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JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 1, JUNE, 2010


SIMULATION MODEL: A TOOL FOR COPING WITH FLUCTUATING DEMAND IN FUEL STATION MANAGEMENT

Jonathan E. Ekpudu
Department of Business Administration, Salem University, Lokoja
E-mail: jonathanekpudu@yahoo.co.uk
and
                      C. J. Agorzie
Department of Management and Accounting, Obafemi Awolowo University, Ile-Ife, Nigeria

 

Abstract
In order to ensure effectiveness in activities planning and scheduling, including efficient use of resources in fuel stations’ management, there is the need for adequate demand forecast or projection. This paper experiments the Monte Carlo’s simulation model on ten days sales of three randomly selected fuel stations in three Local Government of Lagos State to determine its viability in sales projection, to cope with fluctuating demand situations. The result of the study is impressive because it was found that simulation model; aids sales forecasting, enhances effective product planning and activities scheduling to cope with projected demand, asides providing the necessary aids to making informed decisions in unstructured decisional situations

Keywords: Simulation, model, coping, fluctuating, demand.

Introduction
One of the major objectives of any business organization is profit maximization                                                                                                                                                  through customers’ satisfaction. In realizing this, a number of down stream petroleum companies in the Nigeria oil sector setup fuel stations (petrol stations) across the length and breath of Nigeria. However, the manner in which these stations carryout their businesses are of fundamental importance to the achievement of the overall objectives of the oil sector in Nigeria.
Simulation model is a quantitative technique for evaluating alternative courses of actions, through experimentation performed via a mathematical model, in order to represent actual decision-making under condition of uncertainty (Agbadudu, 1996). Simulation is a potent tool for predicting and coping with fluctuation in demand in a distressed economic situation. It is therefore essential for organizations’ planners or policy formulators to be knowledgeable with this ‘potent’ tool for effective planning and strategy towards goals attainment.
However, while the need for efficiency and effectiveness have been realised by owners of fuel stations in Nigeria, the need for the use of simulation models for effective planning and projection of future sales is yet  to be recognized. Thus, product shortages or stock out, long queues, loss of productive hours, and inadequate planning remain common features in most fuel stations’ operations in Lagos state. This paper is to demonstrate the ‘potentiality’ in the application of simulation model to making decisions, through the experimentation of some randomly selected fuel stations in Lagos state.


The importance of simulation model
Despite the impressive advances in mathematical modeling, a number of real-life situations still, are well beyond the capabilities of representing mathematically. As such, the alternative approach to modeling such complex and unstructured systems or situations is through simulation model.
Simulation modeling differs from mathematical modeling in that the relationships between the inputs and outputs need not be stated explicitly. Instead, it breaks-down the real system into (small) modules and then, imitates the actual behaviour of the system by using logical relationships to link them together (Taha, 2002). Chase and Acquilano (2002), refer to simulation as using a computer to perform experiments on a model of real systems. They stressed further that the experiments may be undertaken before a real system is operational, to aid in its design, to see how the system might react to changes in its operating rules, or to evaluate the system’s response to changes in its structure. However, viewing from cost perspective, Schroeder (1993), states that simulation should be used in situations where it is too expensive or difficult to experiment with the real situation. In this direction, the effects of a decision can be tested on a simulation model before implementation. A number of situations or problems have been simulated in this way, including flow of vehicles to fuel stations, the operations of physical distribution networks, factory operations, and arrival and departure of all types; ships and aircraft, among others. That is, simulation is frequently useful in queue problems which have complicated arrival patterns, service, distribution or line discipline. Akingbade (1996), concludes that simulation is an operational research approach involving experimenting on a model, to generate a set of data from which to identify discernible trends to be used as a basis for decision-making.
In the above review, (Taha, 2002; Agbadudu,1996; Schroeder,1993;and Akingbade, 1996 ), there seems to be an agreement that simulation model is best used when the system or problem under consideration involves complex queue, expensive to employ the optimization models to capture the entities in the system, including their pattern of relationships. This paper, in order to determine whether simulation models aid effective planning and scheduling of fuel station’s activities in Lagos state, used the Monte Carlo’s simulation model to forecast the annual demand and  expected profit from ten days sales data of premium motor spirit (PMS) from three randomly selected fuel stations in three local Governments of Lagos state.
Methodology
Three fuel stations were randomly selected from three Local Governments upon which ten days sales were extracted from their sales records. The ten days sales of each of the stations were each used to predict the expected monthly sales for each of the stations, using the Monte Carlo’s simulation technique. The random numbers (data) were generated through the computer system to avoid biasness. To run the simulation, this paper employed a written program. On the whole, the predicted monthly sales for each station were used to predict the expected annual sales and gross profit for each of the stations.


