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Chapter 3 Aggregate Planning

Production Planning Environment

Competitors Behavior

Raw Material Availability

Market Demand

Planning for Production

External Capacity (outsourcing)

Economic Conditions

Current Physical Capacity

Current Inventory

Current Work Force

Required Production Activities

Planning Production

- Long-range plan (3-10 years) updated yearly
- Inputs aggregate forecasts (units) and current

plant capacity (hours) - Decision build new plant, expand an existing

plant, create new product line, expand, contract,

or delete existing product lines - Level of detail Very Aggregated
- Degree of uncertainty High

Planning Production

- Intermediate-range plan (6 month 2 years)

updated quarterly - Inputs aggregate capacity and product decisions

from the long-term plan, units are aggregated by

product line or family and plant department - Decision changes in work force, additional

machines, subcontracting, overtime - Level of detail Aggregated
- Degree of uncertainty Medium

Planning Production

- Short-range plan (1 week 6 month) updated

daily or weekly - Inputs decisions from the intermediate-term

plan, units are aggregated by particular product

and capacity available hours on a particular

machine, short range forecast, inventory levels,

work force levels, processes - Decision overtime and undertime, possibility of

not fulfilling all demand, subcontracting,

delivery dates for suppliers, product quality - Level of detail Very Detailed
- Degree of uncertainty Low

Production Planning Example

- Small company makes one product plastic cases

to hold CDs. - Two different types of mold are used to produce

top bottom. - Two halves are manually put together, placed in

the boxes shipped. - The injection molding machines can make 550

pieces per hour. - A worker can finish 55 cases in 1 hour (10

workers / machine) - Forecasts of demand 80,000 cases per month for

next year ? at 4 weeks/month the demand should be

20,000 cases per week. - Company runs 5 out of 7 days per week 4,000

cases per day needed. - Each worker can not work more than 8 hours per

day - 4,000/8 500 pieces per hour have to be

produced. - Plan 1 machine, 10 workers, 8 hours/day, 5

days/week

Introduction to Aggregate Planning

- Constant production rate can be satisfied with

constant capacity. - Work force is constant, production rate slightly

less that capacity of people machines good

utilization without overloading the facilities. - Raw material usage is also constant.
- If supplier and customers are also close,

frequent deliveries of raw material and finished

goods will keep inventory low. - How realistic is this example?
- Strategies to cope with fluctuating demand?

-- change the demand -- produce at constant rate

anyway -- vary the production rate -- use

combination of above strategies

Introduction to Aggregate PlanningInfluencing

Demand

- Do not satisfy demand during peak periods
- Capacity lt Peak demand , constant production rate
- Loss of some sales
- Japanese car manufacturers often take this

stance - Determine percentage of the market share
- Constant production is set at this level
- Sales personal expected to sell produced amount
- Ease of planning must be compared to lost revenue

Introduction to Aggregate PlanningInfluencing

Demand

- Shift demand from peak periods to non-peak

periods / create new demand for non-peak periods - Creating new demand can be done through

advertising or incentive programs (automobile

industry rebates telephone companys

differential pricing system) - Smoothing demand

Introduction to Aggregate PlanningInfluencing

Demand

- Produce several products with peak demand in

different periods - Products should be similar, so that manufacturing

them is not too different - Snowmobiles and jetskis same engines, similar

body work - Lawn-mowers snowblowers baseball football

equipment

Medium Range Planning Aggregate Production

Planning

- Establish production rates by major product

groups - by labor hours required or units of production
- Attempt to determine monthly work force size and

inventory levels that minimizes production

related costs over the planning period (for 6-24

month)

Relevant Costs Involved

- Regular time costs
- Costs of producing a unit of output during

regular working hours, including direct and

indirect labor, material, manufacturing expenses - Overtime costs
- Costs associated with using manpower beyond

normal working hours - Production-rate change costs
- Costs incurred in substantially altering the

production rate - Inventory associated costs
- Out of pocket costs associated with carrying

inventory - Costs of insufficient capacity in the short run
- Costs incurred as a result of backordering, lost

sales revenue, loss of goodwill costs of

actions initiated to prevent shortages - Control system costs
- Costs of acquiring the data for analytical

decision, computational effort and implementation

costs

Aggregate Units

- The method is based on notion of aggregate units.

