An Optimal Solution To The Linear Programming Problem Using Lingo Solver A Case Study Of An Apparel Production Plant Of Sri Lanka

International Journal of Computer Science and Business Informatics
IJCSBI.ORG
ISSN: 1694-2108 | Vol. 14, No. 2. AUGUST/SEPTEMBER 2014 1
An Optimal Solution to the Linear
Programming Problem using Lingo
Solver: A Case Study of an Apparel
Production Plant of Sri Lanka
Z. A. M. S. Juman and W. B. Daundasekara
Department of Mathematics,
Faculty of Science, University of Peradeniya,
Sri Lanka
ABSTRACT
Operations Research (OR) is often concerned with determining the maximum of profit,
performance, yield etc. or minimum of cost, loss, risk, etc. of some real-world objectives.
The Linear Programming Problem (LPP), a branch of Operations Research consists of an
objective function which is linear and constraints are linear equations or inequalities. This
research paper presents a Mathematical Model of a LPP which is to minimize the
production cost, while satisfying operational limitations, of a production plant producing t-
shirts. This production plant is known as Silk Line (pvt) Ltd which is located in Sri Lanka.
The developed model is considered to be a large scale one which provides a fully functional
cost effective system finding optimum number of machine operators and workers in each of
the departments in the production plant as well as finding optimum raw material for the
entire t-shirts production. The optimal solution to the model is found using the commercial
software package called “LINGO SOLVER”. Moreover, a sensitivity analysis is
performed to complete the target (entire t-shirts production) within a given specific period
of time.
Keywords
Linear Programming Problem, Optimum number of machine operators, Lingo Solver,
Sensitivity analysis.
1. INTRODUCTION
Linear programming is an optimization technique which was developed
during the Second World War. An LPP consists of an objective function
which is linear and constraints are linear equations or inequalities. Objective
function and constraints are formed using the decision variables which are
defined according to the given problem. Decision variables are continuous
to be real valued variables which may have lower or upper bounds.

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Objective function is to be maximized or minimized subject to the
constraints which form a convex feasible region. An LPP can be solved
using an iterative algorithm known as the Simplex Algorithm which was
developed by Dantzig in 1950‟s. This is the most the widely used and
accepted algorithm to solve LPPs because of its simplicity. The optimal
solution of the objective function may be bounded or unbounded whereas
optimal solution to the decision variables may or may not be unique.
Linear Programming has a broader area of applications in the fields of
productions, telecommunications, transportations, scheduling etc. The main
focus of linear programming is to optimize the available resources in the
best possible manner while achieving the objective.
This research paper is focusing on optimizing production cost of a t-shirts
production plant which is located in Sri Lanka. Although the plant‟s
monthly target is 30,000 t-shirts, the records show that the target level has
not been reached in a regular basis. Also, it can be observed that the plant‟s
operational costs are mainly due to workers monthly payments which are
more than what is needed. Due to low productivity and unnecessary
expenditures, at present the plant is facing major financial difficulties and
several other problems in designing the production process. Therefore, the
management is interested in implementing a cost effective system to reduce
the production cost while improving the production efficiency of t-shirts. In
fact, in this research paper, a large scale linear programming model is
developed to achieve these objectives. Then LINGO SOLVER is used to
solve the developed large scale model.
The remainder of this paper is organized as follows: Related literature
review is given in section 2. Section 3 deals with the Methods and Materials
of the LPP. In section 4 the solution to the large scale LPP is summarized.
Finally, the conclusion given in section 5 highlights the limitations and
future research scope on the topic.
2. LITERATURE REVIEW
Linear Programming problem and its solution have been studied by many
authors. Few of them are James and Tom [5], Brain [1], Dantzig [2] and
Taha [13]. A number of computer software is available in obtaining the
solutions to LPP. Some are based on the simplex method and its variants,
e.g. CPLEX, LINDO, TORA, MATLAB, EXCEL SOLVER, AMPL and
LINGO, and some are based on the interior point algorithms, e.g. MOSEX.
See Fourer [3]. Though the software based on simplex method and its
variants have been used widely in solving linear programming problems,
they solve LPP in exponential time. An algorithm that solves LPP in