Simulation program

c Program to simulate demand in fuel stations
C  Reserve arrays for storing data
  dimension isales(10), prob(10), irandom(30),   icum(10),isal(30)
  dimension limit (10), lolimit (10)
  open (unit =1, file 'busad1.in', status ='old')        
  open (unit =2, file 'busad1.dat', status 'old')    
  open (unit =4, file 'busad1.txt', status = 'old')    
  open (unit =3, file 'busad1.out', status = 'new')
c  Read in the input: sales and random numbers for    unbiased  
c  forecast of future sales, and selling and cost prices        and number of litres per month
   read(1,*)isales(i),i=10)        
   read(2, *)(irandom(i),i=l,30)
   read (4,*) sell, cost,litres
C  Summing up the past sales, so we can calculate the          probability       
   do 15 i= 1, 10
   15 sum =sum + isales (i)
C  Calculating the probability     
   do 16 k = 1; 10
16 prob (k) = isales (k) /sum
C Calculating the cumulative probability
  do 20 j = 1; 10
  probsum =prob (j) + probsum
20 icum(j) = probsum*100.   

6 Format(15,3x,F4.2,3x,313)                                      c We determine the lower and upper limits of Monte-Carlo tag        nos.                                                       c Upper limit is denoted by Limit, and lower limit by        lolimit
  do 66 i= 1,10
  66  limit(i) = icum(i)-l
 
10 1imit(1)=0   
  do  67 j = 2, 10
  67 lolimit (j) = limit (j-1) +1
C Writing out the sales, probability, cumulative      probability and   
c  the limits of the Monte-Carlo tag nos.
   do 21 I = 1, 10
21 write (3,6) isales (i), prob(i), icum (i), lolimit    (i), limit (i)
C  Using the random numbers, tag no., and past sales for     Forecast                                                             do 10 I = 1, 30
   do 27 j = 1, 10
   if (irandom (i). ge. lolimit (j). and irandom (i).       le.limit     (j)) then goto 45
   endif

     if (irandom(i) .ge. 11 .and. irandom(i)    . le. 20 ) then
      isal (i) = isales (2)
     goto 45            endif
     if (irandom(i) .ge. 21 .and. irandom(i)    . le. 28 ) then
     isal (i) = isales (3)
goto 45
endif
     if (irandom(i) .ge. 29 .and. irandom(i)  .le. 38) then
      isal (i) = isales (4)
goto 45
endif
     if (irandom(i) .ge. 39 .and. irandom(i)  . le. 48) then
isal (i) = isales (5)
goto 45
endif
     if (irandom(i) .ge. 49 .and. irandom(i) . le. 59 ) then 
     isal (i) = isales (6)
goto 45
endif
     if (irandom(i)  .ge. 60 .and. irandom(i)  . le. 67 ) then
    isal (i) = isales (7)
goto 45
endif
     if (irandom(i)  .ge. 68 .and. irandom(i) . le. 78) then
     isal (i) = isales (8)
goto 45
endif
     if (irandom(i) .ge. 79 .and. irandom(i) . le. 88) then
     isal (i) = isales (9)
goto 45
endif
     if (irandom(i)  .ge. 89 .and. irandom(i)  . le. 99 ) then
     isal (i) = isales (10)
goto 45
endif
27 continue
C Write day, random number and demand forecast       
 45 write(3,*) I,. irandom(i), isal (i)
write (*,*) I, irandom (i), isal(i)
   10  continue
do 99 I = I, 30
99 isum = isum + isal (i)
C Write Total consumption per month
write(3,*) isum
iyearly = 12*isum
c Write Total consumption per year
 write(3,*) iyearly

 iprofit = (sell-cost) *litres
 write Annual profit
 write (3,*) iprofit
 stop
  end.