- They may be
- Actual units of production
- Weight (tons of steel)
- Volume (gallons of gasoline)
- Dollars (value of sales)
- Fictitious aggregate units

Overview of the Problem

- D1, D2, . . . , DT - the forecasts of demand for

aggregate units over the planning horizon

(T periods) - Determine Wt - work force levels
- Pt - production levels
- It inventory levels
- Ht number of workers hired in this period
- Ft number of workers fired in this period
- Ot overtime production in units
- Ut undertime, worker idle time in units
- St number of units subcontracted from

outside - to minimize total costs over the T period

planning horizon

Example of fictitious aggregate units

- One plant produced 6 models of washing machines
- Model hrs. Price sales
- A 5532 4.2 285 32
- K 4242 4.9 345 21
- L 9898 5.1 395 17
- L 3800 5.2 425 14
- M 2624 5.4 525 10
- M 3880 5.8 725 06
- Question How do we define an aggregate unit here?

Price/hours 67.86 70.41 77.45 81.73 97.22 125.

0

Example (continued)

- Notice Price is not necessarily proportional to

worker hours (i.e., cost) why? - One method for defining an aggregate unit
- 0.32(4.2) 0.21(4.9) 0.17(5.1) 0.14(5.2)

0.10(5.4) 0.06(5.8) 4.856 worker hours - Forecasts for demand for aggregate units can be

obtained by taking a weighted average (using the

same weights) of individual item forecasts.

Example (continued)

- The washing machine plant is interested in

determining work force and production levels for

the next 8 months - Forecasted demands for Jan-Aug. are
- 420, 280, 460, 190, 310, 145, 110, 125
- Starting inventory at the end of December is 200

and the firm would like to have 100 units on hand

at the end of August - Find monthly production levels

Step 1 Determine net demand.(subtract

starting inventory from period 1 forecast and add

ending inventory to period 8 forecast)

- Month Forecasted Net Predicted Cum. Net
- Demand Demand

Demand - 1(Jan) 420 420-200220 220
- 2(Feb) 280 280 500
- 3(Mar) 460 460 960
- 4(Apr) 190 190 1150
- 5(May) 310 310 1460
- 6(June) 145 145 1605
- 7(July) 110 110 1715
- 8(Aug) 125 125100225 1940
- Starting inventory - 200 and final inventory -

100 units

Step 2. Graph Cumulative Net Demand to Find

Plans Graphically

Draw a straight line from first point 220 to 1940

units in month 8 The slope of the line is the

number of units to produce each month.

Determine a production plan that doesnt change

the size of the workforce over the planning

horizon. What to do?

Monthly Production 1940 / 8 242.5

(rounded to 243/month)

Any shortfalls in this solution?

How can we have a constant work force plan with

no stockouts?

- Using the graph, find the straight line that

goes through the origin and lies completely above

the cumulative net demand curve

From the previous graph, we see that cum. net

demand curve is crossed at period 3, so that

monthly production is 960/3 320. Ending

inventory each month is found from

- Month Cum. Net. Dem. Cum. Prod.

Invent. - 1(Jan) 220 320 100
- 2(Feb) 500 640

140 - 3(Mar) 960 960

0 - 4(Apr.) 1150 1280

130 - 5(May) 1460 1600

140 - 6(June) 1605 1920

315 - 7(July) 1715 2240

525 - 8(Aug) 1940 2560

620

However

- This solution may not be realistic for several

reasons - It may not be possible to achieve the production

level of 320 unit/mo with an integer number of

workers - Since all months do not have the same number of

workdays, a constant production level may not

translate to the same number of workers each

month - Some thoughts
- Final inventory is 620 units, not 100 units
- Cost of carrying inventory in each period

Production Strategies

- Constant production rate with Zero inventory
- stockouts
- carrying inventory
- Constant production rate with no stockouts
- carrying inventory
- extra inventory at the period T
- Mixed strategy
- few changes in the workforce allowed
- more flexibility
- lower costs

Example 2 (based on example 1)

- The plant has 38 workers who produced 630 units

in a period of 40 days - K 630/(3840) 0.414 ? average number of units

produced by one worker in one day - Assume we are given the following working days

per month - jan 22 apr 20 jul 18
- feb 16 may 21 aug 10
- mar 23 jun 17

Constant Work Force Production Plan 38 workers,

K .414

- Month wk Prod. Cum Cum Nt

End Inv - days Dem Level Prod Dem
- Jan 22 220 346 346

220 126 - Feb 16 280 252 598

500 98 - Mar 23 460 362 960

960 0 - Apr 20 190 315 1275

1150 125 - May 21 310 330 1605

1460 145 - Jun 22 145 346 1951

1605 346 - Jul 21 110 330 2281

1715 566 - Aug 22 125 346 2627

1940 687 - 100

Addition of Costs

- Holding Cost (per unit per month) 8.50
- Hiring Cost per worker

800.00 - Firing Cost per worker

1,250.00 - Payroll Cost ( per worker/day)

