1. Special Session 2 April 12,13 Topics Section 10.7 Intro to Ch 11 (11.1 – 11.2) Aggregate Planning Section 11.3 Intro to MRP Section 11.4

2. Section 10.7 In previous models, we assume no variability In this section we change this by including demand variability during lead time (lead time = time it takes for our supplier to deliver the order) There are two characteristics of this type of problem –Service Level (the percentage of time we will have inventory during the lead time A service level of 98% means we will be out of inventory on 2% of the time during lead time demand. –Variability of demand during lead time (standard deviation)  L

3. Section 10.7 To account for demand variability, we will maintain a safety stock of inventory. This safety stock will protect us from the high side of demand variability. The average inventory increases by the safety stock so its an additional cost. The amount we order does not change The reorder point changes –R = d L + Safety Stock –For example, we always order 20 boxes of cereal (the Q), –Lead time is 4 days and daily demand is 2 boxes, so we reorder at 8 (the R), so the order arrives as we get to zero. –If plan a safety stock of 4 boxes, what happens? The reorder point is 12 boxes (8 from before + the safety stock of 4) so when we get to 12 boxes we send the signal to our supplier, and the new shipment of 20 arrives when we have about 4 left (this is the safety stock)

4. Section 10.7 Calculations –R = d L + ss (L = Lead time, d = demand per lead time unit, ss = Safety Stock) –ss = Z  L Z = Z value from the desired service level –Look out in Appendix 1 the following service levels: –98% : Z = 2.1 (look at the top right column in the appendix, the first value that gets to 0.98, 0.98214 with a Z of 2.1) –99% : Z = 2.35 –99.99%: Z = 3.75  L = Standard deviation of demand during Lead time  d = Standard deviation of demand per time unit L  d 2  L =

5. Section 10.7 Example 1. L = 4 weeks, and  d = 5 units/week, and d = 50 units/week (so in most weeks demand ranges from 45 to 55 units per week) What is R at Service Levels of 98%, 99%, and 99.99%? R = d L + ss = 200 + ss ss = Z  L  L = sqrt (4 x 25) = 10 at SL = 98%, Z = 2.1, R = 200 + 21 = 221 at SL = 99%, Z = 2.35, R = 200 + 23.5 = 223.5 at SL = 99.99%, Z = 3.75, R = 200 + 37.5 = 237.5 So clearly, as the service level increases, the reorder point increases, which results in higher average inventory.

6. Section 10.7 Example 2. L = 9 days, and  d = 12 units/day, and d = 24 units/day What is R at Service Levels of 99% and 99.99%? R = d L + ss = 216 + ss ss = Z  L  L = sqrt (9 x 12 2 ) = 36 at SL = 99%, Z = 2.35, R = 216 + 84.6 = 302.6 at SL = 99.99%, Z = 3.75, R = 216 + 135 = 351

7. Ch 11 Introduction Production Planning is related to capacity planning, but it adds constraints related to time –Look at Figure 11.1 –Emphasis is on the time horizon (planning time) and the time buckets. –As we get to planning for short term (next few days) we add details, like the sequence of events and the time buckets become smaller (instead of a week plan, we plan for the shift).

8. Ch 11. Aggregate Planning Time buckets = months Time horizon = 2-4 months into the future and for several months For example, we are in April, so a manufacturer performing Aggregate Planning today will be be planning for July 2002 – January 2003

9. Ch 11. Aggregate Planning Based on demand for our products –But the demand is aggregate (therefore the name) so we do not know the specific demand per items we make, but overall demand for the typical mix –For example if we make TVs, we know typically we make 50% 25”, 30% 27”, and 20% 42”, so all the variables are based on this mix.

10. Ch 11. Aggregate Planning So look at the example in the text: Demand –Dec 44,000 units –Jan 50,000 units –… Process characteristics –2 hours of labor per unit –Works for 1 shift (8 hours per day), 20 days in a month, thus each worker gives 160 hours per month –Current workforce = 550 workers Cost Characteristics –Holding cost $2/month –..

11. Ch 11. Aggregate Planning The overall objective is to determine which strategy minimizes total cost over the planning horizon considered Strategies determine –The workforce –The inventories –Buying from outside manufacturers (that make TVs for us)

12. Ch 11. Aggregate Planning Strategy 1. Constant Workforce –How many workers we need to make the demand for the complete time horizon Add demand for all six months = 277,000 units How much time will it take to make 277,000 units, 554,000 hours (277,000 units x 2hrs.unit) What is the time per worker in the same time span? –160 hr/month x 5 months = 960 hours/worker So how many workers? RU (554,000/960) = 578

13. Ch 11. Aggregate Planning Given we have 550 to start with, we need to hire 28 workers in the first month. December 44,000 R Units of Labor550 Hire28 Layoffs0 Total Personnel578 Starting workers Workers to hire Calculated before

14. We do not outsource In this strategy December 44,000 R Units of Labor550 Hire28 Layoffs0 Total Personnel578 Required Units44,000 Internal Production46,240 Products Outsourced0 Total Products46,240 What we can make 578 workers x 160 hours/ 2 hrs = 46,240 Sum of what we Can make and what We buy outsource

15. December 44,000 R Units of Labor550 Hire28 Layoffs0 Total Personnel578 Required Units44,000 Internal Production46,240 Products Outsourced0 Total Products46,240 End inventory2,240 Holding Cost4,480 Total Products – Required Units 2,240 x 2 We have this if Ending Inventory >0. If we have Negative inventory (backorders) We have 0 here.

