Chapter 9 Managing Inventory

Transcription

1 Chapter 9 Managing Inventory Types of Inventory ABC Analysis models and P models Supplement C: Special Inventory Models Inventory Management at 44M streaming customers worldwide and 7M DVD customers in US. 89M discs distributed across 39 warehouses in US. Employees inspect the returned discs from mailing envelopes. Discs are scanned by machines to see if any customer has ordered them. Others are shelved for future rentals. Each warehouse can process orders per day. Proper managed inventories can support competitive priorities of variety and delivery speed. 2 1

2 What is Inventory? A stock of materials used to satisfy customer demand or to support the production of services or goods. Manufacturing Inventory raw materials, WIP, maintenance and repairs, supplies, FGI Retail Inventory merchandise, supplies, goods in transit (pipeline inventory) What is a Inventory Management? The planning and controlling of inventories to meet the competitive priorities of the organization. 4 Pressures for Small Inventories Inventory holding cost Cost of capital (opportunity cost) Storage and handling costs: space, labor, machines Taxes Insurance Shrinkage Pilferage by customers or employees Obsolescence due to model changes or new products Deterioration: limited shelf life 5 2

3 Pressures for Large Inventories Customer service: stockout or backorder ing cost: fixed cost of preparing a purchase order Setup cost: fixed cost of changing over a machine to produce a different product. Labor and equipment utilization Transportation cost: full truckload or full container Payments to suppliers (quantity discount) 6 Inventory Costs Purchase Cost Holding or Carrying cost opportunity cost 資金積壓的潛在損失 storage cost 倉儲設備 進出盤點 shrinkage cost 貶值 偷竊 毀損 保費 order too much or too early ing or Setup cost 前置作業成本 order too often or too little 對外採購 : 聯繫 運輸 驗收內部製造 : 停機調整 試產 Shortage costs or Lost Sales 停工減產的損失 延誤交貨的罰款銷售減少的利潤損失 order too little or too late 7 3

4 Types of Inventory Cycle Inventory: Inventory that varies between orders. Safety Stock Inventory: surplus inventory that protects against uncertainties in demand, lead time, and supply changes. Anticipation Inventory: used to absorb uneven rates of demand or supply. (price increase) Pipeline Inventory 在途庫存 : inventory in transit between two stocking points. 8 Cycle Inventory The lot size,, varies directly with the elapsed time (or cycle) between orders. The longer the time between orders for a given item, the greater the cycle inventory must be. + 0 Average cycle inventory = = 2 2 Pipeline Inventory Average demand per period = d Number of periods in the item s lead time = L (fixed) Average Pipeline inventory = dl 9 4

5 Inventory Reduction Tactics 1/2 Cycle inventory: Reduce the lot size Reduce ordering and setup costs and allow to be reduced Increase repeatability to eliminate the need for changeovers Safety stock inventory: Place orders closer to the time when they must be received Improve demand forecasts Cut lead times Reduce supply uncertainties Rely more on equipment and labor buffers 10 Inventory Reduction Tactics 2/2 Anticipation inventory: Match demand rate with production rates Add new products with different demand cycles Provide off season promotional campaigns Offer seasonal pricing plans Pipeline inventory: Reduce lead times Find more responsive suppliers and select new carriers Change in those cases where the lead time depends on the lot size 11 5

6 Economic uantity The lot size,, that minimizes total annual inventory holding and ordering costs. Five assumptions: 1. Demand rate is constant and known with certainty. 2. No constraints are placed on the size of each lot. 3. The only two relevant costs are the inventory holding cost and the fixed cost per lot for ordering or setup. 4. Decisions for one item can be made independently of decisions for other items. 5. The lead time is constant and known with certainty. Use the EO 經濟訂貨量 Make to stock strategy with relatively stable demand. Carrying and setup costs are known and relatively stable 12 On-hand inventory 2 Receive order Inventory depletion (demand rate) Average cycle inventory Time How Many to? 1 cycle

7 Calculating EO Annual Demand = D Annual holding cost = (Average cycle inventory) (Unit holding cost) = Annual ordering cost =(Number of orders/year) (ing or setup costs) = Total costs = C( ) H 1 2 D S H 2 D S d DS C 0 EO 2 * d H Time Between s = EO D 14 Calculating EO Annual cost (dollars) Total cost Holding cost ing cost 15 Lot Size () 7

8 Example 9.2: Bird Feeder Sales are 18 units per week, the supplier charges $60 per unit. ing cost is $45. Annual holding cost is 25 percent of a feeder s value. What is the annual cycle inventory cost of the current policy of using a 390 unit lot size? Would a lost size of 468 be better? D=(18 units/week)(52 weeks/year) = 936 units H=0.25($60/unit) = $15 S=$45 C( ) H 1 2 D S = ($15) + ($45) = $2,925 + $108 = $3, Example 9.3 EO for bird feeders EO 2DS H 2(936)45 15 = or 75 units 17 8