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polynomial time is considered to be efficient. A first attempt of solving LPP
in polynomial time was the development of interior point algorithm by
Karmarkar [8]. How to solve a large scale LPP by interior point method
under MATLAB environment was proposed by Zhang [15]. The existing
interior point algorithms have some drawbacks such as extensive calculation
requirements, large number of iterations and large computer space
requirements. See Terlaky and Boggs [14].In addition, Hitchcock [4] was
first to develop the transportation model. After that, the transportation
problem, a special class of linear programming problem has been studied by
many researchers. Sharma and Sharma [12] presented the transportation
problem in a slightly different form in getting a dual problem which has a
special structure. Then they proposed a new solution procedure to solve the
dual of the incapacitated transportation problem. Sharma and Prasad [11]
presented a heuristic that provides a very good initial solution to the
transportation problem in polynomial time. Schrenk et al. [10] analyzed
degeneracy characterizations for two classical problems: the transportation
paradox in linear transportation problems and the pure constant fixed charge
(there is no variable cost and the fixed charge is the same on all routes)
transportation problems. A new result on complexity of the pure constant
fixed charge transportation problem has been proved. Liu [9] investigated
the transportation problem when the demands and supplies were varying
within their respective ranges. Following these variations the minimal total
cost were also varied within an interval. So, he built a pair of mathematical
programs where at least one of the supply or the demand was varying, to
compute the lower and the upper bounds of the total transportation cost.
Then the Lingo solver was used to solve the both mathematical programs to
attain the lower and the upper bounds of the minimal total transportation
costs. Juman and Hoque [7] demonstrated the deficiency of Liu‟s [9]
method in getting an upper bound of the minimal total costs of
transportation. Then they extended this Liu‟s model to include the inventory
costs of the product during transportation and at destinations, as they are
interrelated factors. In addition, they developed two new efficient heuristic
solution techniques - Algorithms 1 & 2 to find the upper and the lower
minimal total cost bounds respectively. By comparative studies of the
solution techniques on the solutions of small size numerical problems, it is
observed that our proposed heuristic technique (Algorithm1) performs the
same or significantly better in finding the upper bound of the minimal total
cost as compared with Liu‟s [9] approach. Algorithm 2 provided the same
lower bound of the minimal total costs to each of the numerical problems
studied as the one found by Liu‟s [9] approach. Moreover, numerical studies
demonstrated that the inclusion of inventory costs during transportation and
at destinations with the transportation costs changes the lower and the upper
minimal total cost bounds reasonably. Juman, Hoque and Bhuhari [6]

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designed a C++ computational program of Vogel‟s Approximation Method
(to solve an unbalanced transportation problem by considering both the
balanced and unbalanced features respectively with and without adding a
dummy column) in obtaining an initial feasible solution (IFS) to an
unbalanced transportation problem (UTP). In order to get an initial feasible
solution to a large scale TP, this computational program of VAM is
preferred. Moreover, we examine the effect of dealing with the balanced and
the unbalanced features in applying the well-known VAM method for
solving an unbalanced transportation problem. First we illustrated the
solution procedures with numerical examples (chosen from the literature).
Then we demonstrated this effect by a comparative study on solutions of
some numerical problems obtained by VAM by considering the balanced
and the unbalanced features.
3. METHODS AND MATERIAL
3.1Current approach
The current methodology, adopted by the plant, to increase the production
has failed due to several drawbacks. At present, the plant finds a feasible
solution by manually comparing alternative resource allocations. Although
the management is fully committed to improve the production process in
order to reach the optimum production, it has failed to achieve the objective.
It was observed that the current production process in the plant has several
weaknesses. This is mainly due to following reasons:
 Mismanagement of human resources
 Mismanagement of orders
 Improper resource utilization
3.2Data Collection
Data were collected using Questionnaires and Interviews. Then the
mathematical model for the month of August 2012 was formulated using the
collected data.
3.3Formulation of the Mathematical Model
3.3.1Decision Variables of the Model
Decision variables of the proposed model are as follows:
53
52
20
19
2
1 ,
and
, x
x
x
x
,
...
,
x
,
x = # trained and untrained cutter, band knife,
normal, 5-tread, 4-tread, flat lock, button hole, button attach, blind hem,
double needle, and fusing machine operators; 22
21 x
,
x = # mechanics needed