 

 

 

 

Data presentation

Table (A) Sales (fuel station A)

Day

1

2

3

4

5

6

7

8

9

10

Total

Sales in Litres

6090

6026

6684

6324

6100

6040

4935

5938

6361

6057

60555

            Table (B) Sales (fuel station B)

Day

1

2

3

4

5

6

7

8

9

10

Total

Sales in Litres

5604

5253

4920

5341

5658

5472

5030

5460

5156

4972

52866

Table (C) Sales  (fuel station C)

Day

1

2

3

4

5

6

7

8

9

10

Total

Sales in Litres

7702

7200

7250

7224

7836

7700

5348

7221

7037

7150

71668


Data analysis

Table (A) Computer solution

Sales
(in Litres)

Probability

Cumulative
Probability

Monte Carlo Tag No.

No. of
Runs

Random
No.

Demand
forecast

 

 

Lower

Upper

 

 

 

6090

0.1

10

0

9

1

56

6040

6026

0.1

20

10

19

2

95

6057

6684

0.11

31

20

30

3

88

6361

6324

0.1

41

31

40

4

32

6324

6100

0.1

51

41

50

5

36

6324

6040

0.1

61

51

60

6

32

6324

4935

0.08

69

61

68

7

37

6324

5938

0.1

79

69

78

8

42

6100

6361

0.11

89

79

88

9

70

5938

6057

0.1

100

89

99

10

4

6090

 

 

 

 

 

 

11

90

6057

 

 

 

 

 

 

12

72

5938

Total consumption/ month

 

182794

 

13

46

6100

Total consumption per year

 

219352888

 

14

50

6040

Gross Annual profit

 

 

4420392

 

15

40

6100

 

 

 

 

 

 

16

3

6090

 

 

 

 

 

 

17

70

5938

 

 

 

 

 

 

18

12

6026

 

 

 

 

 

 

19

85

6361

 

 

 

 

 

 

20

59

6040

 

 

 

 

 

 

21

51

6040

 

 

 

 

 

 

22

73

5938

 

 

 

 

 

 

23

75

5938

 

 

 

 

 

 

24

28

6684

 

 

 

 

 

 

25

42

6100

 

 

 

 

 

 

26

60

4935

 

 

 

 

 

 

27

79

6361

 

 

 

 

 

 

28

15

6026

 

 

 

 

 

 

29

45

6100

 

 

 

 

 

 

30

44

6100

                Comment:
From the computer solution of Table (A), It means that fuel station (A) projected monthly demand or sales is 182,794 Iitres of PMS, with  an expected annual demand of 2,193,528 Iitres, while the projected annual gross profit stands at N4,420,392.00
 

Table (B) Computer solution

Sales
(in Litres)

Probability

Cumulative
probability

Monte Carlo Tag No.

No. of
Runs

Random
No.

Demand
forecast

Lower

Upper

5604

0.11

10

0

9

1

88

5156

5253

0.1

20

10

19

2

24

4920

4920

0.09

29

20

28

3

44

5658

5341

0.1

39

29

38

4

14

5253

5658

0.11

50

39

49

5

32

5341

5472

0.1

60

50

59

6

35

5341

5030

0.1

70

60

69

7

99

4972

5460

0.1

80

70

79

8

81

5156

5156

0.1

90

80

89

9

54

5472

4972

0.09

100

90

99

10

48

5658

 

 

 

 

 

 

 

 

 

 

 

 

11

94

4972

 

 

 

 

 

 

12

61

5030

Total consumption / month

 

156835

 

13

1

5604

Total consumption per year

 

1882020

 

14

26

4920

Gross Annual profit

 

 

3750528

 

15

89

4972

 

 

 

 

 

 

16

57

5472

 

 

 

 

 

 

17

20

5253

 

 

 

 

 

 

18

69

5460

 

 

 

 

 

 

19

93

4972

 

 

 

 

 

 

20

39

5658

 

 

 

 

 

 

21

6

5604

 

 

 

 

 

 

22

28

4920

 

 

 

 

 

 

23

34

5341

 

 

 

 

 

 

24

91

4972

 

 

 

 

 

 

25

99

4972

 

 

 

 

 

 

26

91

4972

 

 

 

 

 

 

27

82

5156

 

 

 

 

 

 

28

81

5156

 

 

 

 

 

 

29

59

5472

 

 

 

 

 

 

30

61

5030

 

 

 

 

 

 

 

 

 

 

Comment:
From the computer solution of Table (B), It means that fuel station (B) projected monthly demand or sales is 156,835 Iitres of PMS, with  an expected annual demand of 1,882,020 Iitres, while the projected annual gross profit stands at N3,750,528.00


 

                                           Table (C) Computer solution

Sales
(in Litres)

Probability

Cumulative
probability

Monte Carlo Tag No.

