OPERATIONS MANAGEMENT, INVENTORY MANAGEMENT, MODELS, EOQ

1. INVENTORY MANAGEMENT
By:
Er. Vaibhav Agarwal
Asst. Prof.
BBD University, Lucknow
OPERATIONS MANAGEMENT

2. INVENTORY MANAGEMENT AND ANALYSIS
• Inventory generally refers to the materials in stock.
• It is also called the idle resource of an enterprise.
• Inventories represent those items which are either stocked for sale or they are in the process of
manufacturing or they are in the form of materials, which are yet to be utilized.
• The interval between receiving the purchased parts and transforming them into final products varies from
industries to industries depending upon the cycle time of manufacture.
• It is, therefore, necessary to hold inventories of various kinds to act as a buffer between supply and
demand for efficient operation of the system.
• Thus, an effective control on inventory is a must for smooth and efficient running of the production cycle
with least interruptions.
By: Er. VAIBHAV

3. Reasons for keeping inventory
1. TO STABILISE PRODUCTION: The demand for an item fluctuates because of the number of factors,
e.g., seasonality, production schedule etc. The inventories (raw materials and components) should be made
available to the production as per the demand because without which it results in stock out and the
production stoppage takes place for want of materials. Hence, the inventory is kept to take care of this
fluctuation so that the production is smooth.
2. TO TAKE ADVANTAGE OF PRICE DISCOUNTS: Usually the manufacturers offer discount for
bulk buying and to gain this price advantage the materials are bought in bulk even though it is not required
immediately. Thus, inventory is maintained to gain economy in purchasing.
3. TO MEET THE DEMAND DURING THE REPLENISHMENT PERIOD: The lead time for
procurement of materials depends upon many factors like location of the source, demand supply
condition, etc. So inventory is maintained to meet the demand during the procurement (replenishment)
period.
By: Er. VAIBHAV

4. 4. TO PREVENT LOSS OF ORDERS (SALES): In this competitive scenario, one has to meet the delivery
schedules at 100 per cent service level, means they cannot afford to miss the delivery schedule which may
result in loss of sales. To avoid the organizations have to maintain inventory.
5. TO KEEP PACE WITH CHANGING MARKET CONDITIONS: The organizations have to anticipate
the changing market sentiments and they have to stock materials in anticipation of non-availability of
materials or sudden increase in prices.
By: Er. VAIBHAV

5. FUNCTIONS OF INVENTORY
1. To decouple or separate various parts of the production process. This is done to avoid any kind of
unnecessary effect on production due to fluctuations in supply.
2. To decouple the firm from the fluctuations of demand and provide a stock of goods that will provide a
selection for the customers.
3. To hedge against inflation and upward price changes.
By: Er. VAIBHAV

6. Types OF INVENTORY
A firm maintains four types of inventory.
1. Raw-Material Inventory.
2. Work-in-Process Inventory.
3. Maintenance/repair/operating supply inventory.
4. Finished goods inventory.
By: Er. VAIBHAV

7. By: Er. VAIBHAV

8. Types OF INVENTORY
1. Raw-Material Inventory: Materials that are usually purchased but yet have to enter the manufacturing
process. This inventory is used to decouple the manufacturer from the supplier. Tries to eliminate the
supplier variability by in quantity, quality or delivery time so that separation is not needed.
2. Work-in-Process Inventory: Products and components that are no longer raw material and have undergone
some changes but are not completed. It exists because of the time it takes for a transformation which is not
yet complete. It exists because of cycle time. If Cycle time is reduced then inventory levels are also
reduced.
3. Maintenance/repair/operating supply inventory: It is necessary to keep machine and processes
productive. They exists because the need and timing for maintenance and repair of some equipment are
unknown.
4. Finished goods inventory: It is the storage of the items which are complete product and ready to be
shipped. They are ready to be sold but still exists in the books of the company.
By: Er. VAIBHAV

9. Meaning of Inventory Control
1. Inventory control is a planned approach of determining what to order, when to order and how much to
order and how much to stock so that costs associated with buying and storing are optimal without
interrupting production and sales.
2. Inventory control basically deals with two problems:
1. When should an order be placed? (Order level),
2. How much should be ordered? (Order quantity).
3. These questions are answered by the use of inventory models.
4. The scientific inventory control system strikes the balance between the loss due to non-availability of an
item and cost of carrying the stock of an item.
5. Scientific inventory control aims at maintaining optimum level of stock of goods required by the
company at minimum cost to the company.
By: Er. VAIBHAV

