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1. BAHIR DAR UNIVERSITY
BAHIR DAR INSTITUTE OF TECHNOLOGY (BIT)
SCHOOL OF REASRCH AND GRADUATE STUDIES
PRODUCTION ENGINEERING AND MANAGEMENT (MSC)
Research Title O n : Optimization Of Agricultural Cropping Resource By Using Goal Programming Through
Fuzzy -Lexicographic Goal Programming
In The Case of South Gondar Farta Worda
By: Eyaya Bante
Main Advisor: Dr. Betsha.T (Ph.D)

2. Outline of the article review
Abstract
Introduction
Research Questions
Problem Statement
Objective of Research
Significance of Research
Limitation and gab of Research
Methodology

3. Abstract
The purpose of this study is to determine the best way to allocate land for cultivation ,all resource used for agricultural
cropping activities will be optimize by fuzzy-lexico goal programing and better use of technologies and efficiencies, use
properly fertilizer and pesticide without affected environmental and ecological biodiversity by using other natural and risk
minimization of technology alternatives
Fuzzy -Lexicographic Goal Programming approach, to find the best solution, (Maximize Crop production goal , Maximize
net profit goal ,Minimizes the total cost spends and negative effects of fertilizer and pesticide ,and Minimizes the cost
spends on labor requirement,, for four objectives are taken into account in accordance with their prioritization.
In solving goal programming problems, the solution methods reduce the multiple goal programming problems into a single
objective of minimizing a weighted sum of deviations from goals. The solution solved by lingo 20.optimization soft ware.

4. Introduction
 Agricultural crop production sector is at the heart of contemporary societies as well as
civilizations. The sector broadly encompasses ,the cultivation of plants. The agricultural
sector makes an imperative role in meeting the growing food consumption demand across
the in world amidst the ever-increasing population(Z. Zhai, J. F. Martínez,2020).
 The most of peoples the majority (83.8%) of Ethiopians reside in the rural areas. Hence,
subsistence and rain-fed agriculture is the economic base and means of level hood of the
majority of these people.
 Agricultural Development-Led Industrialization (ADLI) is a long term strategy in which,
at the early stages of development, the agricultural sector is expected to play a leading role
in the growth of the economy,
 At this stage, agriculture is considered to be the engine of growth to feed large proportions
of the population and thus is a source of input to the emerging industries (MoFED, 2002,
p.38).

5.  Food crop production is essential for the well-being of humanity, but the frequently changing global
environmental conditions pose a serious threat to crop production due to the unexpected occurrence of
biotic and abiotic stress variables, which cause considerable crop loss and thus challenge global food
security.
Figure 1: Agricultural era from 1.0 to 4.0((Z. Zhai, J. F.
Martínez,2020).

6.  Farta district is one of the administrative divisions of South Gondar zone which is located in northern part
of Ethiopia,
 Which mostly the economics based on agricultural crop activity's which cultivated barley, teff, wheat,
maize, sorghum, bean, pea, potato, garlic, milt and onion ,
 However lack of sufficient cultivated land and poor optimization of agricultural recourse in the rural area
, depletion of soil organic matter, misuse of chemical fertilizer and pesticide ,and soil acidity are major
obstacles to sustained agricultural crop production.
Figure 2: Geographical area of South Gondar-Farta Worda[3].

7. Multi Objective Optimization
 Most real world problems involve simultaneous optimization of several objectives function,
Generally these objectives function are measured in different units and are often computing and
conflicting
 Multi objective optimizations having such conflicting objectives functions gives rise to a set of
optimal solutions ,instead of one optimal solution because no solution can be considered to be better
than any other with respect to all objectives.
 The main cause for using optimization is that the models need to have representations for policies and
technologies that affect more than input and output prices and quantities and there is no past to assess
the resulting decisions for some segments.

8. Source :https://www.researchgate.net/profile/Nodir-Djanibekov
Figure 3 :Workflow of the optimization optimization of crops

9. Research Questions
 How to find a solution of goal programming problem by using Lexicographic and fuzzy goal
programing Method?
 Determining the best satisfying solution under a varying amount of resources and priorities of the
goals?
 How much change of expected initial all multi goals of project, If change the constraint resource when
use sensitivity analysis?
 To what extent are major determinant negative effects of use excessive fertilizer and pesticide
chemicals in human health and environment for a long term cumulatively during harvesting crops?

