1. Operations Research
Lecture 12

2. Operations Research
Inventory Control

3. Inventory
Physical stock of items held in any business for the production or sales

4. Type of Inventory Finished Goods ! Finished Product Raw Material
In-Process
Finished Goods !

5. Inventory Costs Shortage Cost Rs C1 /item/unit time
Item Cost, Rs C1/item Ordering Cost, Rs C2 /order
Holding Cost Rs C /item/unit time
Shortage Cost Rs C /item/unit time

6. Inventory Models (EOQ Models)
The inventory control model can be broadly classified into two categories:
Deterministic inventory problems
Probabilistic inventory problems

7. Model 1: Purchasing Model with no Shortages
The following assumptions are made in deriving the formula for economic order quantity.
Demand (D) is at a constant rate.
Replacement of items is instantaneous (lead time is zero).

8. Cont ! The cost coefficients C1, C2, and C3 are constant.
There is no shortage cost or C4 = 0.

9. Cont !
Quantity
Time

10. Model
The total cost for this model for one cycle is made up of three cost components.
Total cost / period = (Item cost + set up cost + holding cost / period)

11. Cont !
Item cost per period = (Cost of item) x (number of items ordered / period)
Purchase or set up cost per period = C2
(only one set up per period)

12. Cont !
Item holding cost per period = (Holding cost)x(average inventory per period)x(time per period)
Therefore the total cost per period

13. Cont ! But the time for one period
Therefore the total cost per unit time,

14. Purchase cost = Item holding cost.
Cont !
Purchase cost = Item holding cost.

15. Cont !
This Gives

16. Alternate Method
This minimum inventory cost per unit time can also be found by differentiating C with respect to Q and equating it to zero. That is

17. Cont !

18. Further more !
D is the demand per year

19. Example
The demand rate for a particular item is units/year. The ordering cost is Rs 100 per order and the holding cost is Rs 0.80 per item per month. If no shortages are allowed and the replacement is instantaneous, determine:
(a)     The economic order quantity
(b)     The time between orders
(c)     The number of orders per year
(d)     The optimum annual cost,
if the cost of item is Rs 2 per item.

20. Solution C1 = Rs. 2.0 / item C2 = Rs. 100 / order
C3 = Rs. 0.80/item/month
= Rs. 9.6/item/year
D = items/year

21. Cont !
(a)The economic order quantity

22. Cont !
(b)The time between orders

23. Cont !
(c)The number of orders / yr

24. Cont !
(c) The optimum annual cost

25. Model 2
Purchasing Model
with Shortages

26. Operations Research
Lecture 12