Order Quantities - Examples

Transcription

1 Order Quantities - Examples Outline: I. Basic Inventory Planning Questions II. Inventory Models III. EOQ Model IV. EOQ Model Example V. Production Order Quantity Model VI. POQ Model Example VII. Fixed Period Model. Kuliah ke-7: Rabu/5 Nov 2008

2 I. Basic Inventory Planning Questions How much to order? Purchase Order Description Qty. Microwave 1000

3 How much to order? When to order? Purchase Order Description Qty. Microwave 1000

4 II. Inventory Model We need Inventory Models: 1. Economic order quantity 2. Production order quantity 3. Quantity discount Help answer the inventory planning questions!

5 Why Carrying Cost Increases? More units must be stored if more ordered Purchase Order Description Qty. Microwave 1 Order quantity Purchase Order Description Qty. Microwave 1000 Order quantity

6 Why Order Cost Decreases? Cost is spread over more units Example: You need 1000 microwave ovens 1 Order (Postage $ 0.32) 1000 Orders (Postage $320) Purchase Order Description Qty. Microwave 1000 Order quantity Purchase Purchase Order Order Description Purchase Description Purchase Order Order Qty. Qty. Description Description Microwave Microwave Qty. Qty. 1 1 Microwave Microwave 1 1

7 III. EOQ Model Annual Cost 1. How much to order? Order Quantity

8 EOQ Model Annual Cost 1. How much to order? Carrying Cost Order Quantity

9 EOQ Model Annual Cost 1. How much to order? Carrying Cost Order (Setup) Cost Order Quantity

10 EOQ Model Annual Cost 1. How much to order? Total Cost Curve Carrying Cost Order (Setup) Cost Order Quantity

11 EOQ Model Annual Cost 1. How much to order? Total Cost Curve Carrying Cost Order (Setup) Cost Optimal Order Quantity (Q*) Order Quantity

12 EOQ Model: When to Order? Inventory Level 2. When to order? Time

13 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Time

14 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Decrease due to constant demand Time

15 EOQ Model Inventory Level Optimal Order Quantity (Q*) 2. When to order? Instantaneous receipt of optimal order quantity Time

16 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Time

17 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Time

18 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Time

19 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Time

20 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Time

21 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Lead Time Time

22 EOQ Model Inventory Level 2. When to order? Optimal Order Quantity (Q*) Reorder Point (ROP) Lead Time Time

23 EOQ Model Inventory Level Optimal Order Quantity (Q*) 2. When to order? Average Inventory (Q*/2) Reorder Point (ROP) Lead Time Time

24 Problem 1: 1 IV. EOQ Model Example When the inventory of microwaves gets down to 15 units (reorder point), order 35 units (EOQ). 15 left Purchase Order Description Qty. Microwave 35

25 Problem 2: You re a buyer for Wal-Mart. Wal-Mart needs 1000 coffee makers per year. The cost of each coffee maker is $78. Ordering cost is $100 per order. Carrying cost is 40% of per unit cost. Lead time is 5 days. Wal- Mart is open 365 days/yr. What is the optimal order quantity & ROP?

26 A = 1,000 unit S = $ 100 per order c = $ 78 per unit i = 0.40 L = 5 days Working days/year = 365 days Question: a. EOQ =? b. ROP =?

27 EOQ Solution* Q* 2 X A X S = = i X c 2X1000X (78) = 80 units d A 1000 = = = Working Days/Year units / day ROP = d L = X 5 = units

28 V. Production Order Quantity Model 1. Answers how much to order & when to order 2. Allows partial receipt of material (other EOQ assumptions apply) 3. Suited for production environment Material produced, used immediately Provides production lot size 4. Lower carrying cost than EOQ model.

29 POQ Model: Inventory Levels Inventory Level Time

30 POQ Model: Inventory Levels Inventory Level Supply Begins Time

31 POQ Model: Inventory Levels Inventory Level Supply Begins Supply Ends Time

32 POQ Model: Inventory Levels Inventory Level Inventory level with NO demand during supply of optimum order quantity Supply Begins Supply Ends Time

33 POQ Model: Inventory Levels Q* Inventory Level Inventory level with NO demand during supply of optimum order quantity Supply Begins Supply Ends Q* is optimum order qty Time

34 POQ Model: Inventory Levels Inventory Level Q* Quantity used before becoming inventory Supply Begins Supply Ends Time

35 POQ Model: Inventory Levels Inventory Level Decrease due to no supply & constant demand Supply Begins Supply Ends Time

36 POQ Model: Inventory Levels Inventory Level Next Cycle Time

37 POQ Model: Inventory Levels Inventory Level Next Cycle Supply Begins Time

38 POQ Model: Inventory Levels Inventory Level Supply Begins Supply Ends Time

39 POQ Model: Inventory Levels Inventory Level Supply Begins Supply Ends Time

40 POQ Model: Inventory Levels Inventory Level Max. Inventory Q* (1 (1- d/p) Time

41 POQ Model Equations Optimal Order Quantity = Q p * = 2 x A x S H x (1- d/p) Max. Inventory Level Order Cost = Carrying Cost = A Q x S = Q x 1 Q 1 - (d/p) H d p A = Demand per year S = Order cost H = Carrying cost (i X c) d = Demand per day p = Production per day

42 VI. POQ Model Example You re a production planner for Stanley Tools. Stanley Tools makes 30,000 screw drivers per year. Demand is 100 screw drivers per day & production is 300 per day. Production setup cost is $150 per order. Carrying cost is $1.50 per screw driver. What is the optimal lot size? Max. Inv. Level?