10. Problem Statement
 The current agricultural production system is challenged with weather and climate extremes and
variability and economic risks, and also population growth makes it harder to find enough land, Crop
yield,
 In South Gondar in Farta Worda, the yield of major crops was declining due to soil acidity , poor crop
rotation and weed problems faced in this district and the use of much amount fertilizer and chemicals
led to negative impact of human and environment.
 We cannot satisfy the demand of raw material of Ethiopian domestic industry, due to the reason most
food beverage industry in forced to stop operation like, oil industry, biscuit, other child
manipulate food

11.  Excessive and careless use of agro-chemicals (such as mineral fertilizers) poses potential risks in long
term leads to soil quality, heavy metal buildup, eutrophication of the water, and nitrate accumulation..
 Quite a few past studies included some environmental objectives, but they rarely focused on water
and fertilizer consumption, besides, in most cases, these attributes are treated only as negative effects
of various farming and agricultural policy scenarios and not as main objectives in agricultural planning

12.  No, previous research has been conducted on the on Fuzzy -Lexicographic Goal Programming as a
tool that has powerful functions as a quantitative analysis tool that can quickly solve and optimize the
profit depending on available resources, on south Gondar farta worda ,even though there are related
topics with a different focus and research interest.
 The research use a Fuzzy -Lexicographic Goal programming tool for multiple criteria decision-
making), can prioritize the goals and resolve the control. it allows the decision-maker to combine
environmental, organizational, and managerial factors in a model with several goals and priorities.

13. Objective Of The Project
Maine Objective :
Optimization of Agricultural crops by using Goal programming through Fuzzy -Lexicographic Goal
Programming in the case of South Gondar Farta word
Specific objective:
 To identify the problem of current agriculture crop production method .
 To formulate Mathematical Model of Fuzzy -Lexicographic Goal programming model that
would suggest ensuring multi optimum solution .
 To minimize the negative impact of use more fertilizer and pesticide environmental and human
health use without sacrificing crop yield productivity.
 To incorporate the proposed optimal sensitive analysis solution with the gab of existing system.

14. Significance Of The Study
 To increase crop productivity and optimize agricularal recourse which is limited constraints with
sensitivity analysis
 To balance both economic and environmental sustainability and also leads to farmers becoming
profitability .
 To minimize the negative impact of use more fertilizer and pesticide on environmental and human health
by natural method.

15. Scope And Limitation Of Project
 Limited study on specific geographic area ,ecological factor a and crops Varity
 The project do not conduct with big cloud data like arterial intelligence remote
monitoring of control pests.
 Do not consider un control natural variable like ,snow, drought, will being consider
soli analysis testing ,rainfall pattern ,all are being stabile station .

16. Methodology
Primary data collection:
 Direct observation: to find out the gaps of the existing crop production system
 Interviewing the farmers :
 Gather data and information related to production method and types of crops which farmer that
produce , average demand, and cost of pesticide ,fertilizer ,natural and human made constraints of
production system .
 Ask directly farmers to get information the negative impact of use un properly fertilizer and
pesticide on human health and environmental .

17. Secondary data collection
Which used to gain further data
 Internet ,a data related research's which studying scientifically standard study and journal from the
past one ,
 Document ( South Gondar Agricultural institute )

18. Comparison Of Multi Goal Programing
Types of optimization model Description Articles
Lp model  Only one objective function not consider conflict objectives
 Use usually static business environment
 Only use linear, it is difficult to determine social, institutional, financial and other
constraints.
 LP models presents a trial and error
Linear programming model to optimize cropping
pattern in(Alal Jebelli1,2016)
Role of Linear Programming Based Cropland
Allocation to Enhance Performance of
Smallholder Crop Production( Meselu Tegenie
Mellaku)
Goal programming (GP)  Goal programming is one of the oldest multi criteria decision
 That is GP yields only an efficient and satisfactory result rather than optimum
 human beings are more interested and able to reach goals than in the abstract concept of
optimizing each outcome of the decision problem, determine precisely the relative
importance of the goals
 A nonlinear goal programed could not be formulated if the additives condition does hold.
Optimization model to support sustainable crop
planning( Ana Esteso1 ,2021
multi-objective algorithm for crop pattern
optimization in agriculture( Sonal Jain,2020)
Pre-emptive Goal
Programming (Lexicographic
Goal Programming)
 A decision maker may not be able to determine precisely the relative importance of the
goals. I.e. apply pre-emptive goal programming.
 The decision maker must rank his or her goals from the most important (goal 1) to least
important (goal m).
 A model that aims to satisfy both farmers’ welfare and environmental sustainability.
introducing a lexicographic goal programming for
environmental conservation program in farm(
Mashhad, Iran,)