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in cutting and sewing departments; 44
54
24
23 ,
,
, x
x
x
x = # instructors needed in
cutting, sewing, QC (quality control) and packing departments;
42
55
32
31 ,
,
, x
x
x
x = # supervisors needed in cutting, sewing, QC and packing
departments; 30
29, x
x = # table checkers needed in cutting and sewing
departments; 39
26
25 ,
, x
x
x = # helpers needed in cutting, sewing and packing
departments; 43
56
34
33 ,
,
, x
x
x
x = # clerks needed in cutting, sewing, QC and
packing departments; 40
x = # menders needed in packing department; 41
x =
# quality checkers needed in QC department; 45
37
35
38 ,
,
, x
x
x
x = # in chargers
needed in packing, cutting, QC and sewing departments; 48
x = # personal
managers; 47
x = # account clerks; 28
27, x
x = # quality instructors needed in
cutting and sewing departments; 36
x = # production managers; 46
x = # iron
tables; 51
50
49 ,
, x
x
x = # small, medium, large t-shirts produced in a month.
(Here, # denotes „number of ‟)
3.3.2 Objective Function of the Model
The objective of the linear programming model presented below is to
determine the minimum production cost of the production plant.
Mathematical formulation of objective function:
Cost Function
Minimize Production Cost 
 





51
49
46
51
,
50
,
49
,
46
56
1
4500
j
j
j
i
i
i
i x
c
x
x
c
Z , where ci
is the salary of the ith
employee and cj is the raw material cost of the jth
type
t-shirt subject to the following constraints :
3.3.3 Constraints of the Model
All the constraints in the model can be categorized into five different types
as shown in Table 1 below.
Table 1 Types of model constraints
Constraints Inequalities
19
,
,...
9
,
7
,
5
;
120
30 1 

  j
c
x
x j
j
j
;

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Machine

j
c # t-shirts completed in a day by
th
j type of machines in the sewing department
52
,
19
,
17
,...,
5
,
3
,
1
;
1 

  k
c
x
x k
k
k
;

k
c # machine operators needed for the
th
k type of machines in cutting and sewing
departments
Workers
Cutting, Sewing, QC and Packing Departments must have a minimum # workers to
perform the duties.
1
55 
x ; # supervisors needed in QC department.
;
43
56
33 x
x
x 
 same # clerks needed in cutting, QC and packing departments.
;
7
28 
x # quality instructors needed in sewing department.
Raw material 899964
32
30
29 51
50
49 

 x
x
x inches
( raw material needed for the entire t-shirt production)
Raw material cost
1999920
.
36
80
32
36
80
30
36
80
29
51
50
49 Rs
x
x
x 





 






 






 
(raw material cost for the entire production)
Time
minutes
12480
20
66
.
11
20
66
.
11
20
66
.
11
51
50
49 




















x
x
x
( time available for the entire t-shirt production )
3.4 Linear Programming Model (LPM)
Finally, Linear Programming Model (LPM) for the existing problem could
be formulated as below. Optimal solution of the model is obtained using the
software known as LINGO as illustrated below:

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Figure 1 LINGO Mainframe Window
Linear Programming Model:
 
    51
50
49
46
45
38
37
35
36
48
39
26
25
41
47
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44
54
24
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9
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5
53
52
4
3
2
1
36
2560
36
2400
36
2320
4500
20000
20000
20000
20000
30000
14000
4000
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5000
12000
5000
5000
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10000
10000
10000
10000
4500
4500
4500
8000
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10000
10000
15000
15000
10000
10000
6200
4200
6200
4200
6200
4200
6200
4200
6200
4200
6200
4200
6200
4200
6200
4200
6200
4200
6200
4200
6200
4200
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
MinZ



























































(1)
subject to
1500
120
30
;
1500
120
30
;
1500
120
30
;
1500
120
30
;
1000
120
30
;
600
120
30
;
600
120
30
;
1200
120
30
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
















X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(2)
12
;
2
;
3
;
2
;
4
;
8
;
15
;
115
;
2
;
1
;
3
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
53
52
4
3
2
1






















X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(3)

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1200
3
;
1200
3
;
1200
3 53
4
2 

 X
X
X (4)
























20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
22
45
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(5)
0
45 53
52
4
3
2
1
21 





 X
X
X
X
X
X
X ; 0
20 53
52
4
3
2
1
23 





 X
X
X
X
X
X
X (6)
23
24 2X
X  ; 23
54 2X
X  ;
23
44 X
X  (7)
 
53
52
4
3
2
1
31
20 X
X
X
X
X
X
X 




 (8)













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


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

20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
32
60
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X (9)
1
55 
X ;  
46
40
39
42
50 X
X
X
X 

