks affecting price decline cannot be

easily defined. To obtain price and cost at each stage, the fuzzy Delphi

technique was adopted. For example, each expert may give his/her best

estimate on the amount of input factor based on his/her experience as a

triangular fuzzy number. For this purpose, the experts are asked to provide

three estimates of a specific value by determining the minimum, the most

plausible, and the maximum estimate. The estimates are presented in the form

of triangular fuzzy numbers:

A1i = (a i, b i, c i) (4.8)

Where, A is triangular fuzzy number; a, b and c are first, second, and third

elements of the fuzzy number respectively (in which i = 1, 2, .., nth expert). In

triangular fuzzy numbers, the expert believes that the estimate of the item has

a �most likely� or �most plausible� point that is between a maximum and a

minimum boundary. In this work 15 experts were used. In the Delphi

technique, highly qualified experts must be interviewed to give their opinions

regarding specific issues. The minimum number of experts required in the

Delphi technique has been reported as 12 persons (Kaufmann and Gupta,

1988). As per FDM, price and cost data at each stage for all possible decisions

125

and both quality states of color and defect for a case study of the banana

supply chain obtained are shown in Table 4.17.

Table 4.17 Possible actions and possible states with triangular fuzzy

number (TFN)

cs (Color Development

State)

a’s (Defect Development

State)

Price

Rs/Kg

Cost

Rs/Kg

Stage(k)

xka

a b c a b c a b c a b c

x11 1 1 3 8 9 9 8.0 10.0 12.0 5.0 6.0 7.0

x21 1 1 3 7 8 9 9.0 11.0 12.0 8.2 10.5 12.5

1

x21 1 1 3 8 8 9 10.0 11.0 12.0 8.5 11.7 13.0

x31 2 3 5 6 7 8 10.0 13.0 16.0 8.5 12.0 15.0

x32 3 4 5 6 6 7 12.0 14.0 16.0 9.0 12.0 15.0

2

x33 4 5 5 7 8 8 14.0 15.0 16.0 11.0 12.0 15.0

x41 4 5 7 5 6 8 13.0 15.0 17.0 10.0 14.5 16.5 3

x42 4 5 6 6 7 8 15.0 15.5 17.0 14.5 15.5 17.0

x51 4 6 7 4 6 8 15.0 17.0 18.0 13.2 16.0 17.5 4

x52 4 5 6 5 7 8 17.0 17.5 18.0 15.4 16.5 17.5

In Table 4.17, a is defined as a possible minimum value, c is

defined as possible maximum value and b is defined as the most plausible

value. Defuzzification refers to the way a crisp value is extracted from the

fuzzy set into a crisp value. The Centre of Area (COA) method is utilized for

defuzzification.

(4.9)

Triangular fuzzy numbers from Table 4.17 were defuzzified with

equation (4.9) using MATLAB software. For example, cost occurring from

126

desired action, handling and operation is operated from stage 3 to stage 4

through route x31. The defuzzification from TFN to crisp is shown as below.

MATLAB code:

x = 0:0.1:20;

mf = trimf(x,[8.5 12.0 15.0]);

cost = defuzz(x,mf,'centroid')

TFN obtained through FDM from Table 4.17 were applied as the

same manner. The results of crisp value obtained through COA method show

in Table 4.18.

Table 4.18 Possible actions and possible states with defuzzified value

Stage

(k)xka

cs (Color

Development

State)

ds (Defect

Development

State)

Price

Rs/Kg

Cost

Rs/KgProfit

0 1.63 8.70 10.00 6.00 4.00

1.63 8.00 10.67 10.40 0.27 1

1.63 8.30 11.00 11.07 -0.07

3.33 7.00 13.00 11.83 1.17

4.00 6.30 14.00 12.00 2.00

2

4.70 7.70 15.00 12.66 2.34

5.33 6.33 15.00 13.67 1.33 3

5.00 7.00 15.83 15.67 0.16

5.60 6.00 16.67 15.87 0.80 4

5.00 6.67 17.50 16.47 1.03

127

Numerical Illustration

Facilities of handling and operation during transportation and

storage can support approximately 100,000 tons of bananas. Ripeness and

defect levels are to be reached at the final stages, 6 and 7 respectively. Profit

and quality attribute levels were calculated as shown in this numerical

illustrations. The details are given in Table 4.19.