19. Fuzzy goal programing  In conventional GP, parameters of the problems need to be defined precisely. In
most agricultural planning problems, values of some parameters may not be known
precisely, for this condition shall to use fuzzy goal programing
 Sensitivity analysis on different weight structures for the goal
 GP is a technique not designed to find an “optimal point”, but to find an
“acceptable range, good alternative is to use the fuzzy goal programming variant. If
there is uncertainty over the technological coefficient
 FUZZY don’t consider green production of system and not environmental goal
Fuzzy multi-objective programming for agricultural
problems(NAGAR KARIMI ,June 2022
Fuzzy-Lexicographic Goal
Programming)
 great flexibility which enables the decision maker to
easily incorporate numerous variations of constraints
and goals
 This model use the advantage of both fuzzy and lexica
graphics
 some real-world decision-making situations
 it use of environmental friendly production goal
setting

20. General Methodology
Step1 :Problem definition current agricultural cropping system
Step2:Model description of fuzziy-lexecographics model
Step3:Matematical Model formulation of fuzzily –lexicographic and
define the goals coefficient important
Step4:Input data acquisitions
Step5:Testing the modeling of the crop simulation and solution
Step6:Analyzing and interpret the optimal result and compare with
sensitivity analysis

21. Lexicographic Goal Programming
In many situations a decision maker may not be able to determine precisely the relative
important of the goal.
When this is the case preemptive goal programming (PGP) may prove to be a useful
tool.
To apply PGP the decision maker must rank her/his goal from the most important to
least important. P1>>>>P2>>>>>……………. >>Pn; Pi= weight of the goal.

22.  Negative Deviation ,d-): The amount of deviation for a given goal by which it
is less than the aspiration levels.
 (Positive Deviation ,d+):The amount of deviation for a given goal by which it
exceeds the aspiration level.
 (Constraint): A constraint is a restriction upon the decision variables that
must be satisfied in order for the solution to be implementable in practice. This is distinct from
the concept of a goal whose non-achievement does not automatically make the solution no
implementable. A constraint is normally a function of several decision variables and can equality or an
inequality.

23. Matmatical Formulation
Goals :
They also can be kept in order to the priority, Goal1>>Goal2>>Goal3>>Goal4
P1>>P2>>P3>>P4
MinZ=P1 𝒅𝟏−
+ 𝐩𝟐𝒅𝟐−
+p3𝒅𝟑+
+p4𝒅𝟒+
Goal 1: Maximize Crop production goal
𝑐=1
𝑐
𝐴𝑃𝑐𝐴𝑐 ≥ 𝑐=1
𝑐
𝑇𝑝𝑐
Where,
𝑨𝑷𝒄, 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑟𝑜𝑝 𝑐 (𝑞𝑢𝑖𝑛𝑡𝑎𝑙 /ℎ𝑎);
𝑻𝑷𝒄, 𝑡𝑜𝑡𝑎𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑡𝑎𝑟𝑔𝑒𝑡 𝑜𝑓 𝑐𝑟𝑜𝑝 𝑐 (𝑞𝑢𝑖𝑛𝑡𝑎𝑙)
𝑨𝒄, 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑛𝑑 𝑐𝑢𝑙𝑡𝑖𝑣𝑎𝑡𝑒𝑑 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (ℎ𝑎)

24. Goal 2: Maximizes net profit of production
𝑐=1
𝑐
𝑁𝑃𝐶𝐴𝑐 ≥ 𝑁𝑃
Where,
NPc, net profit for crop c (birr);
NP, expected net profit for all crops (birr);
Ac, the area of the land cultivated for crop c (ha)
Goal 3: Minimizing the consumption chemical fertilizers.
The total consumption of fertilizer and other chemicals should be minimal to be expected
𝐶=1
𝐶
𝐴𝐹𝐴𝑐 ≤ 𝑇𝐹
Where,
AF, The amount of fertilizer required for crop cultivation (quintal /ha)
TF, total available of fertilizer resource crop c (quintal)
Ac, the area of the land cultivated for crop c (ha)