9 Managerial Insights from the EO Parameter EO Parameter Change SENSITIVITY ANALYSIS OF THE EO EO Change Comments Demand 2DS H / Setup Costs 2DS H Increase in lot size is in proportion to the square root of D. Weeks of supply decreases and inventory turnover increases because the lot size decreases. Holding Costs 2DS H Larger lots are justified when holding costs decrease. 18 Inventory Control Systems Periodic Review System Continuous Review System Fixed Period P model Fixed uantity model 19 9

10 Continuous Review System model or fixed order quantity system Tracks inventory position (IP) Reorder point system (ROP) and fixed order quantity () Decision Includes scheduled receipts (SR), on hand inventory (OH), and back orders (BO) Inventory position = On hand inventory + Scheduled receipts Backorders IP = OH + SR BO Rule: If IP ROP, place an order of size 20 Continuous Review System On-hand inventory R OH placed IP received placed received placed received TBO L TBO L TBO L Time Selecting the Reorder Point depends on Demand and Lead Times

11 Example 9.4 Demand for chicken soup at a supermarket is always 25 cases a day and the lead time is always 4 days. The on hand inventory has only 10 cases. No backorders currently exist, but there is one open order in the pipeline for 200 cases. Should a new order be placed? R = Total demand during lead time = (25)(4) = 100 cases IP = OH + SR BO= = 210 cases 22 Continuous Review System 2: Variable Demand On-hand inventory R placed IP received placed IP received placed IP received 0 L 1 L 2 L 3 TBO 1 TBO 2 TBO 3 Time Select ROP base on Demand, Lead Times, and Safety Stock

12 Example 9.5 A distribution center receives its inventory from a mega warehouse with a lead time (L) of 5 days. The DC uses a reorder point (R) of 300 sets and a fixed order quantity () of 250 sets. Current on hand inventory at the end of Day 1 is 400 sets. There are no scheduled receipts (SR) and no backorders (BO). All demands and receipts occur at the end of the day. Determine when to order using a system 24 Example 9.5 ROP=300, =250, L=5 days Day Demand OH SR BO IP = after ordering = 500 after ordering = = < R before ordering 250 due =510 after ordering Day = = = =245<R before ordering 250 due = 495 after ordering Day =

13 Continuous Review System 2: Reorder Point Assume variable demand and constant lead time Reorder point = Average demand during lead time + Safety stock Choosing a Reorder Point = dl + Safety stock = dl + z σ dlt 2. Determine the distribution of demand during lead time 1. Choose an appropriate service level policy 3. Use the formula to calculate the safety stock and reorder point levels 26 Distribution of Demand during Lead Time Specify mean and standard deviation of daily demand d Standard deviation of demand during lead time σ dlt = σ d2 L = σ d L σ d σ d = 15 + σ d = 15 + σ d = 15 = σ dlt = Demand for week 1 75 Demand for week 2 75 Demand for week Demand for 3-week lead time 27 13

14 Continuous Review System 2: Service Level Service level = 85% Average demand during lead time ROP Probability of stockout ( = 0.15) z σ dlt Service level = 85% z = (0.85) = NORMINV(0.85,0,1)= Continuous Review System 2 : Safety Stock Safety stock = z =number of standard deviations needed to achieve the service level σ d =stand deviation of daily demand σ dlt =stand deviation of demand during lead time If d=75, σ d =15, L=3 and service level=85%, then safety stock = = Reorder point = R = dl+ safety stock = (25) If service level=95%, safety stock =

15 Continuous Review System 3 When both Demand and Lead Time are Variable ROP = (Average daily demand Average lead time) + Safety stock = d L + Safety stock = d L + zσ dlt where d =average daily (or weekly or monthly) demand L =average lead time σ d =standard deviation of daily (or weekly or monthly) demand σ LT =Standard deviation of the lead time σ dlt = σ d2 + 2 σ LT 2 30 Continuous Review System Two Bin system demand 1st bin 2nd bin demand 1st bin 2nd bin Total Annual System Costs 1st bin 2nd bin Total cost = Annual cycle inventory holding cost + Annual ordering cost + Annual safety stock holding cost D C = (H) + (S) + (H) (Safety stock) 2 order 31 15

16 Periodic Review System Fixed interval reorder system or P model Target On-hand inventory IP 1 IP 3 IP 2 1 IP placed received OH received 2 3 placed placed received L P L P L Time Protection interval Rule: Every P time units, check inventory and then place order 32 Example 9.8 Refer to Example 9.5. Suppose that the management want to use a Periodic Review System for TV sets. The first review is scheduled for the end of Day 2. All demands and receipts occur at the end of the day. Management has set Target Inventory Level = 620 and P = 6 days. Lead time is 5 Days. Determine how much to order () using a P System