16. December 44,000 R Units of Labor550 Hire28 Layoffs0 Total Personnel578 Required Units44,000 Internal Production46,240 Products Outsourced0 Total Products46,240 End inventory2,240 Holding Cost4,480 Backorder cost0 Direct Labor cost924,800 Hire/Layoff5,600 Outsource cost0 578 workers x 160 hours x $10/hour = 924,800 28 workers hired x $200 We do not outsource in this strategy

17. December 44,000 R Units of Labor550 Hire28 Layoffs0 Total Personnel578 Required Units44,000 Internal Production46,240 Products Outsourced0 Total Products46,240 End inventory2,240 Holding Cost4,480 Backorder cost0 Direct Labor cost924,800 Hire/Layoff5,600 Outsource cost0 Sum of all costs 934,880

18. DecemberJanuary 44,00050,000 R Units of Labor550578 Hire280 Layoffs00 Total Personnel578 Required Units44,000 Internal Production46,240 Products Outsourced0 Total Products46,240 End inventory2,240 Holding Cost4,480 Backorder cost0 Direct Labor cost924,800 Hire/Layoff5,600 Outsource cost0 Workers from the previous month We have the Number of workers we need

19. DecemberJanuary 44,00050,000 R Units of Labor550578 Hire280 Layoffs00 Total Personnel578 Required Units44,00047,760 Internal Production46,240 Products Outsourced0 Total Products46,240 End inventory2,240 Holding Cost4,480 Backorder cost0 Direct Labor cost924,800 Hire/Layoff5,600 Outsource cost0 Workers from the previous month We need less as We we have inventory From last month 50,000 – 2,240 = 47,760

20. DecemberJanuary 44,00050,000 R Units of Labor550578 Hire280 Layoffs00 Total Personnel578 Required Units44,00047,760 Internal Production46,240 Products Outsourced00 Total Products46,240 End inventory2,240-1,520 Holding Cost4,4800 Backorder cost07,600 Direct Labor cost924,800 Hire/Layoff5,600 Outsource cost0 We can’t make all We need 46,240 – 47,760 = - 1,520 0 holding 1,520 x 5

21. And so on…. Lets plan for the three more months JuneJuly August 48,00057,00062,000 Workforce is at 700. All other stay variables stay the same

22. Class Example JuneJuly August 48,00057,00062,000 Sum = 167,000 units x 2hours = 334,000 hours Each worker gives 160 x 3 = 480 hours Thus the number of workers is 696.

23. JuneJuly 48,00057,000 R Units of Labor700 Hire0 Layoffs4 Total Personnel696 Required Units48,000 Internal Production55,680 Products Outsourced0 Total Products55,680 End inventory7,680 Holding Cost Backorder cost Direct Labor cost Hire/Layoff Outsource cost Starting number of workers Layoff 4 to get to 696 696 x 160/2

24. JuneJuly 48,00057,000 R Units of Labor700 Hire0 Layoffs4 Total Personnel696 Required Units48,000 Internal Production55,680 Products Outsourced0 Total Products55,680 End inventory7,680 Holding Cost15,360 Backorder cost0 Direct Labor cost1,113,600 Hire/Layoff2,000 Outsource cost0 1,130,960

25. JuneJuly 48,00057,000 R Units of Labor700696 Hire00 Layoffs40 Total Personnel696 Required Units48,00049,320 Internal Production55,680 Products Outsourced00 Total Products55,680 End inventory7,6806,360 Holding Cost15,36012,720 Backorder cost00 Direct Labor cost1,113,600 Hire/Layoff2,0000 Outsource cost00 1,130,960 1,126,320

26. JuneJulyAugust 48,00057,00062,000 R Units of Labor700696 Hire000 Layoffs400 Total Personnel696 Required Units48,00049,32055,640 Internal Production 55,680 Products Outsourced 000 Total Products55,680 End inventory7,6806,36040 Holding Cost15,36012,72080 Backorder cost000 Direct Labor cost1,113,600 Hire/Layoff2,00000 1,130,960 1,126,3201,113,680 TC: 3,370,960

27. Next strategy Vary the workforce – each month find the number of workers each month that will meet the demand –This assumes workers are easily available. –For December we need how many workers? –44,000 x 2 = 88,000/160 = 550 workers –Utilize Required units to calculate the number of workers

