Special Session 2 April 12,13

1
Special Session 2April 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

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 122) 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 Labor 550
Hire 28
Layoffs 0
Total Personnel 578




Starting workers
Workers to hire
Calculated before
14
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 make 578 workers x 160 hours/ 2 hrs
46,240
We do not outsource In this strategy
Sum of what we Can make and what We buy outsource
15
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 2 We have this if Ending Inventory gt0. If
we have Negative inventory (backorders) We have
0 here.
16
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
17
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
18
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
19
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 as We we have inventory From last
month 50,000 2,240 47,760
20
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 cant 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
• June July August
• 48,000 57,000 62,000
• Workforce is at 700. All other stay variables
  stay the same

22
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.

23
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
24
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
25
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
26
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
TC 3,370,960
1,130,960
1,126,320
1,113,680
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
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
We do not outsource In this strategy
980,000
31
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
57,000 x 2/160 713
1,163,480
1,010,000
32
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
TC 3,425,960
1,163,480
1,252,480
1,010,000
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
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 number Of workers that can be Changed is
50, so we have To keep extra workers
36
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 need 53,000 units The number of
workers is 53,000 x 2/160 663
37
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 units The number of workers
is 61,960 x 2/160 775 But we can only hire 50
38
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
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
TC 3,410,280
39
Results

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

40
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

41
Ch 11. Intro to MRPSection 11.4
Car

• MRP Basics
• If we have a car made of a body and two axle
  assemblies, we know we need 10 bodies and 20 Axle
  assemblies.
• If it takes one week to make the car, two to make
  the body and five to make the axle assemblies.
• 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

Body
Axle Assy (2)
w9
w8
w7
w6
w5
w4
w3
w2
w1
car
body
Axle Assy