- 1. Outline © 2008 Prentice Hall, Inc. 12 – 1 Inventory Management Functions of Inventory Types of Inventory Inventory Management ABC Analysis Record Accuracy Cycle Counting Control of Service Inventories
- 2. Outline – Continued © 2008 Prentice Hall, Inc. 12 – 2 Inventory Models Independent vs. Dependent Demand Holding, Ordering, and Setup Costs
- 3. IN ORDER TO MEET THE DEMAND FOR RAW MATERIALS, COMPONENTS OR OTHER INPUTS FROM INTERNAL PROCESSES OF A FIRM AND DEMAND FOR FINISHED PRODUCTS FROM CUSTOMERS, THERE IS NEED TO MAINTAIN STOCK AT EACH STAGE OF PRODUCTION AND DELIVERY. THIS STOCK IS CALLED INVENTORY – LABELLED AS RAW MATERIALS INVENTORY, WORK IN PROGRESS INVENTORY AND FINISHED GOODS INVENTORY. Inventory
- 4. Functions of Inventory © 2008 Prentice Hall, Inc. 12 – 4 1. To decouple or separate various parts of the production process 2. To decouple (isolate) the firm from fluctuations in demand and provide a stock of goods that will provide a selection for customers 3. To take advantage of quantity discounts 4. To hedge against inflation
- 5. Types of Inventory © 2008 Prentice Hall, Inc. 12 – 5 Raw material Purchased but not processed Work-in-process Undergone some change but not completed A function of cycle time for a product Maintenance/repair/operating (MRO) Necessary to keep machinery and processes productive Finished goods Completed product awaiting shipment
- 6. Objectives of Inventory Management 1. Ensure a continuous Supply of Raw Material and Supplies to facilitate uninterrupted production. 2. Maintain Sufficient –finished goods for smooth sales operation and efficient customer service. 3. Inventories permit the procurement of raw materials in economic lot sizes as well as processing these raw materials into finished goods is the most economical quantity known as “Economic Lot Size” 4. Reduce dependencies of one another and enable the organisations to schedule its operations independently of another. 5. Inventory Management helps to reduce Material Handling Costs. 6. It helps to utilize people and equipment reasonably 7. It facilitates product display and service in customers.
- 7. Factors Influencing Inventory Management and Control 1. Type of Product 2. Type of Manufacture 3. Volume of Production Process Of Inventory Management and Control Step 1: Determination of Optimum Inventory Levels and procedure of their review and adjustment. Step 2 : Determination of the Degree of control that is required for the best results. Step 3 : Planning and Design of the inventory control system. Step 4 : Planning of the inventory control Organisation
- 8. The Material Flow Cycle Figure 12.1 Output Input Wait for Wait to Move Wait in queue Setup Run inspection be moved time for operator time time Cycle time 95% 5% © 2008 Prentice Hall, Inc. 12 – 8
- 9. Inventory Management © 2008 Prentice Hall, Inc. 12 – 9 How inventory items can be classified How accurate inventory records can be maintained
- 10. Inventory Control Techniques 1. ABC Analysis ( Always Better Control) also called as SIM ( selective Inventory Control Method). 1. HML ( High , Medium and Low) 2. VED ( Vital, Essential and Desirable) 3. SDE ( Scarce, Difficult and easy to obtain) 4. FSN ( Fast moving, Slow moving and non – moving ) 5. EOQ ( Economic Order Quantity ) 6. Maximum and minimum system 7. Two bin System
