1 BIS APPLICATION 2002-2003 MANAGEMENT INFORMATION SYSTEM Aggregate Planning and learning Curves Chapter outline: 1.The Nature of Aggregate Planning 2.Tradeoffs

1BIS APPLICATION 2002-2003 MANAGEMENT INFORMATION SYSTEM

Aggregate Planning and learning Curves

Chapter outline:Chapter outline:

1. The Nature of Aggregate Planning

2. Tradeoffs between Production and Inventory

3. Nonlinear cost and demand functions

• Introducing Overtime

• Introducing Double or Premium Time

• Tradeoffs between Level and Chase Strategies

4. Learning Curves

• Estimating Learning Curves

• Steep Learning Curves


Key Points

1. The term "aggregate" implies that planning is done for groups of products, or product types (i.e., product "families") rather than for specific or individual products.

2. The goal of aggregate planning is to achieve output objectives at the lowest possible cost.

3. Planners take into account projected demand, capacity, and costs of various options in devising an aggregate plan.

4. Among the variables available to planners are adjustments in output rate, employment level (including overtime/under time, and subcontracting).


5. Due to the nature of aggregate planning, it is seldom possible to structure a plan that is guaranteed optimal. Instead, planners usually resort to trial-and-error methods to achieve an acceptable plan.


Objectives of aggregate planning

1. Minimize costs / maximize profits -

2. Maximize Customer service -

3. Minimize Inventory Investments -

4. Minimize Changes in production rates -

5. Minimize Changes in workforce levels –

6. Maximize utilization of plant and equipment.


Among the aggregate planning strategies, Planners might try to:

1. Maintain a level work force and meet demand variations in some other manner.

2. Maintain a steady rate of output, and use some combination of inventories and subcontracting to meet demand variations.

3. Match demand period by period with some combination of work force variations, subcontracting, and inventories.

4. It is unlikely that planners would attempt to match demand period by period by varying employment levels alone because that would tend to be costly, disruptive, and result in low employee morale.


In order to translate an aggregate plan into meaningful terms for production, it must be disaggregated (i.e., broken down into specific product requirements) to determine labor, material, and inventory requirements.


The Aggregate Planning Strategies

The are two types of aggregate planning strategies:

•CHASE strategy

•LEVEL strategyChoosing a strategy usually depends on the cost entailed and company policy. In order to effectively plan, and in addition to knowledge of company policy, estimates of the following items must be available to planners:a. Demand for each period b. Capacity for each period c. Costs (regular time, overtime, subcontracting, backorders, etc.)


In this strategy, production is set to match forecasted demand. When the forecast goes UP: operations must react by increasing production, often by

•working overtime,

•adding a shift, or

•hiring new employees.

When the forecast goes DOWN: operations must react by lowering production, often by

•Working fewer hours

•Laying off employees

Chase Strategy


If X items are forecasted to be needed over a long period, a fixed percentage of this amount is produced each period. For example, if 12,000 units are forecasted to be needed over the next year, the firm will produce one-twelfth each month, or 1,000.

• When demand is lower than production, inventory increases

• When demand exceeds production, inventory decreases

• The steady production results in lower production costs, but the larger inventories required to avoid a stock out result in higher inventory costs

Level Strategy


The Nature of Aggregate Planning

• The CHASE and the LEVEL strategies are rarely used in their pure form.

• Hybrid of the two is usually more cost-effective and efficient

• What-if scenario management is ideal for analyzing tradeoffs and determining the best aggregate plan


Tradeoffs between Production and Inventory

Bricks and Tiles Corporation is making plans for the production of bricks for the coming year. The total requirements are 3000 bricks, and the corporation has enough facilities and labor to make 250 bricks a month

The corporation currently following the level strategy and makes bricks at a steady rate of 250 per month

Bricks and Tiles CorporationLevel Production, No Overtime

2$25500$10

1 2 3 4 5 6 7 8 9 10 11 12 TotalDemand 50 100 150 200 400 600 250 250 100 300 350 250 3000Make 250 250 250 250 250 250 250 250 250 250 250 250 3000Labor required 500 500 500 500 500 500 500 500 500 500 500 500 6000Cost of labor $12,500 $12,500 $12,500 $12,500 $12,500 $12,500 $12,500 $12,500 $12,500 $12,500 $12,500 $12,500 $150,000Start inventory 0 200 350 450 500 350 0 0 0 150 100 0End inventory 200 350 450 500 350 0 0 0 150 100 0 0Inventory cost $1,000 $2,750 $4,000 $4,750 $4,250 $1,750 $0 $0 $750 $1,250 $500 $0 $21,000Total cost $171,000

Hours per BrickLabor Cost per HourMaximum Straight Labor per MonthUnit Inventory Cost per Month

Yesterday End Inventory

(Unit Make+Start inventory)- Demand

(Start inventory+End inventory)* inventory cost /2


Introducing OvertimeAccording to Chase Strategy:

When demand forecast goes up ------------------------- production must be increase ( working overtime)

To meet the large demand, The bricks and Tiles Corporation will not build up inventories in advance, but rather it will produce the extra bricks using overtime.

