Prepared by Prof. T. K. JANA. Mechanical Engineering Haldia Institute of Technology

1. Inventory Control Prepared by Prof. T. K. JANA. Mechanical Engineering Haldia Institute of Technology

2. Inventory Control Inventory is a detailed list of items (either manufactured or procured) which are required directly orindirectlyto manufacture a complete product. Direct inventory are those which finds its presence in the final product. Example: A crank shaft or a wheel of a car Indirect inventory are those which are not part of the final product, but these are necessary to facilitate the processes by which the product is manufactured. Example:A V-belt or Cutting tool of a lathe.

3. Classification of inventories Raw Inventories: These includes raw materials, purchased parts and semi-finished items obtained from vendors. In process Inventories: Partially completed items at different stages of manufacturing, called work-in-process (WIP). Finished inventories: Finished-products inventories (manufacturing firms) or merchandise (retail stores). Indirect inventories: Spare parts of machineries, tools, oils etc. Pipeline inventory: Goods-in-transit to warehouses or customers.

4. Importance of Inventory control Synchronize with Production process Purchasing materials at an economical rate To store the items at secured place and to avoid pilferage To protect the system against stock-outs To decouple components of the production-distribution system To remain unperturbed against price increases To take advantage of quantity discounts To meet the sudden rise in demands

5. Inventory control refers to procurement of optimum quantity of materials so that thetotal cost will be minimum. • Different cost elements associated with inventory control: • Procurement or Ordering Cost • Holding Cost or Carrying Cost • 3.Shortage Cost or back order cost Inventory Control

6. Average cycle inventory Q 2 On-hand inventory (units) Time Receive order Inventory depletion (demand rate) Variation of Inventory with Time 1 cycle

7. Inventory Model I (Wilson Model) Purchase of items considering instant replenishment and uniform consumption Procurement Cost: Annual procurement cost or ordering cost = Number of orders/Year  Unit Ordering cost Carrying Cost: Annual carrying cost = Average inventory level  Unit carrying cost

8. Inventory Model I (Wilson Model) Total cost = Procurement Cost + carrying cost For minimization of cost This quantity is popularly known as “Economic Order Quantity”.

9. Annual cost EOQ (Q*) Inventory Model I (Wilson Model) Total cost TC min Carrying cost Procurement cost Quantity (Q)

10. Inventory Model I (Wilson Model) Total cost = Note: It is interesting to see that at Q*, Procurement cost = Carrying cost

11. Robustness of the model The total cost is not very sensitive to the moderate changes (deviations) in the amount from EOQ. k is the % change in quantity from Q*

12. Inventory Model I (Wilson Model) • Carrying cost being difficult to calculate, it is sometimes expressed as (I) % of unit material cost (P). • Then • And

13. Inventory model II (Economic Prod. Qty.)

14. Finite replenishment rate (staggered deliveries). • Rate of production is p units/day, • The demand rate is d units/day, • The inventory will be accumulated at a rate of (p-d) units/day. • Production is continued for the period t1 and the inventory is only consumed during the period t2 • Cycle time • Accumulated inventory Inventory model II (Economic Prod. Qty.)

15. Average inventory • Inventory carrying cost • Setting cost • Total cost Inventory model II (Economic Prod. Qty.)

16. For minimization of cost Inventory model II (Economic Prod. Qty.)

17. Maximum accumulated Inventory • Cycle time Inventory model II (Economic Prod. Qty.)

18. Inventory model III (Back order) What is back order? Due to some reasons (intentional or unintentional) the agreed quantity of materials can’t be supplied to the customer. It is therefore practiced that when the next set of materials would be available, immediately the entire backlog or due amount of material would be supplied to the customer. Failure to supply the right amount of material at right time have negative consequences on the organization.

19. Inventory model III (Back order) The credibility of the organization will be on the wane. The organization may loose business opportunity in the future. All these negative impacts can be converted to equivalent financial burden, popularly known as back order cost and it is considered as per unit of short supplied material.

20. Inventory model III (Back order)

21. Inventory model III (Back order) Procurement cost Holding/Carrying cost (per cycle) AnnualHolding/Carrying cost

22. Inventory model III (Back order) Shortage/Backorder cost (per cycle) AnnualShortage/Backorder cost Total cost

23. Inventory model III (Back order) Expanding and rearranging, For minimization of cost, And

24. Inventory model III (Back order) Finally, The total cost =

25. Re-order point, Safety stock, Service level Reorder Point:It is the quantity of an item in hand drops to such an amount that the item is reordered so as to replenish the consumed item to satisfy future requirements. Lead time: It is the time frame between placing an order and getting the item. Safety Stock:Stock which is kept in excess of expected demand to satisfy fluctuations in demand rate and/or lead time. Service Level:Probability that demand will not exceed supply during lead time.

