Spitzen Ltd. has to supply the following number of items at the end of each month.

Month No. | Month | No. of items |
---|---|---|

1 | January | 100 |

2 | February | 200 |

3 | March | 300 |

4 | April | 400 |

Total | 1000 |

Production during a month is available for supply at the end of the
month. The stock holding cost per month is Re. 1 per item. The setup
cost is Rs. 900 per setup and Rs. 2 per item. Find the optimal policy
so that total cost may be minimum.

Solution.

**The production cost Rs. 2 per item is always incurred, whether items
are produced in the beginning or at any other time.
Fixed cost = 1000 X 2 = Rs. 2000**

Requirement = 400

Cost = Rs. 900 (setup cost)

We have the following alternatives.

1. Produce 700 (demand for March & April) items in the beginning
of March.

Cost = 900 + (400 X 1) = Rs. 1300

2. Produce 300 items in March & 400 in April.

Cost = 900 + 900 = Rs. 1800

Hence, the optimal sub-policy for March is: Produce 700 items in March.

We have the following alternatives.

1. Produce 900 items in the beginning of February.

Cost = 900 + 700 X 1 + 400 X 1 = Rs. 2000

2. Produce 500 items now & 400 in April.

Cost = 900 + 300 X 1 + 900 = Rs. 2100

3. Produce 200 items now & 700 in March.

Cost = 900 + 1300 = Rs. 2200

The optimal sub-policy for March was to produce 700 items. Therefore,
in February we have not considered the following case: Produce 200 items
now, 300 items in March & 400 in April.

Hence, the optimal sub-policy for February is: Produce 900 items in
February.

We have the following alternatives.

1. Produce 1000 items in the starting of January.

Cost = 900 + (900 X 1 + 700 X 1 + 400 X 1) = Rs. 2900

2. Produce 600 items now & 400 in April.

Cost = 900 + 500 X 1 + 300 X 1+ 900 = Rs. 2600

3. Produce 300 items now & 700 in March.

Cost = 900 + 200 X 1 + 1300 = Rs. 2400

4. Produce 100 items now & 900 in February.

Cost = 900 + 2000 = Rs. 2900

The minimum cost is Rs. 2400. Hence, the best policy is: Produce 300 items in January & 700 in March.