Chapter 3 Aggregate Planning

1
Chapter 3 Aggregate Planning
2
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
3
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

4
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

5
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

6
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

7
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
8
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

9
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

10
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

11
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)

12
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

13
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

14
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

15
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
16
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.

17
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

18
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

19
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?
20
Monthly Production 1940 / 8 242.5
(rounded to 243/month)
Any shortfalls in this solution?
21
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

22
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

23
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

24
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

25
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

26
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

27
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

28
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

29
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.

30
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

31
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

32
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

33
Cost Reduction in Constant Work Force Plan
34
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.

35

• 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

36
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

37
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

38
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

39
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

40
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

41
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
42
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

43
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?

44
Linear Programming Objective Function and
Constraints

• Number of constraints is 3T, number of unknown
  is 5T
• W0, I0, B0 initial workforce, initial
  inventory/backlog

45
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

46
Linear Programming Product Mixed Planning
Objective Function and Constraints
This model can be used to obtain information
on demand feasibility bottleneck
location product mix
47
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

48
Homework Assignment

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

49
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.