- 11. ABC Analysis © 2008 Prentice Hall, Inc. 12 – 11 Divides inventory into three classes based on annual dollar volume Class A - high annual dollar volume Class B - medium annual dollar volume Class C - low annual dollar volume Used to establish policies that focus on the few critical parts and not the many trivial ones
- 12. ABC ANALYSIS ABC ANALYSIS IS BASED ON THE PRINCIPLE THAT FOR AN ITEM, THE LEVEL OF CONTROL SHOULD BE ACCORDING TO THE POTENTIAL OF SAVINGS FOR THAT ITEM WHICH WOULD IN TURN DEPEND UPON THE VALUE OF ANNUAL CONSUMPTION OF THAT ITEM
- 13. CATEGORIES OF ITEMS IN ABC ANALYSIS In the list of items based on their annual consumption value Category A: Top 10% Category B: 10 to 30 % Category C: 30-100% STEPS INVOLVED IN ABC ANALYSIS 1. Prepare a list of all SKUs and assign a code number to each 2. Determine annual consumption value for each item 3. List items in descending order of annual consumption value 4. Classify items in A,B and C categories as follows Category A: Few high annual consumption value items Category B: Some medium annual consumption value items Category C: Large number of low annual consumption value items
- 14. GRAPHICAL REPRESENTATION - ABC CATEGORIES . Percent from top in the list of items arranged in descending order of annual consumption value 100 100 Aggregate annual consumption value expressed as a percentage 90 30 10 50 70 50 C B A
- 15. INVENTORY CONTROL BASED ON ABC ANALYSIS Level of control Safety stock Frequency of ordering Frequency of deliveries Follow up and expediting Value analysis Number of sources Forecasting Periodicity of review
- 16. ABC Analysis Item Stock Percent of Number of Items Annual Volume Unit Annual Dollar Percent of Annual Dollar Number Stocked (units) x Cost = Volume Volume Class #10286 20% 1,000 $ 90.00 $ 90,000 38.8% A 72% #11526 500 154.00 77,000 33.2% A #12760 1,550 17.00 26,350 11.3% B #10867 30% 350 42.86 15,001 6.4% 23% B #10500 1,000 12.50 12,500 5.4% B © 2008 Prentice Hall, Inc. 12 – 16
- 17. ABC Analysis Item Stock Percent of Number of Items Annual Volume Unit Annual Dollar Percent of Annual Dollar Number Stocked (units) x Cost = Volume Volume Class #12572 600 $ 14.17 $ 8,502 3.7% C #14075 2,000 .60 1,200 .5% C #01036 50% 100 8.50 850 .4% 5% C #01307 1,200 .42 504 .2% C #10572 250 .60 150 .1% C 8,550 $232,057 100.0% © 2008 Prentice Hall, Inc. 12 – 17
- 18. ABC Analysis A Items B Items C Items Percent of annual dollar usage 80 – © 2008 Prentice Hall, Inc. 12 – 18 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percent of inventory items Figure 12.2
- 19. ABC Analysis © 2008 Prentice Hall, Inc. 12 – 19 Other criteria than annual dollar volume may be used Anticipated engineering changes Delivery problems Quality problems High unit cost
- 20. ABC Analysis © 2008 Prentice Hall, Inc. 12 – 20 Policies employed may include More emphasis on supplier development for A items Tighter physical inventory control for A items More care in forecasting A items
- 21. Record Accuracy © 2008 Prentice Hall, Inc. 12 – 21 Accurate records are a critical ingredient in production and inventory systems Allows organization to focus on what is needed Necessary to make precise decisions about ordering, scheduling, and shipping Incoming and outgoing record keeping must be accurate Stockrooms should be secure
- 22. Cycle Counting Items are counted and records updated on a periodic basis Often used with ABC analysis to determine cycle Has several advantages Eliminates shutdowns and interruptions Eliminates annual inventory adjustment Trained personnel audit inventory accuracy Allows causes of errors to be identified and corrected Maintains accurate inventory records © 2008 Prentice Hall, Inc. 12 – 22
