Academy session INVENTORY MANAGEMENT

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1 Academy session INVENTORY MANAGEMENT Part 2: Tools for Inventory Management Time: 9:00-12:00, Saturday, 20/08/2011 Location: 1/F, Sherwood Residence, 127 Pasteur, Dist 3, HCMC Speaker: Dr. Eckart Dutz, General Director, Cartridge World

2 Re-order level systems Periodic review systems Demand-driven lean supply systems (e.g., Just-in-time): The frequency & quantity of orders is driven by demand data passed on directly to suppliers Very small or non-existent inbound inventory stores Requires smooth production process, short lead-times and supplier-guaranteed quality M11:U2:2.5-1

3 Re-order level systems - formula: ROL = (R d x L) + S Where... Re-order level (ROL) = Demand in the lead-time + Safety stock (S) Demand in the lead-time = Rate of demand/usage (R d ) (e.g., per week) x Lead-time (L) (e.g., in weeks)

4 Quantity Basic re-order level stock replenishment system (fixed quantity, variable interval) Fixed order quantity Slope = R d Re-order level Re-order Re-order Re-order Safety stock { Lead-time Time

5 Action Point Re-order level Given the following data, what is the re-order level: Safety stock = 100 units Supply lead-time = 6 weeks Average weekly demand = 200 units

6 Quantity A Periodic review stock replenishment system (fixed interval, variable quantity) Periodic reviews B C D Lead-time Lead-time Lead-time Variable order quantities Safety stock { Fixed review interval Z Lead-time Time

7 Periodic review systems - formula to calculate the order size: Order size = (Demand over the review interval + the lead-time) - (Actual stock) - (Pipeline stock) +(Safety stock) In a periodic review system, the basis for determining the order size (which varies each time) is therefore the (fixed) review interval. M11:U2:2.5-6

8 Action Point Re-order quantity Given the following data, what quantity should be re-ordered? Expected demand per week = 100 Lead time = 3 weeks Review interval = 4 weeks Safety stock = 300 Physical stock = 450 On order (pipeline) = 200 ORDER QUANTITY = Periodic reviews Lead-time Lead-time Lead-time Safety Stock { Review interval What should the next order quantity be? Lead-time M11:U2:2.5-7

9 Cost of placing the order Price discount costs Stock-out costs Working capital costs of inventory Storage costs Obsolescence costs Production inefficiency costs M11:U2:2.6-1

10 Re-order level system 1. Determine the (fixed) most economic order quantity (EOQ) 2. Determine when to place the fixed order each time (i.e., the re-order level), based on your desired level of safety stock Periodic review system 1. Determine broadly the overall level of the most economic order quantity 2. Based on this,fix the review interval, 3. Then, for each order, determine the specific order quantity, based on your desired levels of maximum & safety stock M11:U2:2.6-2

11 Simplified inventory profile: charting the variations in inventory levels over time Demand (D) over period Order quantit y Q Slope = demand rate (steady & predictable) Average inventory = Q/2 Time interval = Q/D Time t Instantaneous deliveries at a rate of D/Q per period M11:U2:2.6-3

12 Inventory level Ordering costs Two alternative inventory plans with different order quantities (Q) Plan A Q = 400 Plan B Q = 100 Demand (D) = 1000 items per year Average inventory for Plan A = 200 Average inventory for Plan B = yr 0.4 yr Time

13 Working capital costs: The cost of borrowing the money needed to pay for one unit of stock. Storage costs: Rent, heat, light per m 2 occupied by one unit of stock. Obsolescence risk costs: Cost of the stock disposed of in a period, apportioned over each unit stored in the period. Holding costs (H) = (P) x (i) x (Q/2) In which: P = Unit purchase costs (i.e., price plus transport and other delivery costs) i = Inventory carrying cost (expressed as a percentage) of P ) Q/2 = Average inventory (the order quantity divided by 2) M11:U2:2.6-5

14 Ordering costs Administrative costs of placing the order Communications costs (with suppliers, transporters, etc.) Ordering costs (O) = (C 0 ) x (D/Q) In which: C o = Cost per order D/Q = The number of orders in the period (i.e., the demand divided by the order quantity) M11:U2:2.6-6

15 So... P Total cost = i Q + C od 2 Q Costs of adopting plans with different order quantities Order quantity Holding costs (Q) Pi Q/2 + Ordering costs C o D/Q = Total costs * Demand (D) = 1,000 units Unit purchase cost (P) = $5 Inventory carrying cost (i) = 20% Cost per order (C o ) = $20 * Minimum total cost M11:U2:2.6-7

16 Cost ($) Graphical representation of the Economic Order Quantity (EOQ) Order quantity Total cost Holding costs Ordering costs C o D EOQ = Pi C o = Cost per order D = Demand over the period P = Purchase cost per unit i = Inventory carrying cost