10. Objectives of Inventory Control
1. To ensure adequate supply of products to customer and avoid shortages as far as possible.
2. To make sure that the financial investment in inventories is minimum (i.e., to see that the Working
capital is blocked to the minimum possible extent).
3. Efficient purchasing, storing, consumption and accounting for materials is an important objective.
4. To maintain timely record of inventories of all the items and to maintain the stock within the desired
limits
5. To ensure timely action for replenishment.
6. To provide a reserve stock for variations in lead times of delivery of materials.
7. To provide a scientific base for both short-term and long-term planning of materials
By: Er. VAIBHAV

11. Benefits of Inventory Control
It is an established fact that through the practice of scientific inventory control, following are the benefits of
inventory control:
1. Improvement in customer’s relationship because of the timely delivery of goods and service.
2. Smooth and uninterrupted production and, hence, no stock out.
3. Efficient utilization of working capital. Helps in minimizing loss due to deterioration, obsolescence
damage and pilferage.
4. Economy in purchasing.
5. Eliminates the possibility of duplicate ordering.
By: Er. VAIBHAV

12. Inventory model for independent demand
There are 3 models for inventory management for INDEPENDENT DEMAND:
• BASIC ECONOMIC ORDER QUANTITY (EOQ) MODEL.
• PRODUCT ORDER QUANTITY MODEL.
• QUANTITY DISCOUNT MODEL.
By: Er. VAIBHAV

13. BASIC ECONOMIC ORDER QUANTITY(EOQ MODEL)
a) EOQ: Economic order quantity, tells about the quantity for which the total cost (ordering cost + holding cost)
of maintaining an inventory is minimum.
b) The various assumptions which are critical for EOQ model are:
a) Demand is known, constant, and independent.
b) Lead time – the time between placing and receiving the order – is known and constant.
c) Receipt of inventory is instantaneous and complete. So inventory from an order arrives in one batch at
a time.
d) Quantity discounts are not possible.
e) The variable costs are the:
1. Cost of setting up or placing an order (setup cost),
2. The cost of holding or storing inventory over time (carrying cost).
f) Stockouts (shortages) can be completely avoided if orders are placed at the right time.
By: Er. VAIBHAV

14. USAGE RATE
AVERAGE INVENTORY ON
HAND (Q/2)
QUANTITY ORDERED = Q
MAX. INVEMTORY LEVEL
MINIMUM INVENTORY
0
TIME
INVENTORYLEVEL
SAWTOOTH SHAPE OF INVENTORY USAGE
By: Er. VAIBHAV

15. • The graph of inventory usage over time is assumed to be as SAW-TOOTH shape.
• Let Q, represent the amount ordered.
• The inventory jumps from 0 to Q, one the order is received/order arrives.
• As demand is constant over time, so the demand drops at a uniform rate over time.
• Each time inventory reaches to 0, the new order is placed and received instantaneously, so the inventory level
jumps again to Q from 0.
• This process carries indefinite period of time.
By: Er. VAIBHAV

16. • The ordering costs and holding costs are only important. These are variable costs.
• All other costs remaining constant.
• The aim is to minimize the total cost of maintaining the inventory for particular quantity.
• TOTAL COST = ORDERING COST + HOLDING COST.
• The inventory ordering costs are inversely proportional to the quantity ordered.
• For larger quantity ordered, the number of order reduces and so the Total Annual Ordering Costs per order also decreases.
• But the inventory holding costs are directly proportional to the quantity ordered.
• So the inventory holding costs/carrying costs increases for larger quantity ordered.
• We need to strike a balance between decreasing Ordering costs and increasing Holding cost, to keep total cost at
minimum.
• A graph is plotted for Ordering costs, Holding costs and Total costs against the quantity ordered.
By: Er. VAIBHAV