- 23. Cycle Counting Example © 2008 Prentice Hall, Inc. 12 – 23 5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) Item Number of Items Class Quantity Cycle Counting Policy Counted per Day A 500 Each month 500/20 = 25/day B 1,750 Each quarter 1,750/60 = 29/day C 2,750 Every 6 months 2,750/120 = 23/day 77/day
- 24. Control of Service Inventories Can be a critical component of profitability Losses may come from shrinkage or pilferage Applicable techniques include 1. Good personnel selection, training, and discipline 2. Tight control on incoming shipments 3. Effective control on all goods leaving facility © 2008 Prentice Hall, Inc. 12 – 24
- 25. Independent Versus Dependent Demand © 2008 Prentice Hall, Inc. 12 – 25 Independent demand - the demand for item is independent of the demand for any other item in inventory Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory
- 26. Holding, Ordering, and Setup Costs © 2008 Prentice Hall, Inc. 12 – 26 Holding costs - the costs of holding or “carrying” inventory over time Ordering costs - the costs of placing an order and receiving goods Setup costs - cost to prepare a machine or process for manufacturing an order
- 27. Holding Costs Table 12.1 © 2008 Prentice Hall, Inc. 12 – 27 Category Cost (and range) as a Percent of Inventory Value depreciation, operating costs, taxes, depreciation, power, operating cost) and insurance on inventory) Housing costs (building rent or insurance) 6% (3 - 10%) Material handling costs (equipment lease or 3% (1 - 3.5%) Labor cost 3% (3 - 5%) Investment costs (borrowing costs, taxes, 11% (6 - 24%) Pilferage, space, and obsolescence 3% (2 - 5%) Overall carrying cost 26%
- 28. Inventory Models for Independent Demand © 2008 Prentice Hall, Inc. 12 – 28 Need to determine when and how much to order Basic economic order quantity Production order quantity Quantity discount model
- 29. Basic EOQ Model © 2008 Prentice Hall, Inc. 12 – 29 Important assumptions 1. Demand is known, constant, and independent 2. Lead time is known and constant 3. Receipt of inventory is instantaneous and complete 4. Quantity discounts are not possible 5. Only variable costs are setup and holding 6. Stockouts can be completely avoided
- 30. TERMS USED IN INVENTORY MODELS Annual demand ... … … … … A Daily demand ... … … … … d Quantity to be ordered … … … … Q Economic order quantity … … … … Q* Buying cost per order ... … … … … B Cost of one unit of purchased item … … … C Inventory carrying cost per year … … … I Inventory carrying cost per unit per year … … CI Lead time … … … … … LT Quantity delivered per day for multiple delivery order p Back order cost per unit per year (in case of a stockout) … b Reorder level ... … … … … R Inventory cycle time … … … … T Inventory cycle time associated with EOQ … … T* No. of orders per year … … … … N No. of orders per year associated with EOQ … N* Annual variable cost … … … … AVC Annual total cost ... … … … … ATC
- 31. Q SYSTEM - CLASSICAL MODEL . Q* Q*/2 R P LT P LT P LT QUANTITY IN STOCK (Q) T* T* T* TIME (T) Assumptions i) Demand is uniform during an inventory cycle and also cycle to cycle ii) Lead time is uniform for each cycle