No. of
Runs

Random
No.

Demand
forecast

Lower

Upper

7202

0.1

10

0

9

1

35

7224

7200

0.1

20

10

19

2

94

7150

7250

0.1

30

20

29

3

53

7700

7224

0.1

40

30

39

4

22

7250

7836

0.11

51

40

50

5

       2

7202

7700

0.11

62

51

61

6

39

7836

5348

0.08

69

62

68

7

91

7150

7221

0.1

80

69

79

8

96

7150

7037

0.1

89

80

88

9

       8

7202

7150

0.1

100

89

99

10

87

7037

 

 

 

 

 

 

11

       0

7202

 

 

 

 

 

 

12

95

7150

Total consumption per month month

 

220915

 

13

92

7150

Total consumption per  year

 

2650980

 

14

       7

7202

Gross Annual profit

 

 

5273136

 

15

54

7700

 

 

 

 

 

 

16

46

7836

 

 

 

 

 

 

17

48

7836

 

 

 

 

 

 

18

10

7200

 

 

 

 

 

 

19

23

7250

 

 

 

 

 

 

20

26

7250

 

 

 

 

 

 

21

89

7150

 

 

 

 

 

 

22

39

7836

 

 

 

 

 

 

23

92

7150

 

 

 

 

 

 

24

19

7200

 

 

 

 

 

 

25

34

7224

 

 

 

 

 

 

26

76

7221

 

 

 

 

 

 

27

50

7700

 

 

 

 

 

 

28

46

7836

 

 

 

 

 

 

29

51

7700

 

 

 

 

 

 

30

71

7221

 

Comment:
From the computer solution of Table (C), It means that fuel station (C) projected monthly demand or sales is 220,915 Iitres of PMS, with  an expected annual demand of 2,650980 Iitres, while the projected annual gross profit stands at N5,273136.00

 

 

 Findings

This paper observed from the results of the analyzed data a number of things which include: Simulation model provides the best option when decisions are made in an unstructured environment; it aids in planning the optimum quantities of stock to hold in a fuel station, to avoid over or under stocking situation which has negative consequences like loss of goodwill, unnecessary capital tie down, among others in fluctuating demand situations; it provides a more replication of a system than the optimization models which makes it capture all the interacting entities and their relationships; finally, it assist fuel stations’ operators in making informed decisions to resolve operations/ activities  scheduling problems, profit projection and the likes.
Conclusion
This paper  present the following conclusion from the study’s findings: Simulation model is a potent tool for making informed decisions in an unstructured business environment; it is useful in inventory planning and control (management); it provides a more realistic solution where and when the optimization technique fails; finally, simulation model application is imperative for operations planning and activities scheduling , including making of sales and profit projections in fuel station management.
Recommendation
Organization that whishes to survive and have a competitive advantage over rivals in today’s  complex, fast changing and competitive business environment, especially fuel stations in Nigeria, must be knowledgeable in the application of the tool called simulation model for a number of reasons which include; to ensure that the objective of  share holders are effectively realised, to ensure that optimum inventory  (stock) is held at all time to cope with fluctuations in demand, and to make informed decisions in an unstructured business environment.  

 

References

Agbadudu, A. B. (1996), Elementary Operations Research. Volume I, Benin City : A.B.Mudiaga                      Limited.

 Akingbade, F. (1996), Basic Operattional Research Techniques. Lagos: Panaf Publishing                      

Banjoko, S. A. (1996), Production and Operations Management. Lagos: Suban Publishing.

Chase and Acquilano J. (2002), Operations Management for competitive advantage.
Ninth Edition, New York: Mc Graw- Hill.

Schroeder, R. (1993), Operations Management; Decision-Making in the operations                      Function. Fourth Edition, New York: Mc Graw-Hill Inc.

Taha, H. A. (2002), Operations Research; An Introduction, New Delhi: Prentice Hall Private Limited,                      .