17 Example 9.8 Target = 620, P = 6 days, L = 5 days Day Demand OH SR BO IP after 340 before ordering = ordering =620 after ordering 280 due Day = = = = = after ordering = before ordering =620 after ordering =395 due Day Periodic Review: variable demand & fixed lead time Selecting the time between reviews Set Target Inventory Level. T must cover demand over a protection interval of P + L Average demand during the protection interval is Safety stock for the protection interval = z is determined by the service level. uantity = T Inventory on hand (OH) 35 17

18 Example 9.9: Bird Feeder Weekly demand for the bird feeder is normally distributed with a mean of 18 units and a standard deviation of 5 units. The lead time is 2 weeks. The system called for an EO of 75 units and a safety stock of 9 units for a cycle service level of 90%. What is the equivalent P system? 75 4 weeks 18 Service level of 90% z=1.28 =18 (4+2) (5) 4 2 = Periodic Review System Total Annual P System Costs = Annual cycle inventory holding cost + Annual ordering cost + Annual safety stock holding cost 2 safety stock The P system requires more inventory for the same level of protection against stockouts or backorders. Optional Replenishment System 選擇補貨系統 : A hybrid system used to review the inventory position at fixed time intervals and, if the position has dropped to (or below) a predetermined level, to place a variable sized order to cover expected needs

19 ABC 庫存分類管理 Pareto s 80/20 principle SKU no. annual demand unit cost annual dollar value There are other ways to do ABC classification. Review ABC classification periodically. 38 Pareto Chart for ABC Analysis 100 Class C Percentage of dollar value 90 Class A Class B Inventory Accuracy by APICS Class A: 0.2% Class B: 1% Class C: 5% Percentage of SKUs 39 19

20 Supplement C: Economic Production uantity 經濟生產批量 Production uantity. Production rate p > the demand rate d, so there is a buildup of (p d) units per time period. Buildup continues for /p periods. I max p Demand during production interval d Production quantity Maximum inventory p d Production & demand Demand only Time 40 Economic Production uantity Max. inventory is: production time Average inventory is no longer /2, it is I max /2 Total annual cost = Annual holding cost + Annual setup cost EP ELS 2DS H p p u 41 20

21 Example C.1 A plant manager must decide the lot size for a product that has a steady demand of 30 units per day. The production rate is 190 units per day, annual demand is 10,500 units, setup cost is $200, annual holding cost is $0.21 per units, and the plant operates 350 days per year. EP 2DS H p p u 2(10500)(200) : What are the advantages of reducing the setup time by 10%? 42 Supplement C: One-Period Decisions 適用於庫存價值低之流行商品採購與製造 旅遊業超額訂位 Example C.3: A gift shop sells a Christmas ornament carved from wood and makes a $10 profit per unit sold during the season, but it takes a $5 loss per unit after the season is over. Step 1: List the demand levels and probabilities. Demand Demand Probability Step 2: Develop a payoff table that shows the profit for each purchase quantity,, at each assumed demand level, D

22 One-Period Decisions Payoff = (Profit per unit)(demand quantity) (Loss per unit)(leftovers) p if Demand uantity = p D l ( D) if Demand < uantity uantity Demand 10 (0.2) 20 (0.3) 30 (0.3) 40 (0.1) 50 (0.1) Expected Payoff Steps 3 &4: Calculate the expected payoff of each and pick the best. 44 Newsboy Problem 1/2 1. 預測報紙需求 D 為常態分布平均值 =90 papers 標準差 =10 papers D~N(E(D), s d 2 ) Decision: 進貨 90 papers P(stockout)=P(D>90)=P(D>E(D))=50% x Goal: P(stockout)<20% P(no stockout)>80% P(D x)>80% P(D E(D)+z s d )>80% Decision: 進貨 (10)=99 papers 無條件進位 45 22

23 Newsboy Problem 2/2 C e = 進貨高估需求的單位成本 = 進價 殘值報紙進價 =0.20 C s = 進貨低估需求的單位成本 = 售價 進價報紙利潤 =0.30 預測報紙需求為 90 份, 目前進貨 90 份, 增加進貨是否能增加利潤? P=P( 增加的進貨賣不出 )=P( 需求 90)=0.5 潛在利潤 (1 P) C s =0.5(0.30) > 潛在損失 P C e =0.5(0.20) Key: 增加進貨量直到 C P sc C e s Optimal service level : 如果 C s << C e, 我們應如何調整進貨量? 46 Airline Overbooking (Revenue Management) 2. 飛機有 90 個座位, 經常有人訂位卻臨時取消或延期假設 probability of no show=10%, 訂位額滿時預期會有 9 個空位 Solution: 超額訂位 Decision: 接受 100 個訂位 no shows ~N(10, s 2 ) P(no shows<10)=50% P(overbooking)=50% 高估 no show 人數 ( 座位不足 ) 的單位成本 =C e 低估 no show 人數 ( 座位未售 ) 的單位成本 =C s Goal: P(no overbooking)>80% 減少超額訂位 47 23