- 32. Q SYSTEM, CLASSICAL MODEL EOQ (Q*)=√(2A.B)/(C.I); AVC (for order quantity Q) = (A.B)/Q+1/2(Q.C.I) [(Buying cost+Carrying cost)] AVC (for order quantity Q*) = (A.B)/Q*+1/2(Q*.C.I)=√(2A.B)(C.I) ATC (for order quantity Q) = AVC+(A.C)=(A.B)/Q+1/2(Q.C.I)+(A.C)[(Buying cost+Carrying cost ` `+Product cost)] ATC (for order quantity Q*) = (A.B)/Q*+1/2(Q*.C.I)+(A.C)=AVC+(A.C)=√(2A.B)(C.I) + (A.C) Inventory cycle time, T*= Q*/A year; No. of orders per year, N*= A/Q*; Reorder Level R= d.LT; Average Inventory = Q*/2; Main bin quantity = Q*- R; Auxiliary bin quantity = R
- 33. EXAMPLE A fan manufacturer produces 40,000 fans per year. Each fan has one aluminum body which costs Rs 100 each. The firm has estimated that its annual inventory carrying costs are 20 % of the value of average inventory carried. The cost of buying has been determined as Rs 1000 per order. For the 40,000 aluminum bodies that the manufacturer buys per year, find the economic order quantity (Q*), annual variable cost (AVC), annual total cost (ATC), number of orders per year (N*), inventory cycle time (T*), reorder level (R), average inventory, quantities in the main bin and auxiliary bin for two bin inventory control system. You may assume that the firm has 300 working days in a year and lead time is 6 working days. ANSWER Given A = 40000; B = 1000; C = 100; I = 20% = 0.2; d = 40000/300 = 400/3 =133.33 EOQ (Q*)=√(2A.B)/(C.I) = √ 2x40000x1000)/(100x0.2) = 2,000 AVC=√(2A.B)(C.I) = √ 2x40000x1000x100x0.2 = 40,000 ATC=AVC+(A.C) = 40,000 + 40000x100 = 40,40,000 N*=A/Q* = 40000/2000 = 20 T*=Q*/A = 2000/40000 = 0.05 year = 0.05x300 = 15 working days R=d.LT = (400/3).6 = 800 Average Inventory = Q*/2 = 2000/2 =1000 Main bin quantity=Q*- R = 2000 – 800 = 1200 Auxiliary bin quantity=R = 800 Q SYSTEM, CLASSICAL MODEL
- 34. Q SYSTEM - QUANTITY DISCOUNT MODEL ATC =Ordering cost + Carrying cost + Product cost =(A.B)/Q +1/2(Q.C.I) + A.C [Accept discount option if ATCdiscount < ATCEOQ] . EXAMPLE For the fan manufacturer example discussed earlier, the vendor has offered a price discount of Rs 2 per fan body, provided the order quantity is 20000 units. Should the fan manufacturer accept the offer? ANSWER For order quantity Q, ATCQ =(A.B)/Q+1/2(Q.C.I)+(A.C) ATCEOQ = 2000 =(40,000x1000)/2,000+1/2(2,000x100x0.2)+(40,000x100) = 40,40,000 For order quantity, 20,000 and cost per unit Rs 98, ATCQ=20000 =(40,000x1000)/20,000+1/2(20,000x98x0.2)+(40,000x98) = 41,18,000 ATCQ=20000 > ATCEOQ Therefore, manufacturer should reject vendor’s offer.
- 35. Q SYSTEM - MULTIPLE DELIVERY MODEL . EOQ (Q*)=√[(2A.B)/(C.I)].[p/(p-d)] p is quantity delivered per day, p>d AVC=√[(2A.B)(C.I)].[(p-d)/(p) EXAMPLE For the fan manufacturer example discussed earlier, if the vendor agrees to deliver 150 fan bodies per day at no extra cost, what should be the order quantity? Also determine the annual variable cost? ANSWER Given p = 150 per day d = 133.33 per day (as calculated earlier) EOQ (Q*)= √[(2A.B)/(C.I)].[p/(p-d)] Or EOQ (Q*)=√[2x40000x1000)/(100x0.2)].[150/(150-133.33)] = √(4000000).(8.9982) = 6000 AVC=√[(2A.B)(C.I)].[(p-d)/(p)] AVC= √[2x40000x1000)(100x0.2)].[(150-133.33)/150] = √(1600000000).(8.9982) = 13335 Note that for EOQ classical model, AVC = 40,000 So multiple delivery model brings down annual variable cost to almost 1/3 of annual variable cost for classical model