 ; 8
29 
X ; 29
30 X
X  (10)













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

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
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
26
9
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X (11)
0
13
20 26
25 
 X
X ; 0
8
20 26
39 
 X
X (12)













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


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


20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
34
40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X (13)
0
4 34
33 
 X
X ; 43
56
33 X
X
X 
 (14)
12
40 
X ; 24
41 
X
(15)
(16)
3
48 
X ; 48
47 X
X  ;
45
161
22 
X ; 7
28 
X ; 0
2 28
27 
 X
X ; 1
36 
X ; 1
45 
X (17)
1
;
1
;
1 37
35
38 

 X
X
X

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8
46 
X ; 899964
32
30
29 51
50
49 

 X
X
X (18)
71997120
2560
2400
2320 51
50
49 

 X
X
X (19)
12480
20
66
.
11
20
66
.
11
20
66
.
11
51
50
49 




















X
X
X (20)
14350
49 
X ; 10450
50 
X ; 5200
51 
X (21)
0

X and integers ; X is the column vector consisting of decision variables. (22)
4. RESULTS
By solving the developed large scale mathematical model (as shown in
section 3.4) using Lingo solver, the solutions obtained are given below in
Table 2 and Figures 2-5. The comparison between the optimal number of
each type of machines and number of machines currently being used in the
plant is shown in the following table:
Table 2The optimal table for the types of machines
Departments Type of machine Available #
machines
Optimal # machines
Department of
cutting
Department of
sawing
Cutter
Band knife
Fusing
Normal
5-tread
4-tread
Flat lock
Button hole
Button attach
Blind hem
Double needle
3
1
2
115
13
8
4
12
12
10
12
3
1
2
115
15
8
8
13
13
13
13
where x1+x2 =# cutter machines;x3+x4= # band knife machines; x52+x53 = #
fusing machines;x5+x6 =# normal machines;x7+x8 =# 5-tread
machines;x9+x10= # 4-tread machines;x11+x12 = # flat lock machines;x13+x14

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= # button hole machines;x15+x16 = # button attach machines; x17+x18= #
blind hem machines; x19+x20= # double needle machines.
The Table 2 clearly shows the available number of machines and their
respective optimal amount. The cutting department consists of three cutter,
one band knife and two fusing machines in the plant. The optimum
quantities for these machines in the cutting department are the same. The
sawing department consists of hundred and fifteen normal machines,
thirteen 5-tread machines, eight 4-tread machines, four flat lock machines,
twelve button hole machines, twelve button attach machines, ten blind hem
machines, and twelve double needle machines. The optimum quantities for
these machines in the sawing department are 115, 15, 8, 8, 13, 13, 13, 13
respectively.
Fig 1
Figure 2 Number of workers currently working in the factory
The bar charts in Figure 2 clearly depict the available number of workers
who are currently working in the plant as follows: The cutting department
consists of a mechanic, three instructors, two quality instructors, eleven
table checkers, two supervisors, three clerks, seventeen helpers, and two
cutting-in-chargers. The sawing department consists of seven mechanics,
1
7
3
1 1 1
2
1
11
12
20
2 2
1
2
3
6
1 1
3
28
17
26
7
3
1
2
1 1 1
14
0
5
10
15
20
25
30
Workers
Number of Workers currently working in the Factory
No. of mechanics in cutting dept.
No. of mechanics in sawing dept
No. of instructors in cutting dept.
No. of instructors in sawing dept.
No. of instructors in QC dept.
No. of instructors in packing dept.
No. of quality instructors in cutting dept.
No. of quality instructors in sawing dept.
No. of table checker in cutting dept.
No. of table checker in sawing dept.
No. of menders in packing dept.
No. of supervisors in cutting dept.
No. of supervisors in sawing dept.
No. of supervisors in QC dept.
No. of supervisors in packing dept.
No. of clerks in cutting dept.
No. of clerks in sawing dept.
No. of clerks in QC dept.
No. of clerks in packing dept.
No. of account clerks
No. of quality checkers in QC dept.
No. of helpers in cutting dept.
No. of helpers in sawing dept.
No. of helpers in packing dept.
No. of personal managers
No. of production managers
No. of cutting in chargers
No. of QC in chargers
No. of packing in chargers
No. of work-study in chargers in sawing dept.
No. of iron tables