17 Some assumptions of the EOQ Demand over the period (e.g., a year) is given, and remains unchanged Price, including transport cost, does not change with order size and remains constant throughout the year Order processing costs and stock holding costs are traceable, and remain constant Lead-time is zero, or accurately predictable, and does not vary (there are no delays)

18 Action Point Calculating the EOQ A company purchases material for its production line at $650 per MT. Its yearly requirement is 288 MT. Inventory carrying costs are calculated at 25% of the average value of inventory, and the cost of placing each order has been set at $50. Calculate the EOQ

19 Costs EOQ takes costs as fixed and unchanging It may be a reasonable framework for order cycle planning in some cases But it should not be a prescriptive tool in complex situations Be proactive, not reactive: seek how to reduce inventory and other costs, e.g., of placing an order... Reducing ordering costs also lowers the EOQ Original total costs Revised total costs Holding costs Revised EOQ Original EOQ Revised ordering costs Original ordering costs Order quantity M11:U2:2.6-

20 Inventory level The Re-order level (ROL) and Re-order point (ROP) depend on the order lead-time and the rate of demand Re-order level R d = 100/wk Re-order 100 point Order lead-time Time But lead-times & rates of demand are usually not fixed And so, generally, safety stock is needed.

21 Safety stock! The main consideration in setting safety stock is: which is the probability that the stock will not have entirely run out before the next replenishment order arrives? The key information needed in calculating how much safety stock to allow for is therefore: what is the probability distribution for usage over the lead-time? Safety stock is therefore usually set to give a predetermined likelihood that stockouts will not occur

22 Inventory level Safety stock helps to avoid stock-outs when demand and/or order lead-time are uncertain How to do this under a re-order level system... Q Re-order level Safety stock d 1 d2 t 1 t 2 t = lead-time d = demand rate over the lead-time Time

23 Example of probability distribution of lead-time usage: gauges buying valves for water Lead-time: Usage rate: Delivery lead-time Percentage of orders 1 week 10% 2 weeks 20% 3 weeks 40% 4 weeks 20% 5 weeks 10% No. of valves used per week Probability % % % % % % 40% 30% 20% 10% 0% weeks 25% 20% 15% 10% 5% 0% units

24 Combining lead-time and usage probabilities Lead-time probabilities 1 week 2 weeks 3 weeks 4 weeks 5 weeks Usage rate probabilities (0.01) 200 (0.02) 300 (0.04) 400 (0.02) 500 (0.01) (0.015) 220 (0.03) 330 (0.06) 440 (0.03) 550 (0.015) (0.025) 240 (0.05) 360 (0.1) 480 (0.05) 600 (0.025) (0.025) 260 (0.05) 390 (0.1) 520 (0.05) 650 (0.025) (0.015) 280 (0.03) 420 (0.06) 560 (0.03) 700 (0.015) (0.01) 300 (0.02) 450 (0.04) 600 (0.02) 750 (0.01) Lead-time usage Probability

25 Composite probabilities for the various ranges of lead-time usage rates 35% 30% 25% 20% 15% 10% 5% 0% units Lead-time usage Probability

26 Risk of stockout for different re-order levels Maximum level of stockout desired 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Minimum re-order level needed Lead-time usage Probability of usage being greater than this Cumulative... Lead-time usage Probability

27 Safety stock, re-order level and stockout risk The weighted average lead-time usage = 375 units (3 weeks X 125 units per week) Re-order level 600 units 225 units Safety stock (average) Wtd. average usage rate = 125/wk Maximum usage rate = 150/wk Average safety stock therefore = 225 units (600 units ROL units average lead-time usage) Wtd. average lead-time (3 wks) Maximum leadtime (5 wks) Stockout risk = 9.5%

28 Action Point Calculating the re-order level Probability distribution of the lead-time Delivery lead-time Percentage of orders 1 week 30% 2 weeks 40% 3 weeks 15% 4 weeks 10% 1. Combined lead-time and usage probabilities Usage Lead-time probabilities rate probabilities 1 week 2 weeks 3 weeks 4 weeks 5 weeks weeks 5% Probability distribution of the usage rate 2. Composite probabilities for the various ranges of lead-time usage rates No. of valves used per week Probability Lead-time usage Probability % % % % 140 5% 3. Cumulative probabilities of lead-time usage rates Lead-time usage Probability of usage being greater than this

Calculating the re-order level (continued) Action Point 2.

average usage rate = /wk Maximum usage rate = /wk Wtd.