- 36. Q SYSTEM - PLANNED STOCKOUT MODEL . EOQ (Q*)=√[(2A.B)/(C.I)].[(C.I+b)/(b)]; AVC=√[(2A.B)(C.I)].[(b)/(C.I+b) Where b is stock out cost per unit per year EXAMPLE For the fan manufacturer example discussed earlier, the firm is prepared to work with shortages, since the item can be procured from an alternate source at slightly higher price off the shelf. The cost of shortage has been determined as half the inventory carrying cost per unit per year. Find EOQ and the annual variable cost (AVC) ANSWER Inventory carrying cost per unit per year (C.I) = 100x0.2 = 20 Given b = ½ C.I = 10 EOQ (Q*)= √[(2A.B)/(C.I)].[(C.I+b)/(b)] Or EOQ (Q*)=√[2x40000x1000)/(100x0.2)].[(20+10/10)] = √(4000000).(3) = 3464 AVC=√[(2A.B)(C.I)].[b/(C.I+b)] AVC= √[2x40000x1000)(100x0.2)].[(10/(20+10)] = √(1600000000).(0.33) = 23094 Note that for EOQ classical model, AVC = 40,000 So planned stock out model brings down annual variable cost to little over half the annual variable cost for classical model
- 37. Q SYSTEM - ECONOMIC BATCH QUANTITY (EBQ) EBQ = √(2A.B')/(C.I) A is annual demand or annual production; B' is batch set up cost; C is cost of production per unit; I is the inventory carrying cost per year AVC (for order quantity Q) = (A.B')/Q+1/2(Q.C.I) [(Set up cost+Carrying cost)] EXAMPLE An automobile manufacturer has found that the annual demand for a particular model of car is 1,00,000 units. The cost of production per car is Rs 1.5 lakhs. Set up time is 6 days. The assembly line can produce 1000 cars per day. Each car contributes gross profit of Rs 50,000. Set up cost is determined as the loss of profit during the set up time when there is no production. Inventory carrying cost is 20 percent per annum. Determine the economic batch quantity (EBQ). Also determine EBQ if the set up time is reduced to i) 3 days ii)1 day iii) ½ day. A=1,00,000 B'=Rs 5,00,00,000/day C= 1,50,000 I = 0.2 Set up time (days) 6 3 1 0.5 EBQ =√(2A.B')/(C.I) (2A.B')/(C.I) 2000000000 1000000000 333333333 166666667 EBQ =√(2A.B')/(C.I) 44721 31623 18257 12910 AVC = (A.B')/Q+1/2(Q.C.I) Rs Crores 134.16 94.87 54.77 38.73 Note that for 6 days’ set up time AVC is Rs 134 Cr, for ½ day set up time, AVC is Rs 39 Cr
- 38. P SYSTEM . Tp* = √(2B)/(A.C.I) where Tp is optimal review period EXAMPLE An engineering and fabrication company has collected following data with respect to some C category items that it determined that it uses regularly. Assuming that buying cost per order is Rs 400 and inventory carrying cost is 20 percent per annum, determine optimal review period for all the items. Also suggest what should be the frequency of review for each item. Assume 365 days in a year. GIVEN A as per table, B = Rs200 per order C as per table, I = 20% Tp2 = (2B)/(A.C.I) Tp = √(2B)/(A.C.I) Year Days Review Item Unit B A C I= 0.2 Tp 2 Tp Yearx365 Period Lubricating oil litre 200 1600 175 0.2 0.0071 0.0845 31 1 month Grease kg 200 600 300 0.2 0.0111 0.1054 38 1 month Welding electrodes Nos 200 10000 10 0.2 0.02 0.1414 52 1.5 months Grinding wheels Nos 200 300 214 0.2 0.0312 0.1765 64 2 months Polishing wheels Nos 200 400 108 0.2 0.0463 0.2152 79 2.5 months A4 paper 500 sheets/pkt Pkt 200 300 245 0.2 0.0272 0.1650 60 1.5 months ANSWER
- 39. Inventory Usage Over Time Figure 12.3 Order quantity = Q (maximum inventory level) Usage rate Average inventory on hand Q 2 Inventory level © 2008 Prentice Hall, Inc. 12 – 39 Time Minimum inventory 0
- 40. Minimizing Costs Objective is to minimize total costs Table 11.5 Annual cost Order quantity Curve for total cost of holding and setup Holding cost curve Setup (or order) cost curve Minimum total cost © 2008 Prentice Hall, Inc. 12 – 40 Optimal order quantity (Q*)