Table 4.19 Numerical illustration for dynamic programming solution

Stage

kDecision (Rupees/kg)

(Rupees/kg)

0.80 5.60 6.00 4

1.03* 5.00 6.67

2.36* 5.33 6.33 3

2.19 5.00 7.00

3.53 3.33 7.00

4.36 4.00 6.30

2

5.70* 4.70 7.70

5.97* 1.63 8.00 1

5.63 1.63 8.30

0 9.97* 1.63 8.70

The optimal solution can be calculated through equation 4.8,

yk=(action)=(profit, color state, defect state), as below.

128

From the above alternative action, maximum profit and most

preferred quality state for can be considered. For actions of harvest, fruit

bunches should be cut with de-handing ( . Followed by actions of

collection, fruit should be carried by truck, and kept in natural air ( .

Then, during collection from brokers to commission agents, product should be

carried by truck and kept in natural air. For postharvest treatment before

reaching wholesalers, fruit should be cleaned, ripen ageing, and stored in

controlled air storage ( . For actions between wholesalers and

distributors, fruit should be stored in natural air ( . Finally, for actions

from distributors to relaters, fruit should be delivered by small truck with air

control ( . From this proposed optimal route, decision ( gives a

higher quality state but operation cost is also higher. Increasing rate for

handling cost is higher than increasing rate for expected selling price. So this

action is not selected. From this approach, fuzzy data were defuzzified to

crisp mean values. Then, those crisp means were applied to DP. Not only

profit criterion but also acceptable quality attribute level was taken into

account to find most plausible profit. When alternative actions were

considered in profit, acceptable and preferable quality attribute states

are also evaluated. However in this situation, using only the defuzzified value

for analysis may not reflect the tolerance between mean value and upper or

lower limits. Hence which the fuzzy goal programming approach is

considered for further study.

129

4.4 ANALYSIS OF POST-HARVEST SUPPLY CHAIN

NETWORK USING MULTISTAGE FUZZY GOAL

PROGRAMMING

The general linear programming method cannot reflect risk or

chance of the problem occurring in the worst case or best case. Sometimes,

even though average profit value is acceptable, if the worst case occurs, they

may not able to continue their business due to the significant impact. In the

fresh food supply chain problem environment, all stages of actions are defined

but information at each stage and reward is vague. This is deterministic

system which is described by its state transition. Fuzzy dynamic programming

method was explained (Kacprzyk and Esogbue 1996; Zimmermann 2001) to

work in this case. It�s basic elements are: a fuzzy goal G in X, a fuzzy

constraint C in X and a fuzzy decision D in X; X is a space of alternative

decisions.

k=0, 1 (4.10)

where, are the states at control stage k and k+1,

respectively and is the action at k. At each , is

subjected to a fuzzy constraint and fuzzy goal is imposed

on . Based on Kacprzyk and Esogbue (1996), fuzzy dynamics

programming is extended with multiple fuzzy goal problems.

The performance of the multistage decision making process is

evaluated by the fuzzy decision which is assumed to be a decomposable fuzzy

set. , is

130

(

(4.11)

where is an initial state, �s are given by (4.10), N is the termination

time (fixed and specified in this case) with an optimal sequence of controls

, so

(

(4.12)

With multiple goals, at each k fuzzy goal are given. Some fuzzy

goals may be conflict with each other. Then, the fuzzy decision is

(

and , so

(

(4.13)

i=1,.., N (4.14)

Notations are defined in the following section.

: A group of possible decisions at stage k with respect to

alternative of handling method with amount of in which affect to color

development state and defect development state .

131

, , , and : A a month of banana to be applied at stage 0, 1, 2, 3,

and 4 respectively.

, , , and : Handling method to be applied at stage 0, 1, 2, 3, and 4

respectively.

, , , and : Color development state at stage 1, 2, 3, 4, and 5

respectively, determined by handling or operation conditions, and throughput

time.

, , , and : defect development state at stage 1, 2, 3, 4, and 5

respectively, determined by handling or operation conditions, and throughput

time.

, , , and : profit estimation state for a decision at stage 0, 1, 2, 3,

and 4 respectively, determined by capital investment and quality(color and

defect) attribute state.

