Simulation of inventory problem
Simulation of inventory problem
A dealer of electrical appliances has a certain product for which the probability distribution of demand per day and the probability distribution of the leadtime, developed by past records are as shown in Table 9.23 and 9.24 respectively.

Demand (Units)

2

3

4

5

6

7

8

9

10















Probability

0.05

0.07

0.09

0.15

0.20

0.21

0.10

0.07

0.06



























Lead Time (Days)

1

2

3

4










Probability

0.20

0.30

0.35

0.15









The various costs involved are,
Ordering Cost = ` 50 per order
Holding Cost = ` 1 per unit per day
Shortage Cost = ` 20 per unit per day
The dealer is interested in having an inventory policy with two parameters, the reorder point and the order quantity, i.e., at what level of existing inventory should an order be placed and the number of units to be ordered. Evaluate a simulation plan for 35 days, which calls for a reorder quantity of 35 units and a reorder level of 20 units, with a beginning inventory balance of 45 units.
Solution:
Assigning of random number intervals for the demand distribution and leadtime distribution is shown in Tables 9.25 and 9.26 respectively.

Demand per Day

Probability

Cumulative Probability

Random Number Interval











2

0.05

0.05

0004











3

0.07

0.12

0511











4

0.09

0.21

1220











5

0.15

0.36

2135











6

0.20

0.56

3655











7

0.21

0.77

5676











8

0.10

0.87

7786











9

0.07

0.94

8793











10

0.06

1.00

9499


















Table 9.26: Random Numbers Assigned for Leadtime












Lead Time (Days)

Probability

Cumulative Probability

Random Number Interval











1

0.20

0.20

0019











2

0.30

0.50

2049











3

0.35

0.85

5084











4

0.15

1.00

8599


















Day

Random

Demand

Random

Lead

Inventory at

Qty.

Ordering

Holding

Short




Number


Number (Lead

Time

end of day

Received

Cost

Cost

age Cost




(Demand)


Time)

(Days)








0

–

–

–

–

45

–

–

–

–















1

58

7

–

–

38

–

–

38

–















2

45

6

–

–

32

–

–

32

–















3

43

6

–

–

26

–

–

26

–















4

36

6

73

3

20

–

50

20

–















5

46

6

–

–

14

–

–

14

–















6

46

6

–

–

8

–

–

8

–















7

70

7

–

–

1

35

–

36

–















8

32

5

–

–

31

–

–

31

–















9

12

4

–

–

27

–

–

27

–















10

40

6

–

–

21

–

–

21

–















11

51

6

21

2

15

–

50

15

–















12

59

7

–

–

8

–

–

8

–















13

54

6

–

–

37

35

–

37

–















14

16

4

–

–

33

–

–

33

–















15

68

7

–

–

26

–

–

26

–















16

45

6

45

2

20

–

50

20

–















17

96

10

–

–

10

–

–

10

–















18

33

5

–

–

40

35

–

40

–















19

83

8

–

–

32

–

–

32

–















20

77

8

–

–

24

–

–

24

–















21

05

3

–

–

21

–

–

21

–















22

15

4

76

3

17

–

50

17

–















23

40

6

–

–

11

–

–

11

–















24

43

6

–

–

5

–

–

5

–















25

34

5

–

–

35

35

–

35

–















26

44

6

–

–

29

–

–

29

–















27

89

9

96

4

20

–

50

20

–















28

20

4

–

–

16

–

–

16

–















29

69

7

–

–

9

–

–

9

–















30

31

5

–

–

4

–

–

4

–















31

97

10

–

–

29

35

–

29

–















32

05

3

–

–

26

–

–

26

–















33

59

7

94

4

19

–

50

19

–















34

02

2

–

–

17

–

–

17

–















35

35

5

–

–

12

–

–

12

–





















Total

300

768

–


























Reorder Quantity = 30 units, Reorder Level = 20 units, Beginning Inventory = 45 units
The simulation of 35 days with an inventory policy of reordering quantity of 35 units at the time of inventory level at the end of day is 20 units, as worked out in Table 9.27. The table explains the demand inventory level, quantity received, ordering cost, holding cost and shortage cost for each day.
Completing a 35 day period, the costs are:
Total ordering cost = (6 × 50) = ` 300.00
Total holding cost = ` 768.00
Since the demand for each day is satisfied, there is no shortage cost.
Therefore, Total cost = 300 + 768
= ` 1068.00
For a different set of parameters, with a reorder quantity of 30 units and the same reorder level of 20 units, if the 35day simulation is performed, we get the total of various costs as shown in Table 9.28.
Total ordering cost = 6 × 50 = ` 300.00
Total holding cost = ` 683.0
Total shortage cost = ` 20.00
Therefore, Total cost = 300 + 683 + 20
= ` 1003.00
If we analyze the combination of both the parameters, Case II has lesser total cost than Case I. But at the same time, it does not satisfy the demand on 33rd day, that might cause customer dissatisfaction which may lead to some cost.
In this type of problems, the approach with various combinations of two parameter values is simulated a large number of times to find the total cost of each experiment, compare the total cost and select the optimum alternative, i.e., that one which incurs the lowest cost.