43 Production Order Quantity Model Solution* Qp * = 2 A S = d H p Max. Inventory Level = = 300 A = Demand Per Year = unit S = Order Cost = $ 150 per order H = Carrying Cost = $ 1,5 per unit d = Demand Per Day = 100 unit p = Production Per Day = 300 unit =

44 VII. Fixed Period Model Answers how much to order Orders placed at fixed intervals Inventory brought up to target amount Amount ordered varies No continuous inventory count Possibility of stockout between intervals Useful when vendors visit routinely Example: P&G representative calls every 2 weeks

45 Inventory Level in a Fixed Period System Various amounts (Q i ) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to target maximum On-Hand Inventory Q 1 Q 2 Q 3 p p p Target maximum Q 4 Time

46 Sistem P (Periode( Tetap) Kapan memesan? Inventory Level Target maximum Q1 Q2 Q3 Periode Periode Periode Waktu

47 VII. Quantity Discount Model Answers how much to order & when to order Allows quantity discounts Reduced price when item is purchased in larger quantities Other EOQ assumptions apply Trade-off is between lower price & increased holding cost

48 Quantity Discount Models Reduced prices are often available when larger quantities are purchased Trade-off is between reduced product cost and increased holding cost Total cost = Setup cost + Holding cost + Product cost A QH TC = S + + ca Q 2

49 Quantity Discount Model: How Much to Order? Total Cost Order Quantity

50 Quantity Discount Model: How Much to Order? Total Cost Price 1 Discount Quantity 1 Order Quantity

51 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Discount Quantity 1 Discount Quantity 2 Order Quantity

52 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 Discount Quantity 1 Discount Quantity 2 Order Quantity

53 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 Discount Quantity 1 Discount Quantity 2 Order Quantity

54 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 Q* Discount Quantity 1 Discount Quantity 2 Order Quantity

55 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 Discount Quantity 1 Discount Quantity 2 Order Quantity

56 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 Q* Disc Qty 1 Discount Quantity 2 Order Quantity

57 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 Outside discount range Outside discount range Q* Disc Qty 1 Discount Quantity 2 Order Quantity

58 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 Discount Quantity 1 Discount Quantity 2 Order Quantity

59 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 Discount Quantity 1 Q* Discount Quantity 2 Order Quantity

60 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 TC for Discount 1 TC for Discount 2 TC for Discount 3 Outside discount range Disc Qty 1 Q* Discount Quantity 2 Order Quantity

61 Quantity Discount Model: How Much to Order? Total Cost Price 1 Price 2 Price 3 Quantity Ordered TC for Discount 1 TC for Discount 2 TC for Discount 3 Lowest cost not in discount range Discount Quantity 1 Discount Quantity 2 Order Quantity

62 Quantity Discount Model Steps Compute EOQ for each quantity discount price Is computed EOQ in discount range? If not, use the lowest cost quantity in discount range Compute total cost for EOQ or lowest cost quantity in discount range Select quantity with lowest total cost

63 Contoh: Quantity Discount Schedule Discount Number Discount Quantity Discount (%) 1 0 to 999 No discount Discount Price (P) $ ,000 to 1,999 4 $ ,000 and over 5 $4.75

64 Quantity Discount Models Steps in analyzing a quantity discount 1. For each discount, calculate Q* 2. If Q* for a discount doesn t t qualify, choose the smallest possible order size to get the discount 3. Compute the total cost for each Q* or adjusted value from Step 2 4. Select the Q* that gives the lowest total cost

65 Quantity Discount Example Calculate Q* for every discount Q* = 2S ic 2(5,000)(49) Q 1 * = = 700 cars order (.2)(5.00) 2(5,000)(49) Q 2 * = = 714 cars order (.2)(4.80) 1,000 adjusted 2(5,000)(49) Q 3 * = = 718 cars order (.2)(4.75) 2,000 adjusted

66 Quantity Discount Example Discount Number Unit Price Order Quantity Annual Product Cost Annual Ordering Cost Annual Holding Cost Total 1 $ $25,000 $350 $350 $25,700 2 $4.80 1,000 $24,000 $245 $480 $24,725 3 $4.75 2,000 $ $ $950 $24, Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit Table 12.3

67 VIII. Probabilistic Models and Safety Stock Answer how much and when to order Used when demand is not constant or certain Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the number of orders per year

68 Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Number of Units Probability ROP

69 Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Safety Stock Additional Holding Cost Stockout Cost Total Cost 20 (20)($5) = $100 $0 $ (10)($5) = $50 (10)(.1)($40)(6) = $240 $290 0 $0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960 A safety stock of 20 frames gives the lowest total cost ROP = = 70 frames

70 Probabilistic Demand Inventory level ROP Minimum demand during lead time Maximum demand during lead time Mean demand during lead time ROP = safety stock of 16.5 = Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) Safety stock 16.5 units Figure Lead time Place Receive order order Time

71 Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + ZσZ dlt where Z = number of standard deviations dlt = standard deviation of demand during lead time σ dlt

72 Probabilistic Example Average demand = μ = 350 kits Standard deviation of demand during lead time = σ dlt = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = Zσ dlt = 1.65(10) = 16.5 kits Reorder point = expected demand during lead time + safety stock = 350 kits kits of safety stock = or 367 kits

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