In this section, we provide an example of how **simulation models** can be used in **inventory control**.

Zicom Electronics wants to determine the order size for calculators. The demand and lead time are probabilistic and their distributions are given below:

Demand / week (thousands) | Probability | Lead time | Probability |
---|---|---|---|

0 | 0.2 | 2 | 0.3 |

1 | 0.4 | 3 | 0.4 |

2 | 0.3 | 4 | 0.3 |

3 | 0.1 |

The cost of placing an order is Rs. 100 per order and the holding cost
for 1000 calculators is Rs. 2 per week. The shortage cost is Rs. 20
per thousand. Whenever the inventory level is equal to or below 2000,
an order is placed equal to the difference between the current inventory
balance and specified maximum replenishment level equal to 4000.

Simulate the policy for 10 weeks. Assume the following

- the beginning inventory is 3000 units
- no back orders are permitted
- each order is placed at the beginning of the week following the drop in inventory level to (or below) the reorder point
- the replenishment orders are received at the beginning of the week.

Solution.

Using the daily demand and lead time distributions, we assign a set of random numbers to represent the range of values of variables as shown in table 1 & table 2.

Table 1

Demand / week (thousands) | Probability | Cumulative Probability | Random Numbers |
---|---|---|---|

0 | 0.2 | 0.2 | 00-19 |

1 | 0.4 | 0.6 | 20-59 |

2 | 0.3 | 0.9 | 60-89 |

3 | 0.1 | 1.0 | 90-99 |

Table 2

Lead time (weeks) | Probability | Cumulative Probability | Random Numbers |
---|---|---|---|

2 | 0.3 | 0.3 | 00-29 |

3 | 0.4 | 0.7 | 30-69 |

4 | 0.3 | 1.0 | 70-99 |

At the start of *simulation*, the first random number 31 generates a
demand of 1000 units, as shown in table 3. The demand is determined
from the cumulative probability values in table 1. At the end of first
week, the closing balance is 2000 units, which is equal to the reorder
level; therefore, an order for 2000 (4000-2000) units is placed. The
random number generated is 29, so the lead time is 2 weeks. The lead
time is determined from the cumulative probability values in table 2.
Since closing balance is 2000 units, the holding cost is Rs. 4

In the second week, the random number 70 generates a demand of 2000 units. Therefore, the closing balance at the end of second week is reduced to zero units.

In the third week, the demand for 1000 units can't be fulfilled because
the available inventory is zero. This results in the shortage cost of
Rs. 20.

The 2000 units ordered in the first week are received at the beginning of fourth week. The random number 86 generates a demand of 2000 units, and, hence closing stock is zero. Therefore, an order for 4000 (4000-0) units is placed. The random number generated is 83, so the lead time is 4 weeks. Therefore, the second shortage occurs in the fifth week. The units ordered at the end of fourth week are received in the beginning of ninth week.

Table 3

Week | Opening Balance Inventory ('000) | Demand | Closing Balance Inventory ('000) | Lead Time | Quantity Ordered ('000) | Costs | |||
---|---|---|---|---|---|---|---|---|---|

Random Numbers | Units ('000) |
Random Numbers | Weeks | Holding Cost (Rs.) | Shortage Cost (Rs.) | ||||

1 | 3 | 31 | 1 | 2 | 29 | 2 | 2 | 4 | - |

2 | 2 | 70 | 2 | 0 | - | - | - | - | - |

3 | 0 | 53 | 1 | -1 | - | - | - | - | 20 |

4 | 2* | 86 | 2 | 0 | 83 | 4 | 4 | - | - |

5 | 0 | 32 | 1 | -1 | - | - | - | - | 20 |

6 | 0 | 78 | 2 | -2 | - | - | - | - | 40 |

7 | 0 | 26 | 1 | -1 | - | - | - | - | 20 |

8 | 0 | 64 | 2 | -2 | - | - | - | - | 40 |

9 | 4* | 45 | 1 | 3 | - | - | - | 6 | - |

10 | 3 | 12 | 0 | 3 | - | - | - | 6 | - |

Total | 13 | 6 |

Note: * includes order quantity just received.

Average Inventory = 8000/10 = 800 units.

The average inventory is calculated by adding the closing inventory
balances (ignoring negative balances) and dividing by the number of
weeks.

Weekly average cost = Ordering Cost + Inventory Holding Cost + Shortage Cost

Ordering Cost = (100 X 2)/10

= Rs. 20

Inventory Holding Cost = (800 X 2)/1000

= Rs. 1.60

Shortage Cost = [20 X (1 + 1 + 2 + 1 + 2)]/10 = Rs. 14

Weekly average cost = Rs. 20 + Rs. 1.60 + Rs. 14

= Rs. 35.60

It should be noted that the shortage cost is high as compared to holding cost. The shortage cost can be reduced by increasing the reorder level.

Average lead time = 6/2 = 3 weeks

Average demand per week = 13000/10 = 1300 units

Average demand during lead time = 3 X 1300 = 3900 units

Maximum lead time = 4 weeks

Maximum weekly demand = 2000 units

Maximum demand during lead time = 4 x 2000 = 8000 units

Thus, the best reorder point should be somewhere between 3900 to 8000 units.