IJCSBI.ORG
one instructor, one quality instructor, twelve table checkers, two
supervisors, six clerks, twenty six helpers, and one work-study-in-charger.
The QC department consists of one instructor, one supervisor, one clerk,
twenty eight quality checkers, and one QC in-charger. The packing
department consists of one instructor, twenty menders, two supervisors, one
clerk, seven helpers, and one packing in-charger. In addition to there are
three account clerks, three personal managers, one production manager, and
fourteen iron tables in the factory.
Figure 3 Optimum number of workers needed for the monthly production
The bar charts in Figure 3 clearly depict the optimum number of workers
needed for the monthly production of the plant as follows: The cutting
department consists of one mechanic, one instructor, eight table checkers,
one supervisor, two clerks, fourteen helpers, and one cutting-in-charger. The
sawing department consists of four mechanics, one instructor, eight table
checkers, three supervisors, five clerks, twenty two helpers, and one work-
study-in-charger. The QC department consists of one instructor, twenty four
1
4
1 1 1 1
0 0
8 8
12
1
3
0
1
2
5
0 0
3
24
14
22
9
3
1 1 1 1 1
8
0
5
10
15
20
25
Optimum Number of Workers needed
for the Monthly Production
No. of mechanics in cutting dept.
No. of mechanics in sawing dept
No. of instructors in cutting dept.
No. of instructors in sawing dept.
No. of instructors in QC dept.
No. of instructors in packing dept.
No. of quality instructors in cutting dept.
No. of quality instructors in sawing dept.
No. of table checker in cutting dept.
No. of table checker in sawing dept.
No. of menders in packing dept.
No. of supervisors in cutting dept.
No. of supervisors in sawing dept.
No. of supervisors in QC dept.
No. of supervisors in packing dept.
No. of clerks in cutting dept.
No. of clerks in sawing dept.
No. of clerks in QC dept.
No. of clerks in packing dept.
No. of account clerks
No. of quality checkers in QC dept.
No. of helpers in cutting dept.
No. of helpers in sawing dept.
No. of helpers in packing dept.
No. of personal managers
No. of production managers
No. of cutting in chargers
No. of QC in chargers
No. of packing in chargers
No. of work-study in chargers in sawing dept.
No. of iron tables

IJCSBI.ORG
quality checkers, and one QC in-charger. The packing department consists
of one instructor, twelve menders, one supervisor, nine helpers, and one
packing in-charger. In addition to there are three account clerks, three
personal managers, one production manager, and eight iron tables in the
factory.It should be noted that the total number of workers working in the
plant is 182 (see Figure 2). The Optimum number of workers needed for the
monthly production of t-shirts is 137 (see Figure 3). Thusour model which is
presented in this paper reduces the total number of workers by 32.9 %.
Expected number of T-shirts to be produced in August 2012
The bar charts in Figure 4 clearly depict the expected total number of t-
shirts to be produced in August 2012. The expected numbers of small,
medium and large size t-shirts are 14350, 10450, and 5200 respectively.
Figure 5 Number of medium size t-shirts produced in normal and over time
14350
10450
5200
0
2000
4000
6000
8000
10000
12000
14000
16000
No. of small t-shirts
No. of medium t-
shirts
No. of large t-shirts
Figure 4 Expected numbers of t-shirts (small, medium, and large) to be
produced in August
7057
3393
0
5000
10000
15000
Number of
Medium T-
shirts
1
Medium T-shirts
Result obtained in the Proposed Model
No. of medium t-shirts
produced in over time
No. of medium t-shirts

IJCSBI.ORG
The bar chart in Figure 5 clearly shows the exact numbers of medium size t-
shirts produced in normal and over times. The bottom of the bar chart
represents that the 7057 medium size t-shirts are produced in normal time
whereas the remaining 3393 (shown in top of the bar chart) are produced in
over time. It should be noted that, in order to complete the entire t-shirts
production in a specific time period, 3393 medium sized t-shirts must be
produced in overtime. See the Figure 5 given above.
Figure 6 clearly shows that the optimal monthly production cost of the plant
is Rs. 3,802,183. But, for the same month the plant estimated average
monthly production cost for this plant to be Rs. 4,230,283.
5. CONCLUSION
According to the optimal solution of the proposed model for the month of
August 2012, the monthly optimal production cost of the plant is Rs.
3,802,183. But in the same month the plant‟s estimated average monthly
cost is Rs.4,230,283. This clearly indicates that the plant is spending in
excess of Rs.428,100 than what is actually needed. Therefore, the plant can
save a maximum of Rs. 428,100 (10%) per month by implementing the
proposed method. Moreover, a sensitivity analysis is performed to complete
4,230,283
3,802,183
3,500,000
3,600,000
3,700,000
3,800,000
3,900,000
4,000,000
4,100,000
4,200,000
4,300,000
Current & Optimum Production
Cost in August 2012
Current
production
cost
Optimum
production
cost
Figure 6 Comparative result of current and optimum production cost

