chapter 4 a case study of banana in...
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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
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(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.
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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
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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
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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
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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.
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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
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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
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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
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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.
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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.
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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
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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
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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),
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(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.
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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
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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
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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
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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
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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
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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
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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).
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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
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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)
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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
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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.
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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)
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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
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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.
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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.
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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.
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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
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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
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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.
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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.
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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.