Special Session 2 April 12,13 Topics Section 10.7 Intro to Ch 11 (11.1 – 11.2) Aggregate Planning...
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Transcript of Special Session 2 April 12,13 Topics Section 10.7 Intro to Ch 11 (11.1 – 11.2) Aggregate Planning...
Special Session 2April 12,13
TopicsSection 10.7
Intro to Ch 11 (11.1 – 11.2)
Aggregate Planning Section 11.3
Intro to MRP Section 11.4
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
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)
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 d2L =
Section 10.7Example 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 = 221at SL = 99%, Z = 2.35, R = 200 + 23.5 = 223.5at 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.
Section 10.7Example 2.L = 9 days, and d = 12 units/day, and d = 24 units/dayWhat is R at Service Levels of 99% and 99.99%?
R = d L + ss= 216 + ss
ss = Z L
L = sqrt (9 x 122) = 36
at SL = 99%, Z = 2.35, R = 216 + 84.6 = 302.6at SL = 99.99%, Z = 3.75, R = 216 + 135 = 351
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).
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
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.
Ch 11. Aggregate PlanningSo 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– ..
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)
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
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 Labor 550
Hire 28
Layoffs 0
Total Personnel 578
Starting workers
Workers to hire
Calculatedbefore
We do not outsourceIn this strategy
December
44,000
R Units of Labor 550
Hire 28
Layoffs 0
Total Personnel 578
Required Units 44,000
Internal Production 46,240
Products Outsourced 0
Total Products 46,240
What we can make578 workers x 160 hours/ 2 hrs = 46,240
Sum of what weCan make and whatWe buy outsource
December
44,000
R Units of Labor 550
Hire 28
Layoffs 0
Total Personnel 578
Required Units 44,000
Internal Production 46,240
Products Outsourced 0
Total Products 46,240
End inventory 2,240
Holding Cost 4,480
Total Products – Required Units
2,240 x 2We have this if EndingInventory >0. If we haveNegative inventory (backorders) We have 0 here.
December
44,000
R Units of Labor 550
Hire 28
Layoffs 0
Total Personnel 578
Required Units 44,000
Internal Production 46,240
Products Outsourced 0
Total Products 46,240
End inventory 2,240
Holding Cost 4,480
Backorder cost 0
Direct Labor cost 924,800
Hire/Layoff 5,600
Outsource cost 0
578 workers x 160 hours x $10/hour = 924,800
28 workers hired x $200
We do not outsource in this strategy
December
44,000
R Units of Labor 550
Hire 28
Layoffs 0
Total Personnel 578
Required Units 44,000
Internal Production 46,240
Products Outsourced 0
Total Products 46,240
End inventory 2,240
Holding Cost 4,480
Backorder cost 0
Direct Labor cost 924,800
Hire/Layoff 5,600
Outsource cost 0 Sum of all costs
934,880
December January
44,000 50,000
R Units of Labor 550 578
Hire 28 0
Layoffs 0 0
Total Personnel 578 578
Required Units 44,000
Internal Production 46,240
Products Outsourced 0
Total Products 46,240
End inventory 2,240
Holding Cost 4,480
Backorder cost 0
Direct Labor cost 924,800
Hire/Layoff 5,600
Outsource cost 0
Workers from the previous month
We have the Number of workers we need
December January
44,000 50,000
R Units of Labor 550 578
Hire 28 0
Layoffs 0 0
Total Personnel 578 578
Required Units 44,000 47,760
Internal Production 46,240
Products Outsourced 0
Total Products 46,240
End inventory 2,240
Holding Cost 4,480
Backorder cost 0
Direct Labor cost 924,800
Hire/Layoff 5,600
Outsource cost 0
Workers from the previous month
We need less asWe we have inventoryFrom last month
50,000 – 2,240 =47,760
December January
44,000 50,000
R Units of Labor 550 578
Hire 28 0
Layoffs 0 0
Total Personnel 578 578
Required Units 44,000 47,760
Internal Production 46,240 46,240
Products Outsourced 0 0
Total Products 46,240 46,240
End inventory 2,240 -1,520
Holding Cost 4,480 0
Backorder cost 0 7,600
Direct Labor cost 924,800
Hire/Layoff 5,600
Outsource cost 0
We can’t make allWe need
46,240 – 47,760 =- 1,520
0 holding
1,520 x 5
And so on….
Lets plan for the three more months
June July August
48,000 57,000 62,000
Workforce is at 700. All other stay variables stay the same
Class Example
June July August
48,000 57,000 62,000
Sum = 167,000 units x 2hours = 334,000 hours
Each worker gives 160 x 3 = 480 hours
Thus the number of workers is 696.