17. BASIC EOQ MODEL: MINIMIZING COSTS
By: Er. VAIBHAV

18. • From the diagram, the intersection point denotes the point where the total cost curve is at its minimum.
• At this intersection point the ordering cost = holding costs.
• The optimal order quantity is the quantity for which the ordering cost = holding cost, and the total cost is minimum.
• Let Q = Number of units per order.
• Q* = Optimum number of units per order (EOQ).
• D = Annual demand in units for the inventory item.
• S = Setup or ordering cost for each order.
• H = Holding or carrying cost per unit per year.
1. Annual set up cost = (Number of order placed per year) x (Setup or order cost per order)
=
𝐴𝑛𝑛𝑢𝑎𝑙 𝐷𝑒𝑚𝑎𝑛𝑑
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑜𝑟𝑑𝑒𝑟
× 𝑆𝑒𝑡𝑢𝑝 𝑜𝑟 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟
=
𝐷
𝑄
(𝑆)
2. Annual holding cost = (Average inventory level) x ( Holding cost per unit per year)
=
𝑂𝑟𝑑𝑒𝑟 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦
2
(Holding cost per unit per year)
=
𝑄
2
(H) =
𝑄
2
𝐻
By: Er. VAIBHAV

19. 3. Optimal order quantity is found when annual setup cost equals holding cost, namely..
𝑫
𝑸
S =
𝑸
𝟐
𝑯
4. To solve Q*,
=> 2DS = Q2H
=> Q2 =
2𝐷𝑆
𝐻
=> Q* =
2𝐷𝑆
𝐻
Hence this is the expression for Economic order quantity for which the total cost will be minimum.
Expected no. of Orders = N =
𝐷𝑒𝑚𝑎𝑛𝑑
𝑂𝑟𝑑𝑒𝑟 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦
=
𝐷
𝑄∗
Expected time between orders = T =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑑𝑎𝑦𝑠
𝑁
Total Annual Cost =
𝑫
𝑸
S +
𝑸
𝟐
𝑯
By: Er. VAIBHAV

20. REORDER POINTS
• After knowing how much to order, it is necessary to know when to order.
• As the lead time is always there between placing order and receiving the order.
• Simple inventory model assumes lead time to be zero, but practical situation need to include the lead time.
• The reordering lead time may be short to few minutes to as long as days.
• So it is necessary to know when-to-order, or the REORDER POINT of the inventory.
• The quantity of the inventory just at which a new order needs to be placed, is called as Re-Order Point.
• The reorder point is given as:
• ROP = (demand per day) x ( lead time for a new order in days)
• ROP = d x L
• It assumes that the demand during the lead time is constant and also the lead time is constant.
• In case of not constant lead time we keep extra inventory called as SAFETY STOCK.
• The demand per day is ‘d’ =
𝐴𝑛𝑛𝑢𝑎𝑙 𝐷𝑒𝑚𝑎𝑛𝑑
𝑁𝑜.𝑜𝑓 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑎 𝑦𝑒𝑎𝑟By: Er. VAIBHAV

21. AVERAGE INVENTORY ON
HAND (Q/2)
QUANTITY ORDERED = Q
MAX. INVEMTORY LEVEL
MINIMUM INVENTORY
0
TIME
INVENTORYLEVEL
SAWTOOTH SHAPE OF INVENTORY USAGE
LEAD TIME = L
ROP (units)
Slope = units/day
By: Er. VAIBHAV

22. PRODUCTION ORDER QUANTITY MODEL
• Previously the entire inventory was received at once.
• There are times when firm may receive its inventory over a period of time.
• This model is applicable under two situations:
• When inventory continuously flows or builds up over a period of time after an order has been placed.
• When units are produced and sold simultaneously.
• So we have to take care into account daily production rate and daily demand rate.
• This model is suitable for the production environment.
• It is useful when inventory continuously builds up over time, and traditional economic order quantity
assumptions are valid.
• We can determine the expression for annual inventory holding cost for the production order quantity model.
• Q= No. of units per order.
• H= Holding cost per units per year.
• p = Daily production rate
• d = Daily demand rate, or usage rate.
• t = Length of the production run in days.
1. 𝑨𝒏𝒏𝒖𝒂𝒍 𝒊𝒏𝒗𝒆𝒏𝒕𝒐𝒓𝒚 𝒉𝒐𝒍𝒅𝒊𝒏𝒈 𝒄𝒐𝒔𝒕 = (Average inventory level) x ( Holding cost per unit per year)
2. (Average inventory level) = (Maximum inventory level)/2
3. (Maximum inventory level) = (Total production during the production run)-(total used during the
production run)
= pt-dt By: Er. VAIBHAV