25. Goal 4: Minimizes the cost spends on labor and machine hours requirement in each
activity,
𝐶=1
𝐶
𝐿 𝑡𝐴𝑐 ≤ 𝐿
Where,
L, 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑎𝑏𝑜𝑟 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ( 𝑝𝑒𝑟𝑠𝑜𝑛 − 𝑑𝑎𝑦𝑠
𝑳𝒄, 𝑙𝑎𝑏𝑜𝑟 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑎𝑟𝑒𝑎 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (𝑝𝑒𝑟𝑠𝑜𝑛 − 𝑑𝑎𝑦𝑠/ℎ𝑎)
𝑨𝒄, 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑛𝑑 𝑐𝑢𝑙𝑡𝑖𝑣𝑎𝑡𝑒𝑑 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (ℎ𝑎)

26. Hard constraint
Land availability constraints,
𝐶=1
𝐶
𝐴𝑐 ≤ 𝑇𝐴
Where,
𝑻𝑨, 𝑇𝑜𝑡𝑎𝑙 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑙𝑎𝑛𝑑 (ℎ𝑎)
𝑨𝒄, 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑛𝑑 𝑐𝑢𝑙𝑡𝑖𝑣𝑎𝑡𝑒𝑑 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (ℎ𝑎)
Number of harvesting time per seasons in month
𝐶=1
𝐶
𝑇𝑐𝐴𝑐 ≤ 𝑇𝑇)
Where,
𝑻𝑪, 𝑡𝑜𝑡𝑎𝑙 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑜𝑓 ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 (𝑑𝑎𝑦𝑠)
𝑻𝑻, ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑎𝑟𝑒𝑎 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (𝑑𝑎𝑦𝑠)
𝑨𝒄, 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑛𝑑 𝑐𝑢𝑙𝑡𝑖𝑣𝑎𝑡𝑒𝑑 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (ℎ𝑎)

27. water requirement in seasons,
𝐶=1
𝐶
𝑊𝑐𝐴𝑐 ≤ 𝑇𝑊
𝑊ℎ𝑒𝑟𝑒,
𝑾𝑪, 𝑡𝑜𝑡𝑎𝑙 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑖𝑛 (𝑟𝑎𝑖𝑛 𝑓𝑒𝑒𝑑𝑖𝑛𝑔/𝑖𝑟𝑟𝑒𝑔𝑎𝑡𝑖𝑜𝑛) (𝑑𝑎𝑦𝑠)
𝑻𝑾, 𝑤𝑎𝑡𝑒𝑟 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑎𝑟𝑒𝑎 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (𝑑𝑎𝑦𝑠)
𝑨𝒄, 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑛𝑑 𝑐𝑢𝑙𝑡𝑖𝑣𝑎𝑡𝑒𝑑 𝑓𝑜𝑟 𝑐𝑟𝑜𝑝 𝑐 (ℎ𝑎)

28. General form of the model:
In summary, goal programming model is consist of objective function, objective constraints, absolute
constraints and variable non-negative constraints
Object function .
MinZ= 𝑘=1
𝑞
𝑝𝑘 𝑗=1
1
𝑤𝑘𝑗𝑑𝑗− + 𝑤𝑗𝑘𝑑𝑗+ where j=1,2
Object constraint
𝑗=1
𝑛
𝑐𝑖𝑗𝑥𝑖𝑗 + 𝑑𝑗−
+𝑑𝑗+

29. Absolut constraint
𝑗=1
𝑛
𝑎𝑖𝑗𝑥𝑗 = ≤≥ 𝑏𝑖, (𝑖 = 1,2, , , , 𝑚(𝑗 = 1,2, , , 𝑚)
Non-negative constraints
xj≥ 0 𝑗 = 1,2, … . . 𝑛 𝑑𝑖 𝑑𝑖+, 𝑑𝑖− ≥ 0((𝑗 = 1,2, , , 𝑚)

30. Step Action
Step 1
Embed the relevant data set. Set the first goal set as the current goal set.
STEP 2
Obtain a Linear Programming (LP) solution defining the current goal set as the objective Function.
STEP: 3
If the current goal set is the final goal set, a. set it equal to the LP objective function value obtained in Step 2, and STOP.
Otherwise, go to Step 4.
Step 4.
Step 5
If the current goal set is achieved or overachieved.
a. set it equal to its aspiration level and add the constraint to the constraint set, Go to Step 5.
b. Otherwise, if the value of the current goal set is underachieved, set the aspiration level of the current goal equal to the LP
objective function value obtained in Step 2. Add this equation to the constraint set. Go to Step 5
Set the next goal set of importance as the current goal set. Go to Step 2.