75.00 - Shortage Cost (unit short/month) 50.00

Cost Evaluation of Constant Work Force Plan

- Assume that the work force at end of Dec was 32
- Cost to hire 6 workers 6800 4,800
- Inventory Cost ? accumulate ending inventory

(126980125145346567687) 2,095 - (100 units at the end of the august in

included in 687 units inventory) - Hence Inventory Cost 20958.517,809.37
- Payroll cost
- (75/worker/day)(38 workers )(167days)

475,950 - Cost of plan
- 475,950 17,809.37 4800 498,559.37

Cost Reduction in Constant Work Force Plan

- In the original cum net demand curve, consider

making reductions in the work force one or more

times over the planning horizon to decrease

inventory investment.

Cost Evaluation of Modified Plan with One

Workforce Adjustment

- The modified plan calls for
- hiring 6 workers in Jan (to 38)
- reducing the workforce to 23 (from 38) at start

of April - cost of hiring is 4,800.00

4,800.00 - cost of layoffs is 18,750.00

0.00 - payroll cost is 356,700.00

475,950.00 - holding costs are 2,528.93

17,809.37 - shortage costs are 7,770.40

0.00 - The total cost of the modified plan is

390,548.33 - Original plan had cost of 498,559.37

Cost Evaluation of Modified Plan with Two

Workforce Adjustment

- The modified plan calls for
- hiring 6 workers in January
- firing 8 workers at start of April
- firing 12 workers at start of June
- Two One None
- cost of hiring is 4,800.00

4,800.00 4,800.00 - cost of layoffs is 25,000.00

18,750.00 0.00 - payroll cost is 353,850.00

356,700.00 475,950.00 - holding costs are 3,452.87

2,528.93 17,809.37 - shortage costs are 0.00

7,770.40 0.00 - The total cost 387,102.87

390,548.33 498,559.37

Constant Work Force Production Plan 38 workers,

K .414

- Month wk Prod. Cum Cum Nt

End Inv - days Dem Level Prod Dem
- Jan 22 220 346 346

220 126 - Feb 16 280 252 598

500 98 - Mar 23 460 362 960

960 0 - Apr 20 190 315 1275

1150 125 - May 21 310 330 1605

1460 145 - Jun 22 145 346 1951

1605 346 - Jul 21 110 330 2281

1715 566 - Aug 22 125 346 2627

1940 687 - 100

Cost Reduction in Constant Work Force Plan

Zero Inventory Plan (Chase Strategy)

- Idea
- change the workforce each month in order to

match the workforce with monthly demand as

closely as possible - This is accomplished by computing the units

produced by one worker each month (by multiplying

K by days per month) - Then take net demand each month and dividing by

this quantity. The resulting ratio is rounded up

and possibly adjusted downward.

- At the end of December there are 32 workers
- Period hired fired
- 1 7 Cost of

this - 2 17

plan - 3 6

461,732.08 - 4 25
- 5 13
- 6 20
- 7 4
- 8 13

Hybrid Strategies

- Use a combination of options
- Build-up inventory ahead of rising demand use

backorders to level extreme peaks - Finished goods inventories Anticipate demand
- Back orders lost sales Delay delivery or allow

demand to go unfilled - Shift demand to off-peak times Proactive

marketing - Overtime Short-term option
- Pay workers a premium to work longer hours

Hybrid Strategies

- Undertime Short-term option
- Slow the production rate or send workers home

early (lowers labor productivity, but doesnt tie

up capital in finished good inventories) - Reassign workers to preventive maintenance during

lulls - Subcontracting Medium-term option
- Subcontract production or hire temporary workers

to cover short-term peaks - Hire fire workers Long-term option
- Change the size of the workforce
- Layoff or furlough workers during lulls

Another APP Example

Quarter Sales Forecast (lb) Spring 80,000 Summer

50,000 Fall 120,000 Winter 150,000

- _________________________
- Hiring cost 100 per worker
- Firing cost 500 per worker
- Inventory carrying cost 0.50 per pound per

quarter - Production per employee 1,000 pounds per

quarter - Beginning work force 100 workers

Level Production Strategy

- Sales Production
- Quarter Forecast Plan Inventory
- Spring 80,000 100,000 20,000
- Summer 50,000 100,000 70,000
- Fall 120,000 100,000 50,000
- Winter 150,000 100,000 0
- 400,000 140,000
- Cost 140,000 pounds x 0.50 per pound 70,000

