Mechanical Engineering 101

Transcription

1 Mechanical Engineering 101 University of California, Berkeley Lecture #10 1

2 Today s lecture Supply Chain Management (SCM) Variance acceleration Safety stock Raw materials factory wholesaler retailer customer 2

3 Periodic Ordering? D = demand, SS = safety stock, = lead time, Q = order quantity, I = inventory Say you order weekly, want 1 week of safety stock target inventory I* = D + SS = 2D current inventory = I say = 1 week, then Q = D + I* - I = D + 2D I = 3D I R = order-up-to-target (note how if demand stays at D, I = 2D & order is for D each week) Now say = 2 weeks, then Q = D + I* I cur I on-order = 2D + 2D I cur I on-order = 4D I cur I on-order R 3

4 Forecasting and Supply Chains Assumes naïve forecast Forecast that this week s demand = last week s D(t) = D(t-1) Issues amplifies variations in demand large fluctuations in orders/production extra inventory w/ slight demand variations So let s try using exponential smoothing 4

5 Inventory and supply chains Example: 2 stage supply chain factory & retailer mean demand units/week weekly orders and deliveries 2 week lead time Strategy 1 week safety stock based on forecasting demand with exponential smoothing Forecast is same for any period in future 5

6 Example week: R order-up-to target I current inventory I on order Q order quantity demand forecasted demand w1 6

7 Example week: R order-up-to target I current inventory I on order Q order quantity demand forecasted demand w1 w2 7

8 Example week: w1 w2 w3 R order-up-to target I current inventory I on order Q order quantity demand 112 forecasted demand 105 8

9 Example week: R order-up-to target I current inventory I on order Q order quantity demand forecasted demand w1 w2 w w % retail demand change = 32% order change! = change in demand factory sees 9

10 Example week: w1 w2 w3 w4 R order-up-to target 420 I current inventory 188 I on order Q order quantity 132 demand forecasted demand

11 Example week: w1 w2 w3 w4 w5 R order-up-to target 420? I current inventory 188? I on order 132 Q order quantity 132 x demand forecasted demand

12 Example 1. 0<=x< <=x< <=x< <=x< <=x< <=x< <=x< <=x< <=x week: R order-up-to target I current inventory I on order Q order quantity demand forecasted demand w w w5?? 132 x 12

13 Variance acceleration small changes in demand exaggerated going up the supply chain worse with more stages the bull whip effect 14

14 Announcements Coming soon! The beer game simulation Laptop survey? 16

15 Today s lecture Supply Chain Management Variance acceleration Safety stock 17

16 Variability in Demand Frequency - Demand Average demand confidence interval ( 3 ) Forecasts need to include variability in demand data Caution: data not always normally distributed (why?) 18

17 Stats Background Survey What is the highest level of formal statistics you ve studied? 1. some mention in high school math 2. some coverage in college classes 3. AP stats in high school 4. significant coverage in college classes 5. took one or more college class(es) focused on statistics 19

18 Stats Quiz For a normal distribution, percent of area under curve between red lines is approximately: 1. 25% 2. 33% 3. 50% 4. 67% 5. 75% 6. 95% 7. 98% 8. none of the above

19 Standard deviation for a normal population with standard deviation : 22

20 Make to stock Constant demand Q batch size D demand rate SS safety stock Inventory position Q safety stock SS time Q/D 24

21 .Safety stock (Say EOQ tells us to produce 1x/mo) monthly demand = standard deviation = 15 If we keep 30 products in safety stock, what percentage of the time will we be able to fill orders from stock? 25

22 Normal distribution mean standard deviation % %

23 .Safety stock (Say EOQ tells us to produce 1x/mo) monthly demand = standard deviation = 10 How much safety stock should we keep on hand to guarantee 97 1/2 % of demand can be filled from stock? 30

24 Role of Information info can substitute for safety stock more info on order reqs, scheduling can minimize shortages 33

25 Yen per $1 34

26 .Exchange Rates During ~last decade, Yen vs. US$ increased almost 2:1 What happens when $1 buys half as many yen as before? 35

27 Conclusions Variance will cost us money Bull whip effect will exaggerate it! 38

28 Homework 5 Reading Askin pp , 43-48, Askin problems 2.8 (shortage costs) , changing D to 25,000 for inventory cost, include both FGI and WIP.5 per year = 50% per year 6.15 (assume processed in order given) At least one question may not provide all the info you need! What info is missing? Use the appropriate variable letter name(s) in place of the missing info -- thus your answer will be in terms of the variable(s). 39

29 Fixed setup cost problems assumptions demand is continuous and constant throughout working hours additional setups are free Operator doing setups would otherwise do no useful work E.g. contract states can only work with this one machine, does both internal and external setup, no one else available to help external elements performed while machine runs unattended But can t start setup for a part type while machine is making that same type we ve streamlined setup as much as possible can t reduce internal or external setup times further 40

30 HW5 extra credit To assemble a coffee table, four table legs and one table top are needed. A work center produces the legs and tops in turn; i.e., it first produces a batch of legs, then a batch of tops, then a batch of legs, and so on. The batch size of the legs should be four times that of the tops such that they can be assembled and shipped properly. Assume setup cost is only labor and labor cost is fixed. Also assume that only one worker is assigned to the work center at a time, and the same worker does both the internal and external setups, and the machine can run unattended during the processing time. You may assume the same batch sizes are used throughout the day. The work center operates hours per week. The weekly demand is 125 coffee tables. Setup times and processing times are given below (in minutes). Internal Setup Time External Setup Time Table Legs Table Tops Unit Processing Time 41

31 HW5 extra credit continued a) Find the batch sizes for tops and legs that the textbook claims will minimize holding costs (while meeting the demand). How much time out of the total factory operating time are both the machine and the operator idle for these batch sizes? b) Do these batch sizes really minimize the inventory cost (while meeting the demand)? Show why or why not. If not, what are the batch sizes that actually minimize the inventory cost (while meeting the demand)? Show your work. Draw a timeline as part of showing your work 42