26. Re-order point, Safety stock, Service level The customer service level increases as the risk of stock out decreases. Considering variability of demand and/or lead time, ROP = expected demand during lead time + safety stock is the std. deviation of demand and is the standard normal statistic value for a given service level.

27. Re-order point, Safety stock, Service level Service level = 1 – Risk If only demand is variable, If only lead time is variable, If both demand and lead time are variable Finally, the reorder point becomes

28. Classification of Purchase model A. Fixed order quantity system (Q system) In this system, an order amounting to EOQ is placed when the inventory touches the re-order level. Reorder level = d(LT) + RS + SS B. Fixed order quantity system (P system) In this system, the stock position is reviewed periodically and the order is placed.

29. Advantages of Q system The frequent review of each item helps to maintain adequate stock. If higher quantity results from fixed lot sizes, quantity discount may be availed. Lower safety stocks reduces carrying cost.

30. Advantages of P system Convenient, since items are replenished at fixed regular intervals. Orders for multiple items can be combined together. This ensures reduction in procurement cost and transportation cost. Stock is reviewed at fixed time, thereby streamlining the process.

31. Inventory model with Quantity discount Quantity discounts are reduction in unit price for large orders to attract people to buy in large quantities. Usually, the price per unit decreases as order quantity is increased beyond a threshold value. Under such condition, the buyer must evaluate the potential benefits of reduced purchase price and the fewer orders resulted from large quantities purchase against the burden of increased carrying cost caused by higher average of inventories.

32. Inventory model with Quantity discount The objective of such analysis is to determine the order quantity that will minimize the total cost, where the total cost is the sum of Procurement cost Carrying cost, and Material cost.

33. Ordering cost EOQ Quantity TCA Inventory model with Quantity discount TCB Total Cost Decreasing Price TCC Carrying cost – A,B,C EOQ Quantity

34. Inventory model with Quantity discount Total cost = Procurement cost + Carrying cost + Material cost Where, is the price of the raw material depending on the range of the quantity.

35. Inventory model with Quantity discount Solution Strategy for fixed carrying cost: Compute the common minimum point by using the basic EOQ model. 2. Only one of the unit prices willhave the minimum point in its feasible range since the ranges do not overlap. Identify that range: a) if the feasible minimum point is on the lowest price range, that is the optimal order quantity. b) if the feasible minimum point is any other range, compute the total cost for the minimum point and for the price breaks of all lower unit cost. Compare the total costs and finally the quantity that yields the lowest cost is the optimal order quantity.

36. Inventory model with Quantity discount Solution Strategy for variable carrying cost: Start with the lowest unit price to compute the minimum quantity for each price range until a feasible minimum point is reached (i.e., until a minimum point falls in the quantity range of its price). If the minimum point for the lowest unit price is feasible, it is the optimal order quantity. 3. If the minimum point is not feasible in the lowest price range, compare the total cost at the price break for all lower prices with the total cost of the feasible minimum point. The quantity which yield the lowest total cost is the optimum.

37. Selective Inventory An important aspect of inventory management is that various items held in inventory are not of equal significancein terms of monetary value, profit potential, sales or usage volume, or stock out penalties. It would be unwise to pay equal attention to each of these items. It is therefore prudent to exercise control according to the relative importance of various items in inventory. This approach is called A-B-C classification approach

38. A-B-C Analysis Well known Pareto analysis is carried out to categorize items into value against the volume A Items– 10% of the items accounts for 70% of the inventory value B Items– An additional 20% of the items accounts for 20% of the inventory value C Items– The remaining 70% of the items accounts for merely 10% of the inventory value

39. A-B-C Analysis

40. Selective Inventory The basic idea of ABC analysis can be extended to apply it in other similar situations, thereby giving rise to several other titles. V-E-D Analysis: V – Vital E – Essential D – Desirable FSN Analysis: F = Fast Moving S = Slow Moving N = Non-moving HML Analysis: H = High Cost Items M = Medium Cost Items L = Low Cost Items

41. Thank You