, , and : profit loss estimation state for a decision at stage 0, 1,

2, 3, and 4 respectively, determined by capital investment, and quality

(color and defect) attribute state.

, , , and : maximum profit estimation state for a decision at

stage 0, 1, 2, 3, and 4 respectively, determined by capital investment, and

quality (color and defect) attribute state.

When players try to achieve multiple objectives at multi-stages of

decision making in the fresh supply chain environment, they need to

maximize profit and minimize risk in capital investment loss. Moreover,

customers need to be satisfied with the product at the desired quality level

(with both ripeness and defect attributes). All associated objectives were

132

considered. The solution procedure for multistage fuzzy goal programming is

summarized in the following section.

The algorithm

Step 1: Define goals with upper or lower tolerance at state to stage .

Step 2: Find feasible region solution based on resource constrains

Step 3: With reference to Pal and Moitra (2003), based on goal and

tolerance upper and lower limit, develop membership grade for

each goal at state to stage with respect to amount of x and

handling method y

Step 4: Compute the optimal solution through equation (4.13)

Numerical Computations

From the banana supply chain environment in Tamil Nadu, all

possible actions were considered throughout possible routes of banana supply

chains from Theni District to Chennai and Bangalore. With fuzzy information

environments of banana supply chains and data from interviews and

decisions, goals for each stage are defined.

Step 1: With cost available at 1,200,000 Rupees decision makers want to

achieve profits of 100,000. Expected maximum profits up to 200,000 Rupees

accept maximum loss at 50,000 Rupees respectively. Ripeness and defect

levels to be reached at stage 5 are 6 and 7 respectively.

: Expected maximum cost is 1,200,000 Rupees.

: Expected average profit is 100,000 Rupees.

: Expected lower tolerance (maximum loss) -50, 000 Rupees.

133

: Expected maximum profit is 200,000 Rupees.

: Expected approximate ripen level is 6.

: Expected approximate acceptable defect level is 6.

Step 2: For 10 tons of bananas per truckload, space limitation and available

capital to operate with bananas, capital investment of 50 tons (minimum) to

100 tons is preferred. A feasible amount of bananas can be X: (50,000,

60,000, 70,000, 80,000, 90,000, and 100,000 kilograms) and a feasible

solution handling method Y:

Step 3: Develop membership grade for each decision variable with respective

goals.

From expected maximum capital investment ( , expected

average profit ( ), expected lower tolerance (maximum loss) ( ), expected

maximum profit ( ), expected approximate quality attribute (ripen ( ) and

color ( ) development state as defined in step 1 and step 2. Results of the

membership grade for each goal through fuzzy Delphi method are shown in

table 4.21.

Step 4: Compute the optimal solution

=50000

= max (0.50, 0.38) = 0.50

=60000

134

= max (0.60, 0.45) = 0.60

=70000

= max (0.60, 0.53) = 0.60

=80000

= max (0.40, 0.60) = 0.60

=90000

= max (0.2, 0.68) = 0.68

=100,000

= max (0, 0.63) = 0.63

From all feasible solutions,

135

= max

The possible action by decision maker is to transport 90,000 units

quantity with air control from stage 4 to stage 5.

In the same manner, computation is done to stage 3, stage 2, stage 1

and stage 0 and the optimal solution is given below.

From the fuzzy dynamic programming approach, the following

observations are made.

1. At stage 4, a distributor chooses 90,000 units and

transportation with air control conditions.

2. At stage 3, a wholesaler chooses 100,000 units and storage

with air control.

3. At stage 2, a commission agent chooses 100,000 units through

action 3 which includes activities: cleaning, ripen aging and

storage in controlled air storage.

136

4. At stage 1, the broker chooses 80,000 units through action 2

which includes activities: arranging in baskets, carrying by

truck, keeping in cold storage.

5. At Stage 0, the farmer chooses the plan with an 80,000 unit

expectation.

From post harvest handling alternative in a particular stage along

the supply chain, an application of fuzzy logic with the dynamic programming

approach was presented to develop an integrated supply chain management

process (accounting for the complex system, dynamic behavior and uncertain

nature of supply chain risks). Fuzzy dynamic programming is more flexible

than classical dynamic programming for brokers, commission agents,

wholesalers and distributors. When price is suddenly increased or decreased,

they can adjust quickly by negotiating with partners at earlier stages but a

farmer has less control.