Chase Demand Strategy (Zero Inventory)

Hiring cost 100 per worker Firing cost

500 per worker Inventory carrying cost 0.50

per pound per quarter Production per employee

1,000 pounds per quarter Beginning work force

100 workers

- Sales Production Workers Workers Workers
- Quarter Forecast Plan Needed Hired Fired
- Spring 80,000 80,000 80 - 20
- Summer 50,000 50,000 50 - 30
- Fall 120,000 120,000 120 70 -
- Winter 150,000 150,000 150 30 -
- 100 50
- Cost (100 workers hired x 100) (50 workers

fired x 500) - 10,000 25,000 35,000

APP By Linear Programming

- Min Z 100 (H1 H2 H3 H4) 500 (F1 F2

F3 F4) 0.50 (I1 I2 I3 I4) - Subject to
- P1 - I1 80,000 (1) Demand
- I1 P2 - I2 50,000 (2) constraints
- I2 P3 - I3 120,000 (3)
- I3 P4 - I4 150,000 (4)
- P1 - 1,000 W1 0 (5) Production
- P2 - 1,000 W2 0 (6) constraints
- P3 - 1,000 W3 0 (7)
- P4 - 1,000 W4 0 (8)
- W1 - H1 F1 100 (9) Work force
- W2 - W1 - H2 F2 0 (10) constraints
- W3 - W2 - H3 F3 0 (11)
- W4 - W3 - H4 F4 0 (12)

where Ht hired for period t Ft fired for

period t It inventory at end of period

t Wt workforce at period t Pt units

produced at period t

Optimal Solutions to Aggregate Planning Problems

Via Linear Programming

- Dt the forecasts of demand for aggregate units

for period t, t 1 T - nt number of units that can be made by one

worker in period t - CtP cost to produce one unit in period t
- CtW cost of one worker in period t
- CtH cost to hire one worker in period t
- CtL cost to layoff one worker in period t
- CtI cost to hold one unit in inventory in

period t - CtB cost to backorder one unit in period t
- Wt number of workers available in period t
- Pt number of units produced in period t
- It number of units held in the inventory at the

end of period t - Ht number of workers hired in period t
- Ft number of workers fired in period t

Optimal Solutions to Aggregate Planning

Problems Via Linear Programming

- LP
- s.t constraints
- All variables are continuously divisible is it

a problem? - Solution Produce 214.5 of aggregated units
- Hire 56.38 workers
- IP
- s.t constraints
- Some variables are continuously divisible, some

are real number only problem?

Linear Programming Objective Function and

Constraints

- Number of constraints is 3T, number of unknown

is 5T - W0, I0, B0 initial workforce, initial

inventory/backlog

Linear Programming Product Mix Planning

- Multiple products processed on various

workstation - i an index of product, i 1, , m
- j an index of workstation, j 1, , n
- t an index of period, t 1, , T
- Dit the maximum demand for product i for period

t - dit the minimum sales allows of product i for

period t - aij time required on workstation j to produce

one unit of product i - cjt capacity of workstation j in period t in

the same units as aij - ri net profit from one unit of product i
- hi cost to hold one unit of product i for one

period in the inventory - Xit amount of product i produced in period t
- Sit amount of product i sold in period t
- Iit number of units of product i held in the

inventory at the end of period t

Linear Programming Product Mixed Planning

Objective Function and Constraints

This model can be used to obtain information

on demand feasibility bottleneck

location product mix

Product Mix Planning

- Demand feasibility
- Determine if the set of demands is

capacity-feasible - If SitDit then demand is feasible, otherwise

demand is infeasible - If could not find a feasible solution, then

lower bound dit is too high for a given capacity - Bottleneck locations
- Constraints restrict production on each

workstation in each period - Observe binding constraints to determine which

workstations limit capacity - Consistently binding workstation is a

bottleneck - Require close management attention
- Product mix
- If capacity is an issue, then model will try to

maximize revenue by utilizing products with high

net profit

Homework Assignment

- Read chapter 3, sections 1 4
- Problems
- 3.5
- 3.9 3.11
- 3.14 3.16

References

- Presentations by McGraw-Hill/Irwin and

Wilson,G.R. - Production Operations Analysis by S.Nahmias
- Factory Physics by W.J.Hopp, M.L.Spearman
- Inventory Management and Production Planning and

Scheduling by E.A. Silver, D.F. Pyke, R.

Peterson - Production Planning, Control, and Integration

by D. Sipper and R.L. Bulfin Jr.

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