Special Session 2 April 12,13

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


• 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– ..


• 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)


• 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


• 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


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


Hire 28

Layoffs 0

Total Personnel 578





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


Hire 28

Layoffs 0

Total Personnel 578





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


Hire 28

Layoffs 0

Total Personnel 578





End inventory 2,240

Holding Cost 4,480

Backorder cost 0


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





End inventory 2,240

Holding Cost 4,480

Backorder cost 0


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


Hire 28 0

Layoffs 0 0


Required Units 44,000 47,760




End inventory 2,240

Holding Cost 4,480

Backorder cost 0


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


Hire 28 0

Layoffs 0 0



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


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


Hire 0

Layoffs 4

Total Personnel 696





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


Hire 0

Layoffs 4

Total Personnel 696





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


Hire 0 0

Layoffs 4 0




Products Outsourced 0 0


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


Hire 0

Layoffs 100

Total Personnel 600


Internal Production

48,000

Products Outsourced

0


End inventory 0

Holding Cost 0

Backorder cost 0


Hire/Layoff 20,000

980,000

We do not outsourceIn this strategy

June July August

48,000 57,000 62,000


Hire 0 113

Layoffs 100 0




Products Outsourced

0 0


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


Hire 0 113 62

Layoffs 100 0 0


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


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


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


Hire 0 13

Layoffs 50 0



Internal Production

52,000

Products Outsourced

0


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


Hire 0 13 50

Layoffs 50 0 0


Required Units 48,000 53,000 61,960

Internal Production

52,000 53,040

Products Outsourced

0 0


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


Hire 0 13 50

Layoffs 50 0 0


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


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

Results

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

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

Special Session 2 April 12,13

Documents

Transcript of Special Session 2 April 12,13