- 41. ode o del l Q* = Optimal number of pieces 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 Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order Setup or order cost per order = The EOQ M Annual setup cost = D Q S Q = Number of pieces per order = (S) D Q © 2008 Prentice Hall, Inc. 12 – 41
- 42. ode o del l Q* = Optimal number of pieces 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 Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity 2 = (Holding cost per unit per year) = (H) Q 2 The EOQ M Annual setup cost = D Q S Q = Number of pieces per order Annual holding cost = Q H 2 © 2008 Prentice Hall, Inc. 12 – 42
- 43. ode o del l Q* = Optimal number of pieces 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 Optimal order quantity is found when annual setup cost equals annual holding cost The EOQ M Annual setup cost = D Q S Q = Number of pieces per order Annual holding cost = Q H 2 D S = Q H Q 2 Solving for Q* 2DS = Q2H Q2 = 2DS/H Q* = 2DS/H © 2008 Prentice Hall, Inc. 12 – 43
- 44. An EOQ Example Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year Q* = 2DS H Q* = 0.50 2(1,000)(10) = © 2008 Prentice Hall, Inc. 12 – 44 40,000 = 200 units
- 45. An EOQ Example © 2008 Prentice Hall, Inc. 12 – 45 Determine optimal number of needles to order Q* = 200 units D = 1,000 units S = $10 per order H = $.50 per unit per year = Expected orders Demand number of = N = Order quantity D Q* N = 1,000 = 5 orders per year 200
- 46. An EOQ Example Determine optimal number of needles to order Q* = 200 units N = 5 orders per year D = 1,000 units S = $10 per order H = $.50 per unit per year Expected time between = T = orders Number of working days per year N T = 250 = 50 days between orders © 2008 Prentice Hall, Inc. 12 – 46 5
- 47. An EOQ Example © 2008 Prentice Hall, Inc. 12 – 47 Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC = D S + Q H Q 2 TC = 1,000 ($10) + 200 ($.50) 200 2 TC = (5)($10) + (100)($.50) = $50 + $50 = $100
- 48. Robust Model © 2008 Prentice Hall, Inc. 12 – 48 The EOQ model is robust It works even if all parameters and assumptions are not met The total cost curve is relatively flat in the area of the EOQ
- 49. An EOQ Example S = $10 per order H = $.50 per unit per year N = 5 orders per year T = 50 days TC = D S + Q H Q 2 Management underestimated demand by 50% D = 1,000 units 1,500 units Q* = 200 units © 2008 Prentice Hall, Inc. 12 – 49 TC = 1,500 ($10) + 200 ($.50) = $75 + $50 = $125 200 2 Total annual cost increases by only 25%
- 50. An EOQ Example S = $10 per order H = $.50 per unit per year N = 5 orders per year T = 50 days TC = D S + Q H Q 2 Actual EOQ for new demand is 244.9 units D = 1,000 units 1,500 units Q* = 244.9 units © 2008 Prentice Hall, Inc. 12 – 50 TC = 1,500 ($10) + 244.9 ($.50) 244.9 2 TC = $61.24 + $61.24 = $122.48 Only 2% less than the total cost of $125 when the order quantity was 200
- 51. Reorder Points EOQ answers the “how much” question The reorder point (ROP) tells when to order ROP = Lead time for a new order in days Demand per day = d x L d = D Number of working days in a year © 2008 Prentice Hall, Inc. 12 – 51
- 52. Reorder Point Curve Q* ROP (units) Inventory level (units) Time (days) Figure 12.5 Lead time = L Slope = units/day = d © 2008 Prentice Hall, Inc. 12 – 52
- 53. Reorder Point Example © 2008 Prentice Hall, Inc. 12 – 53 Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days d = D Number of working days in a year = 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units