IJCSBI.ORG
the t-shirts production within the specified period of time (one month). After
performing a sensitivity analysis, it was revealed that the production plant
needs at least 22760 meters of raw material to meet the given target.
In this research only the production cost is considered while assuming that
the monthly demand is a fixed quantity. But, in practice, for the manufacture
(production plant), there are setup costs and inventory costs of raw-material,
work-in-process and finished goods as well. In addition, buyers incur
transportation costs, ordering costs and inventory costs during transportation
and at the destination (buyer/retailer). Thus, future research might be carried
out by taking these costs of setup, inventory, ordering and transportation
into account. Also, demand can be considered as stochastic. Hence, an
integrated single-manufacture-multi-buyer model with stochastic demand
can be obtained. How to develop a streamline method to tackle this large
scale LPP after considering these costs is challenging and potential future
research.
ACKNOWLEDGMENTS
The authors acknowledge that this research is supported by the research
grant of University of Peradeniya, Sri Lanka. Also, they are grateful to the
referees for their valuable, constructive commentsand suggestions.
REFERENCES
[1] Brain, D.B. Basic Linear Programming. London, Spottiswoode Ballantyne Ltd,1984.
[2] Dantzig, G.B. Linear Programming and extensions. Princeton, NJ: Princeton
University press, 1963.
[3] Fourer, R. Survey of linear programming software. OR/MS today, (2001), pp. 58-68.
[4] Hitchcock, F.L. The distribution of a product from several sources to numerous
locations. Journal of mathematical physics, 20, (1941), pp. 224-230.
[5] James, P.I. and Tom, M.C. Linear Programming. Prentice, Hall, Inc, 1994.
[6] Juman, Z.A.M.S., Hoque, M.A. and Buhari, M.I.A sensitivity analysis and an
implementation of the well-known Vogel‟s approximation method for solving
unbalanced transportation problems. Malaysian Journal of Science, 32,1(2013), pp. 66-
72.
[7] Juman, Z.A.M.S., Hoque, M.A. A heuristic solution technique to attain the minimal
total cost bounds of transporting a homogeneous product with varying demands and
supplies. European Journal of Operational Research, 239, (2014)pp. 146-156.
[8] Karmarkar, N. A new polynomial time algorithm for linear programming.
Combinatorial, 4, (1984), pp. 373-395.
[9] Liu, S.T. The total cost bounds of the transportation problem with varying demand and
supply.Omega, 31,(2003), pp.247-251.

IJCSBI.ORG
[10]Schrenk, S., Finke, G and Cung, V.D. Two classical transportation problems revisited:
Pure constant fixed charges and the paradox. Mathematical and Computer Modeling,
54,(2011), pp. 2306-2315.
[11]Sharma, R.R.K. and Prasad, S. Obtaining a good primal solution to the uncapacitated
transportation problem. European Journal of Operational Research, 144, (2003) , pp.
560-564.
[12]Sharma, R.R.K and Sharma, K.D. A new dual based procedure for the transportation
problem. European Journal of Operational Research, 122, 3 (2000),pp. 611-624.
[13]Taha H. A. Operation Research: An introduction. Prentice-Hall of India, 8th
edition,
2006.
[14]Terlaky, T. and Boggs, P.T. Interior point method. Faculty of information technology,
Delft. Netherlands, 2005.
[15]Zhang, Y. Solving large scale linear programming by interior point method under
MATLAB environment. Technical report, Mathematics Department, University of
Maryland, Baltimore Country, 1996.
This paper may be cited as:
Juman, Z. A. M. S. and Daundasekara, W. B., 2014. An Optimal Solution to
the Linear Programming Problem using Lingo Solver: A Case Study of an
Apparel Production Plant of Sri Lanka. International Journal of Computer
Science and Business Informatics, Vol. 14, No. 2, pp. 1-15.

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