23. • However, Q = total produced = pt, and thus t=Q/p. Therefore;
• Maximum inventory level :
= p
𝑄
𝑝
-d
𝑄
𝑝
= Q -
𝑑
𝑝
Q
= Q 1 −
𝑑
𝑝
• Annual inventory holding cost =
=
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑙𝑒𝑣𝑒𝑙
2
(H)
=
𝑄
2
1 −
𝑑
𝑝
H
By: Er. VAIBHAV

24. MAX. INVENTORY
TIME
INVENTORYLEVEL
CHANGE IN INVENTORY LEVELS OVER
TIME FOR THE PRODUCTION MODEL
t
Demand part of cycle with
no production (only usage
takes place)
Part of inventory cycle
during which production
(and usage) takes place
By: Er. VAIBHAV

25. • We solve the optimal number of pieces per order by equating setup costs and holding cost:
Setup Cost = (D/Q)S
Holding Cost =
1
2
HQ 1 −
𝑑
𝑝
• Set ordering cost equal to holding cost to obtain Qp* :
𝐷
𝑄
S =
1
2
HQ[1-(d/p)]
Q2 =
2𝐷𝑆
𝐻[1−
𝑑
𝑝
]
 Qp* =
2𝐷𝑆
𝐻[1−
𝑑
𝑝
]
 We use above equation, Qp*, to solve for the optimum order or production quantity when inventory is consumed as it is
produced.
By: Er. VAIBHAV

26. • We can also calculate Qp* when annual data are available. When annual data are used, we can express Qp* as:
Qp* =
2𝐷𝑆
𝐻 1−
𝐴𝑛𝑛𝑢𝑎𝑙 𝐷𝑒𝑚𝑎𝑛𝑑 𝑅𝑎𝑡𝑒
𝐴𝑛𝑛𝑢𝑎𝑙 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒
By: Er. VAIBHAV

27. QUANTITY DISCOUNT MODEL
• To increase sales, many companies offer quantity discounts to their customers.
• A quantity discount is simply a reduced price (P) for an item when it is purchased in larger quantities.
• Discount schedules with several discounts for large orders are common.
• Placing a very high quantity order, in order to get higher discounts, it may not minimize total inventory costs.
• As Discount quantity goes up, production costs goes down.
• But holding costs goes up.
• So in case of quantity discounts, we need a trade-off between reduced product cost and. increased holding cost.
• Total cost = Setup Cost + Holding Cost + Product Cost
or
TC =
𝑫
𝑸
S +
𝑄
2
H+PD
• Where Q = Quantity Ordered
D = Annual Demand in Units
S = Ordering or setup cost per order or per setup
P = Price per unit
H = Holding Costs per unit per year
By: Er. VAIBHAV

28. Discount no. Discount Quantity Discount % Discount Price (P)
1 0 to 999 No discount $ 5.00
2 1000 to 1999 4 $ 4.80
3 2000 to over 5 $ 4.75
A QUANTITY DISCOUNT SCHEDULE
By: Er. VAIBHAV

29. By: Er. VAIBHAV

30. Step 1: Calculate a value for optimal order size Q*, using the following equation:
Q* =
2𝐷𝑆
𝐼𝑃
• H is replaced by IP.
• The price of the item is a factor in annual holding cost.
• It is common to express the holding cost as a percent (I) of unit price (P) instead of as a constant cost per unit per year, H.
Step 2:
• We need to adjust the order quantity to the quantity which qualify for the discount, for e.g. adjust the quantity to 1000 units to get a 4%
discount below which there was no discount.
• The total cost curve is broken into 3 parts.
• There is a total cost curve for the first (0<Q<999), the second (1000<Q<1999) and the third (2000 and above).
Step 3:
• Using the total cost equation, compute a total cost for every Q* determined in step 1 and 2.
• If you had to adjust Q* upward because it was below the allowable quantity range, be sure to use the adjusted value for Q*.
Step 4:
• Select the Q* that has the lowest total cost, as calculated in step 3. It will be the quantity that will minimize the total inventory cost.By: Er. VAIBHAV

31. By: Er. VAIBHAV

32. By: Er. VAIBHAV

33. By: Er. VAIBHAV