29 Calculating the re-order level (continued) Action Point Re-order level units units Safety stock (average) Wtd. average usage rate = /wk Maximum usage rate = /wk Wtd. average lead-time ( wks) Maximum leadtime ( wks) Stockout risk = 5%

30 Inventory level How to do this under a periodic review system Order size = (Demand over the review interval + the lead-time) - (Actual stock) - (Pipeline stock) + (Safety stock) In practice: calculate the replenishment order size to bring inventory up to a maximum pre-determined level... I max. Q1 Q2 Q3 T0 T 1 T2 T 3 t 0 t 1 t 2 t 3 Time Review interval Review interval Review interval

31 Determining the review interval... using the EOQ (an example): EOQ = 2C o D Pi = 2 x $25 $2.5 x x 0.2 2,000 = 447 The optimum review interval between orders t r is therefore: t r = EOQ D = 447 = years 2,000 = 2.7 months (i.e., every two months and three weeks) It may seem paradoxical to calculate the review interval using a fixed demand value, when demand is uncertain. Uncertainties in demand and lead-time will later be accounted for by setting I max to allow for the desired probability of stockout.

32 Inventory level Determining maximum & safety stock under the periodic review approach Imax. Q1 Average usage rate Safety stock Maximum usage rate T0 T 1 T2 Review interval Average lead-time Maximum lead-time To illustrate this, let us return to our earlier example Stockout risk Time

33 Combining review interval + lead-time and usage rate probabilities Usage Review interval (7 weeks) + Lead-time probabilities rate probabilities 8 weeks 9 weeks 10 weeks 11 weeks 12 weeks (0.01) 900 (0.02) 1,000 (0.04) 1,100 (0.02) 1,200 (0.01) (0.015) 990 (0.03) 1,100 (0.06) 1,210 (0.03) 1,320 (0.015) (0.025) 1,080 (0.05) 1,200 (0.1) 1,320 (0.05) 1,440 (0.025) ,040 (0.025) 1,170 (0.05) 1,300 (0.1) 1,430 (0.05) 1,560 (0.025) ,120 (0.015) 1,260 (0.03) 1,400 (0.06) 1,540 (0.03) 1,680 (0.015) ,200 (0.01) 1,350 (0.02) 1,500 (0.04) 1,650 (0.02) 1,800 (0.01) Usage ,085 1,086-1,228 1,229-1,371 1,372-1,514 1,515-1,657 1,658-1,800 Probability

34 Composite probabilities for the various ranges of usage rates over review period + lead-time 30% 25% 20% 15% 10% 5% 0% ,085 1,086-1,228 1,229-1,371 1,372-1,514 1,515-1,657 1,658-1,800 Usage ,085 1,086-1,228 1,229-1,371 1,372-1,514 1,515-1,657 1,658-1,800 Probability

35 Risk of stockout for different I max levels Maximum level of stockout desired 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Minimum I max level needed ,085 1,228 1,371 1,514 1,657 1,800 Usage ,085 1,228 1,371 1,514 1,657 1,800 Probability of usage being greater than this Cumulative... Usage ,085 1,086-1,228 1,229-1,371 1,372-1,514 1,515-1,657 1,658-1,800 Probability

36 I max & safety stock I max.: 1,514 units The weighted average review period + lead-time usage = 1,250 units (10 weeks X 125 units per week) Q1 Wtd. average usage rate = 125/wk 264 units Safety stock (average) Maximum usage rate = 150/wk T0 T 1 T2 Average safety stock therefore = 264 units (1,514 units I max - 1,250 units average usage) Review interval (7 weeks) Wtd. average lead-time:3 wks Maximum lead-time: 5 wks Stockout risk =5%

37 Action Point Calculating I max Probability distribution of the lead-time Delivery lead-time Percentage of orders 1 week 30% 2 weeks 40% 3 weeks 15% 4 weeks 10% 5 weeks 5% Probability distribution of the usage rate No. of valves used per week Probability % % % % 140 5% 1. Combined review interval + lead-time and usage probabilities Usage Review interval (7 weeks) + Lead-time probabilities rate probabilities week 9 weeks 10 weeks 11 weeks 12 weeks Composite probabilities for the various ranges of usage rates over the review interval + lead-time Usage Probability 3. Cumulative probabilities of usage rates over the review interval + lead time Usage Probability of usage being greater than this

38 Action Point Calculating I max & safety stock (continued) I max.: units Q1 Wtd. average usage rate = units Safety stock (average) Maximum usage rate = T0 T 1 T2 Review interval (7 weeks) Wtd. average lead-time: Maximum lead-time: Stockout risk =5%

from bin 2 No need to record issues for low-value items Re-estimate usage each time by noting how long it

39 Two-bin and three-bin ordering systems Items being used Re-order level inventory + Safety stock Bin 1 Bin 2 Two-bin system Process: Start by using only the items from bin1 Re-order when stock has to be issued from bin 2 No need to record issues for low-value items Re-estimate usage each time by noting how long it takes to use bin 1 Items being used Re-order level inventory Safety stock Bin 1 Bin 2 Three-bin system Bin 3

40 THANK YOU & HAVE A GREAT WEEKEND

Slide Chapter 12 Inventory management

Slide Chapter 12 Inventory management Slide 12.1 Chapter 12 Inventory management Slide 12.2 Inventory management Direct Design Operations management Develop Inventory management Deliver The market requires a quantity of products and services