31. Fuzzy goal programming (FGP) model description
 The fuzzy goals for the problem are transformed to their respective linear constraint
form. In this formulation, as the tolerance variables are to be minimized, the
tolerances be needed will be close to unity for each fuzzy goal. This causes the grade
of membership to become larger.
 In particular, if the tolerance variables are zero then there is no need to assign
tolerances to fuzzy goals. Therefore, the objective function for the agricultural land
allocation problem is defined as (Kim and Whang, 1998)

32. FGP formulation using the concept of membership functions which are defined on the interval
[0, 1].
The membership function for the kth goal has a value of 1 when this goal is attained and the
decision making is completely satisfied; otherwise the membership function assumes a value
between 0 and 1
Where LK (Uk) is lower (upper) tolerance limit for kth fuzzy goal Gk (x) which are either
subjectively chosen by decision makers or tolerances in a technical process (Chen and Tsai,
2001)

33. In fuzzy goal programming, the membership function corresponding to the k𝑡ℎ fuzzy goal of type k G ( x
) ≥ b is defined as:
𝜇zx=
1 𝑖𝑓 𝐺𝑧(𝑥) ≥ 𝑏𝑘
𝐺𝑧 𝑥 − 𝑏𝑥 − 𝑙𝑘 𝑖𝑓 𝑏𝑘 − 𝑙𝑘 ≤ 𝐺𝑧(𝑥) < 𝑏𝑘
/𝑙𝑘
0 𝑖𝑓 𝐺𝑧 < 𝑏𝑘 − 𝑙𝑘
the k𝑡ℎ fuzzy goal of type k G ( x )≤ 𝑏𝑘 is defined as:
𝜇zx=
1 𝑖𝑓 𝐺𝑧(𝑥) ≤ 𝑏𝑘
𝑏𝑥 + 𝑢𝑘 − 𝐺𝑧 𝑥 𝑖𝑓 𝑏𝑘 < 𝐺𝑧 𝑥 < 𝑏𝑘 + 𝑢𝑘
/𝑙𝑘
0 𝑖𝑓 𝐺𝑧 > 𝑏𝑘 + 𝑢𝑘

34. crop production goal and net profit goal are of type Gk ( x ) ≥ b .
In addition, labor or machine utilization requirements, and fertilizer requirements and
are of type k k G ( x ) ≤ b .
If crop production and net profit goals are completely achieved then no tolerances for
them are needed and the grades of membership for the goals should be unity. When
these goals are either perfectly or partially unachieved, tolerances for them are required.

35. The concept of tolerance to convert an FGP model to a single objective LP problem.
If 𝑈𝑖+(−)
= 1,2 …are the lower (upper) tolerances and 𝐵𝑖+(−)
∈ 0 1 , i = 1,2 are the
grades of membership, 𝛾𝑖−=1 − 𝛽𝑖−,i=1,2 and 𝛾𝑖+=1 − 𝛽𝑖+,i=1,2
then the corresponding crop production, net profit, labor requirement, water
requirement and machine utilization goals can be transformed as fuzzy goals. The fuzzy
goals for the problem are transformed to their respective linear constraint form

36. Min: 𝑖=1
2
𝑤𝑖𝛾𝑖−
+ 𝑖=3
4
𝑤𝑖𝛾𝑖+
Where wi, i=1, 2, 3, and 4 are the respective weights corresponding to the fuzzy goals and the sum of all
weights is one. :
St
𝑐=1
𝑐
𝐴𝑃𝑐𝐴𝑐 + 𝛾1−
𝜇1−
≥ 𝑐=1
𝑐
𝑇𝑝𝑐 𝐶=1
𝐶
𝐴𝐹𝐴𝑐 − 𝛾1+
𝜇1+
≤ 𝑇𝐹
𝑐=1
𝑐
𝑁𝑃𝐶𝐴𝑐 + 𝛾2−
𝜇2−
≥ 𝑁𝑃 𝐶=1
𝐶
𝐿 𝑡𝐴𝑐 − 𝛾2+
𝜇2+
≤ 𝐿
𝐶=1
𝐶
𝑊𝑐𝐴𝑐 ≤ 𝑇𝑊 𝐶=1
𝐶
𝐴𝑐 ≤ 𝑇𝐴
𝐶=1
𝐶
𝑇𝑐𝐴𝑐 ≤ 𝑇𝑇)

37. Using Analysis Tool And Software
Using Analysis Tools
 Pare to :Using to studying and analysis of priority of the goal programming
 Cause and effect diagram: Using to identifying the cause and effect of poor production current
agricultural crop harvesting system
.

