1. Operations Research
Lecture 13

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. D is the demand per year

11. Model 2
Purchasing Model
with Shortages

12. In this model, shortages are allowed and consequently a shortage cost is incurred. Let the shortages be denoted by ‘S’ for every cycle and shortage cost by C4 per item per unit time. This model is illustrated in Figure

14. Q T Q Im s t t2 t1
t = t1 + t2

15. Figure shows that the back ordering is possible (i. e
Figure shows that the back ordering is possible (i.e.) once an order is received, any shortages can be made up as the items are received. Consequently shortage costs are due to being short of stock for a period of time.
The cost per period includes four cost components.
Total cost per period = Item cost + Order cost + Holding cost + Shortage cost

16. Item cost per period = (item cost) x (number of items/period) = C1xQ
Order cost per period = C2
Holding Cost per period = Average stock / period x t1 x holding cost / unit / unit time
Shortage Cost per period = Average shortages / period x t2 x shortage cost

19. Example

20. The demand for an item is 18000 units/year
The demand for an item is units/year. The cost of one purchase is Rs 400. The holding cost is Rs 1.2 per unit per year. The item cost is Rs 1 per item. The shortage cost is Rs 5 per unit per year. Determine:
(a)     The optimum order quantity.
(b)     The time between orders.
(c)     The number of orders per year.
(d)     The optimum shortages.
(e)     The maximum inventory.
(f)      The time of items being held.
(g)     The optimum annual cost.

21. = 1500 units / month C1 = Rs 1.0 / item C3 = Rs 1.2 / year/ item
Data
D = units / year
= 1500 units / month
C1 = Rs 1.0 / item
C3 = Rs 1.2 / year/ item
C2 = Rs 400 /order
C4 = Rs 5.0 / year / item

22. Optimum Order Quantity

23. Time Between Orders

24. Number of Orders
per year
Number of orders
per year
= 12 / 2.57
= 4.66

25. Optimum Shortages

26. Maximum Inventory

27. The Time when
Items being held

28. Order cost = Rs 400 per order
Optimum Annual Cost
Annual cost = Item cost
+ Ordering cost
+ Holding cost
+ Shortage cost
Item cost = Rs 3857 per order
Order cost = Rs 400 per order

29. Holding Cost

30. Shortage Cost

31. Total Cost per order

32. = (Number of orders / year) x Cost = Rs 4.66 x 4656.89 = Rs 21701
Annual Cost
Annual Cost
= (Number of orders / year)
x Cost
= Rs 4.66 x
= Rs 21701

33. Operations Research
Lecture 13