June July
48,000 57,000
R Units of Labor 700
Hire 0
Layoffs 4
Total Personnel 696
Required Units 48,000
Internal Production 55,680
Products Outsourced 0
Total Products 55,680
End inventory 7,680
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
June July
48,000 57,000
R Units of Labor 700
Hire 0
Layoffs 4
Total Personnel 696
Required Units 48,000
Internal Production 55,680
Products Outsourced 0
Total Products 55,680
End inventory 7,680
Holding Cost 15,360
Backorder cost 0
Direct Labor cost 1,113,600
Hire/Layoff 2,000
Outsource cost 0
1,130,960
June July
48,000 57,000
R Units of Labor 700 696
Hire 0 0
Layoffs 4 0
Total Personnel 696 696
Required Units 48,000 49,320
Internal Production 55,680 55,680
Products Outsourced 0 0
Total Products 55,680 55,680
End inventory 7,680 6,360
Holding Cost 15,360 12,720
Backorder cost 0 0
Direct Labor cost 1,113,600 1,113,600
Hire/Layoff 2,000 0
Outsource cost 0 0
1,130,960 1,126,320
June July August
48,000 57,000 62,000
R Units of Labor 700 696 696
Hire 0 0 0
Layoffs 4 0 0
Total Personnel 696 696 696
Required Units 48,000 49,320 55,640
Internal Production
55,680 55,680 55,680
Products Outsourced
0 0 0
Total Products 55,680 55,680 55,680
End inventory 7,680 6,360 40
Holding Cost 15,360 12,720 80
Backorder cost 0 0 0
Direct Labor cost 1,113,600 1,113,600 1,113,600
Hire/Layoff 2,000 0 0
1,130,960 1,126,320 1,113,680
TC:3,370,960
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
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
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
June July August
48,000 57,000 62,000
R Units of Labor 700
Hire 0
Layoffs 100
Total Personnel 600
Required Units 48,000
Internal Production
48,000
Products Outsourced
0
Total Products 48,000
End inventory 0
Holding Cost 0
Backorder cost 0
Direct Labor cost 960,000
Hire/Layoff 20,000
980,000
We do not outsourceIn this strategy
June July August
48,000 57,000 62,000
R Units of Labor 700 600
Hire 0 113
Layoffs 100 0
Total Personnel 600 713
Required Units 48,000 57,000
Internal Production 48,000 57,040
Products Outsourced
0 0
Total Products 48,000 57,040
End inventory 0 40
Holding Cost 0 80
Backorder cost 0 0
Direct Labor cost 960,000 1,140,800
Hire/Layoff 50,000 22,600
1,010,000
57,000 x 2/160 = 713
1,163,480
June July August
48,000 57,000 62,000
R Units of Labor 700 600 713
Hire 0 113 62
Layoffs 100 0 0
Total Personnel 600 713 775
Required Units 48,000 57,000 61,960
Internal Production 48,000 57,040 62,000
Products Outsourced
0 0 0
Total Products 48,000 57,040 62,000
End inventory 0 40 40
Holding Cost 0 80 80
Backorder cost 0 0 0
Direct Labor cost 960,000 1,140,800 1,240,000
Hire/Layoff 50,000 22,600 12,400
1,010,000 1,163,480 1,252,480
TC:3,425,960
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.
Third strategy for the class example
• Modify workforce to a maximum of 50 (hire or layoff a max of 50), outsource any needed units
June July August
48,000 57,000 62,000
R Units of Labor 700
Hire 0
Layoffs 50
Total Personnel 650
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 numberOf workers that can beChanged is 50, so we haveTo keep extra workers
June July August
48,000 57,000 62,000
R Units of Labor 700 650
Hire 0 13
Layoffs 50 0
Total Personnel 650 663
Required Units 48,000 53,000
Internal Production
52,000
Products Outsourced
0
Total Products 52,000
End inventory 4,000
Holding Cost 8,000
Backorder cost 0
Direct Labor cost 1,040,000
Hire/Layoff 25,000
Outsource cost 0
TOTAL Cost 1,073,000
Given we really need53,000 unitsThe number of workers is53,000 x 2/160 = 663
June July August
48,000 57,000 62,000
R Units of Labor 700 650 663
Hire 0 13 50
Layoffs 50 0 0
Total Personnel 650 663 713
Required Units 48,000 53,000 61,960
Internal Production
52,000 53,040
Products Outsourced
0 0
Total Products 52,000 53,040
End inventory 4,000 40
Holding Cost 8,000 80
Backorder cost 0 0
Direct Labor cost 1,040,000 1,060,800
Hire/Layoff 25,000 2,600
Outsource cost 0 0
TOTAL Cost 1,073,000 1,063,480
We need 61,960 unitsThe number of workers is61,960 x 2/160 = 775But we can only hire 50
June July August
48,000 57,000 62,000
R Units of Labor 700 650 663
Hire 0 13 50
Layoffs 50 0 0
Total Personnel 650 663 713
Required Units 48,000 53,000 61,960
Internal Production
52,000 53,040 57,040
Products Outsourced
0 0 4,920
Total Products 52,000 53,040 61,960
End inventory 4,000 40 0
Holding Cost 8,000 80 0
Backorder cost 0 0 0
Direct Labor cost 1,040,000 1,060,800 1,140,800
Hire/Layoff 25,000 2,600 10,000
Outsource cost 0 0 123,000
TOTAL Cost 1,073,000 1,063,480 1,273,800
TC:3,410,280
We outsource thedifference ofwhat is required andwhat we can make61,960 – 57,040 = 4,920
Outsource cost25 x 4,920 = 123,000
Ch 11. Intro to MRPSection 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
Ch 11. Intro to MRPSection 11.4
MRP Basicso If we have a car made of a body and two axle
assemblies, we know we need 10 bodies and 20 Axle assemblies.
o If it takes one week to make the car, two to make the body and five to make the axle assemblies.
o W 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
carbody
w9w8w7w6w5w4w3w2w1