38. Optimization software Description
Genetic algorism Be difficult to optimize and can
be time-consuming to run
they may not find the global optimum and can be
stuck in local optima.be difficult to optimize
Microsoft Excel Solver has limit of 200 decision
variables, for both linear and
nonlinear problems.
limit is to change your model
Lingo completely integrated package
that includes a powerful
language for expressing
optimization models
LINGO 20, it is the recent versatile software to be
solver the multi optimal mathematical mode,
precisely to remove un certain error , full featured
environment for building and editing problems, and a
set of fast built-in solvers
Soft ware
so, for using Lingo software due to solve multi goal
optimization problem.

39. What Is LINGO?
LINGO (Linear, Interactive, and General Optimizer)
LINGO is an interactive computer-software package that can be
used to solve linear, integer, and nonlinear programming
problems.

40. The File menu commands allow you to manipulate your LINGO data files in various
ways. You can use this menu to open, close, save, and print files, as well as perform
various tasks unique to LINGO.

41. Creating a LINGO Model
An optimization model consists of three parts:
 Objective function
 Variables
 Constraints MODEL:
MIN (or MAX)= Objective function;
Constraint 1;
Constraint 2; …
Constraint n; END

42. LINGO Example

45. objective /variety crops x1 x2 x3 x4 x5 x6 x7 Targe
t
Toleran
ce
Total
availab
le
1.Average yield Production (‘000 qtl) /harvest season
2. Net profit (birr. ‘000) cm/harvest season
3. Labor requirement (‘000 man-days) cm/harvest season
5. Water requirement (‘000 cubic cm/harvest season
6. harvesting time in moth

46. Crops Name of crops Decision
variables
coeffi
cient
s
Sellin
g
price
birr
/kg
Mean
estimate
d
Cost of
seed
birr/ha
duratio
n of
harvesti
ng time
in moth
Mean
estima
ted
Fertiliz
er
req./h
a
mean Net profit in
birr.
Labor
requirement-
(man-
days/ha)days)
Land
allocated
for each
crop in
hectares
Mean
estimated
Water
requirement
in cubic cm
Cereals Maize x1 c1
Barely x2 c2
Teff x3 c3
Wheat x4 c4
Bean x5 c5
Pea x6 c6
Millet x7 c7
Vegeta
bles
Potato x8 c8
Garlic x9 c9
Cabbages x10 c10

47. Influence Of Crop Type On The Daily Crop
Water Needs
suppose in a certain area the standard grass crop needs 5.5 mm of water per day.
Then, in that same area, maize will need 10% more water. Ten percent of 5.5 mm = 10/100 × 5.5
= 0.55 mm. Thus maize would need 5.5 + 0.55 = 6.05 or rounded 6.1 mm of water per day.
Source :https://www.fao.org/3/s2022e/s2022e02.htm

48. Fertilizer requirement for each crop
 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟 𝑘𝑔/ℎ𝑎 = 𝑘𝑔/ℎ𝑎 𝑛𝑢𝑡𝑟𝑖𝑒𝑛𝑡 ÷ % 𝑛𝑢𝑡𝑟𝑖𝑒𝑛𝑡 𝑖𝑛 𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟 𝑥 100
 𝑁𝑒𝑡 𝑝𝑟𝑜𝑓𝑖𝑡/ℎ𝑎 = (𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑦𝑖𝑒𝑙𝑑 ∗ 𝐴𝑟𝑒𝑎 ∗ 𝑆𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒) − (𝑠𝑒𝑒𝑑 𝑐𝑜𝑠𝑡 ∗ 𝑎𝑟𝑒𝑎) −
(𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 ∗ 𝑎𝑟𝑒𝑎) − (𝐿𝑎𝑏𝑜𝑟 𝑐𝑜𝑠𝑡 ∗ 𝑎𝑟𝑒𝑎)