Table 4.20 Goals at Stage 0 – Stage 4

Stage G1 G2 G3 G4 G5 G6

Capitalinvestment

Average profit

MinimumLoss

Maximumprofit

Colour State

Defect

State

Stage 0 600,000 800,000 -30,000 800,000 1 7

Stage 1 800,000 600,000 -50,000 200,000 1 7

Stage 2 1,200,000 400,000 -75, 0000 250,000 4 7

Stage 3 1,200,000 200,000 -75, 0000 250,000 5 6

Stage 4 1,200,000 100,000 -50, 0000 200,000 6 6

137

Table 4.21 Membership grade for each goal through the fuzzy Delphi

method and center of area method

Membership grade with respective Goal Feasible x5

(Kgs) G1 G2 G3 G4 G5 G6

50000 1.00 0.50 0.50 1.00 0.83 0.67

1.00 0.50 0.38 0.50 1.00 0.83

60000 1.00 0.60 0.60 0.80 0.83 0.67

1.00 0.60 0.45 0.60 1.00 0.83

70000 1.00 0.70 0.70 0.60 0.83 0.67

1.00 0.70 0.53 0.70 1.00 0.83

80000 0.93 0.80 0.80 0.40 0.83 0.67

0.90 0.80 0.60 0.80 1.00 0.83

90000 0.80 0.90 0.90 0.20 0.83 0.67

0.76 0.90 0.68 0.90 1.00 0.83

100,000 0.67 1.00 1.00 0.00 0.83 0.67

0.63 1.00 0.75 1.00 1.00 0.83

Farmer also has to consider both risk in operation cost and risk in

selling price. From downstream stages of chain, a backward solution was

started from stage 4 to stage 0 which states that decision makers can start their

business from stage 4 and extend to invest their business more in the earlier

stages. They also get more ownership in the upstream supply chain stages as

with several fresh retail enterprises involved in fresh supply chain today. As

the solution from the fuzzy dynamic programming method, though the

post-harvest technology and handling required more cost, it can help avoid

loss from uncertainty of quality attributes.

138

4.5 CONCLUSION

Interview in balance supply chain group discussions were made to

explore all possible risk issues. The Fuzzy Delphi method is applied to screen

elementary risk factors. A Causal Loop Diagram is developed to understand

the complexity and interrelation among all elementary factors and risk issues.

Six possible post-harvest technological alternatives are pairwise

compared with 9 evaluating criteria that influence the post-harvest technology

selection. Experts from academia, agribusiness business and government

sectors were interviewed. Data obtained from experts in agribusiness sector

were vague and ambiguous. FDM was used to quantify those fuzzy to crisp

values before evaluating them through AHP. FDM and AHP were used to

integrate expert�s opinions to evaluate the significance of various evaluation

criteria. The results from experts of different fields were compared and

analyzed. The results of all experts were used as the evaluation index for

post-harvest technology selection. From this, modified atmosphere packing

technology is the most highly recommended for application. Integration of

FDM and AHP is useful for selecting future post-harvest technology.

Integrating quality issues into supply chain management is a vital

issue and has become a challenge for enhancing performance of the

postharvest supply chain. DP can be used to tackle quality attributes (like

ripeness and defect) which are affected by postharvest handling methods.

Fuzzy data are quantified and given as input data for DP. Profit and quality

attributes from postharvest handling method scenarios are well quantified.

The application of FDM and DP is very useful and more flexible to deal with

uncertainties in order to reach desire quality states at particular stages in the

supply chain.

139

Fuzzy goals programming is very useful and more flexible. Profit

and loss risk from post harvest handling method scenarios is well quantified.

From fuzzy set theory, fuzzy membership degree was applied as the aspiration

level on profit and acceptable risk level with respect to different goals at

different stages in the supply chain. Then FDP can be used by taking quality

attributes like ripeness and defect which are affected by post harvest handling

method into account simultaneously in order to reach desired quality states in

a particular stage in the supply chain. Addressing quality problems in supply

chain management does not only help improve benefits for partner in the

chain but also for consumers by providing better product quality alternatives.