28. Vary the workforce Same process as before For Jan, 50,000 x 2/160 = 625, so hire 75 Note that for May we use 39,960 to determine the number of workers –39,960 x 2/160 = 500

29. Class Example Lets apply strategy 2 to the next three months. –We have 700 workers –Demand for June is 48,000 48,000 x 2/ 160 = 600, so we need to layoff 100 workers

30. JuneJulyAugust 48,00057,00062,000 R Units of Labor700 Hire0 Layoffs100 Total Personnel600 Required Units48,000 Internal Production 48,000 Products Outsourced 0 Total Products48,000 End inventory0 Holding Cost0 Backorder cost0 Direct Labor cost960,000 Hire/Layoff20,000 980,000 We do not outsource In this strategy

31. JuneJulyAugust 48,00057,00062,000 R Units of Labor700600 Hire0113 Layoffs1000 Total Personnel600713 Required Units48,00057,000 Internal Production48,00057,040 Products Outsourced 00 Total Products48,00057,040 End inventory040 Holding Cost080 Backorder cost00 Direct Labor cost960,0001,140,800 Hire/Layoff50,00022,600 1,010,000 57,000 x 2/160 = 713 1,163,480

32. JuneJulyAugust 48,00057,00062,000 R Units of Labor700600713 Hire011362 Layoffs10000 Total Personnel600713775 Required Units48,00057,00061,960 Internal Production48,00057,04062,000 Products Outsourced 000 Total Products48,00057,04062,000 End inventory040 Holding Cost080 Backorder cost000 Direct Labor cost960,0001,140,8001,240,000 Hire/Layoff50,00022,60012,400 1,010,000 1,163,4801,252,480 TC: 3,425,960

33. Third Strategy Outsource –We keep the initial workforce –If we need more than we can make, buy from someone else (outsource) –Should be easy to follow on the course notes.

34. Third strategy for the class example Modify workforce to a maximum of 50 (hire or layoff a max of 50), outsource any needed units

35. JuneJulyAugust 48,00057,00062,000 R Units of Labor700 Hire0 Layoffs50 Total Personnel650 Required Units Internal Production Products Outsourced Total Products End inventory Holding Cost Backorder cost Direct Labor cost Hire/Layoff Outsource cost TOTAL Cost We only need 600 (48,000 x 2/160), But the maximum number Of workers that can be Changed is 50, so we have To keep extra workers

36. JuneJulyAugust 48,00057,00062,000 R Units of Labor700650 Hire013 Layoffs500 Total Personnel650663 Required Units48,00053,000 Internal Production 52,000 Products Outsourced 0 Total Products52,000 End inventory4,000 Holding Cost8,000 Backorder cost0 Direct Labor cost1,040,000 Hire/Layoff25,000 Outsource cost0 TOTAL Cost 1,073,000 Given we really need 53,000 units The number of workers is 53,000 x 2/160 = 663

37. JuneJulyAugust 48,00057,00062,000 R Units of Labor700650663 Hire01350 Layoffs5000 Total Personnel650663713 Required Units48,00053,00061,960 Internal Production 52,00053,040 Products Outsourced 00 Total Products52,00053,040 End inventory4,00040 Holding Cost8,00080 Backorder cost00 Direct Labor cost1,040,0001,060,800 Hire/Layoff25,0002,600 Outsource cost00 TOTAL Cost 1,073,0001,063,480 We need 61,960 units The number of workers is 61,960 x 2/160 = 775 But we can only hire 50

38. JuneJulyAugust 48,00057,00062,000 R Units of Labor700650663 Hire01350 Layoffs5000 Total Personnel650663713 Required Units48,00053,00061,960 Internal Production 52,00053,04057,040 Products Outsourced 004,920 Total Products52,00053,04061,960 End inventory4,000400 Holding Cost8,000800 Backorder cost000 Direct Labor cost1,040,0001,060,8001,140,800 Hire/Layoff25,0002,60010,000 Outsource cost00123,000 TOTAL Cost 1,073,0001,063,4801,273,800 TC: 3,410,280 We outsource the difference of what is required and what we can make 61,960 – 57,040 = 4,920 Outsource cost 25 x 4,920 = 123,000

39. Results Best strategy is to have a constant workforce based on total cost.

40. Ch 11. Intro to MRP Section 11.4 MRP - intermediate level planning –Time buckets is typically in weeks –Plan for the next 2-16 weeks –Is based on product structure (the components) and lead time for the parent product and its components

41. Ch 11. Intro to MRP Section 11.4 MRP Basics oIf we have a car made of a body and two axle assemblies, we know we need 10 bodies and 20 Axle assemblies. oIf it takes one week to make the car, two to make the body and five to make the axle assemblies. oW need 10 cars by week 9 then We need to start making the cars in week 8 We need to start the bodies in week 6 We need to start the axle assemblies in week 3 Car Body Axle Assy (2) Axle Assy car body w9w8w7w6w5w4w3w2w1