Bricks and Tiles CorporationOvertime, No Inventory

2$25.0$37.5

500$10

1 2 3 4 5 6 7 8 9 10 11 12 TotalDemand 50 100 150 200 400 600 250 250 100 300 350 250 3000Make 50 100 150 200 400 600 250 250 100 300 350 250 3000Labor required 100 200 300 400 800 1200 500 500 200 600 700 500 6000Cost of labor $2,500 $5,000 $7,500 $10,000 $23,750 $38,750 $12,500 $12,500 $5,000 $16,250 $20,000 $12,500 $166,250Start inventory 0 0 0 0 0 0 0 0 0 0 0 0End inventory 0 0 0 0 0 0 0 0 0 0 0 0Inventory cost $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0Total cost $166,250

Unit Inventory Cost per Month

Hours per BrickLabor Cost per HourOvertime Labor Cost per HourMaximum Straight Labor per Month

If labor required < 500, labor required * 25, else (500 * 25)+ (labor required –500) * 37.3


Introducing Overtime

using a nonlinear functionThe result of introducing overtime is drop in the cost to $166,250, and a savings of $4,750.

But is this a better way to operate ?

Its NOT all the time. Some time this plan may cost more !!!!

This plan can be useful or operate better and result in a savings only if excess labor can be put to productive or when less labor can be used without cost.

To minimizing the total production cost

• The Cost Function must be determined.

•This function depends on whether overtime is required or not

•It’s a nonlinear function

•When the number of labor hours needed is under 500, the cost function is – N*25

•When the number of labor hours needed is over 500, the cost function consists of two parts: first part is the cost of straight time labor = 500 * 25

second part is the overtime labor cost = (N- 500)* 37.5

Total labor cost = 500 * 25 + (N-500)* 37.5Total labor cost = 500 * 25 + (N-500)* 37.5


Introducing Overtime

using a nonlinear function

Find the optimum solution (minimum cost) using Solver with a constraint in the value of the inventory which must be nonnegative

Bricks and Tiles CorporationOptimum Solution

2$25.0$37.5

500$10

1 2 3 4 5 6 7 8 9 10 11 12 TotalDemand 50 100 150 200 400 600 250 250 100 300 350 250 3000Make 50 100 150 250 350 600 250 250 150 250 350 250 3000Labor required 100 200 300 500 700 1200 500 500 300 500 700 500 6000Cost of labor $2,500 $5,000 $7,500 $12,500 $20,000 $38,750 $12,500 $12,500 $7,500 $12,500 $20,000 $12,500 $163,750Start inventory 0 0 0 0 50 0 0 0 0 50 0 0End inventory 0 0 0 50 0 0 0 0 50 0 0 0Inventory cost $0 $0 $0 $250 $250 $0 $0 $0 $250 $250 $0 $0 $1,000Total cost $164,750

Unit Inventory Cost per Month

Hours per BrickLabor Cost per HourOvertime Labor Cost per HourMaximum Straight Labor per Month

If labor required < 500, labor required * 25, else (500 * 25)+ (labor required –500) * 37.3


Introducing Double or Premium Time

• The method of solution for nonlinear problems is not as reliable as that for linear problems.

• Linear programming is a mathematical procedure for finding the one best solution to a problem described by a linear equation and subject to linear constraints.

• Not all overtime is treated the same. Often, overtime worked in the weekend, holidays, or on third shift has an extra cost.this overtime is called double time or premium time.


•The problem now is to balance the work assignments with inventory.

•To get ready for large demand, should they build inventories or wait and go on overtime and premium.

•Should follow a Chase or Level strategy

•When inventory cost are low, a substantial inventory is build up to help meet the demand

•When inventory costs are high, it is better to use more overtime and premium time




Bricks and Tiles CorporationCurrent Solution For Flower Pots

Cost Maximum$25.0 250$37.5 150$50.0

$53

1 2 3 4 5 6 7 8 9 10 11 12 TotalDemand 50 50 150 2,000 900 100 300 100 300 500 400 200 5,050Production

Regular 250 250 250 250 250 250 250 250 250 250 250 200 2,950Overtime 150 150 150 150 150 0 0 0 0 71 129 0 950Premium 0 0 0 1,093 57 0 0 0 0 0 0 0 1,150

Slack CapacityRegular 0 0 0 0 0 0 0 0 0 0 0 50 50Overtime 0 0 0 0 0 150 150 150 150 79 21 150 850

Start inventory 0 350 700 950 443 0 150 100 250 200 21 0End inventory 350 700 950 443 0 150 100 250 200 21 0 0Cost

Regular $18,750 $18,750 $18,750 $18,750 $18,750 $18,750 $18,750 $18,750 $18,750 $18,750 $18,750 $15,000 $221,250Overtime $16,875 $16,875 $16,875 $16,875 $16,875 $0 $0 $0 $0 $8,036 $14,464 $0 $106,875Premium $0 $0 $0 $163,931 $8,569 $0 $0 $0 $0 $0 $0 $0 $172,500

Inventory cost $875 $2,625 $4,125 $3,482 $1,107 $375 $625 $875 $1,125 $554 $54 $0 $15,822Total Cost $36,500 $38,250 $39,750 $203,038 $45,302 $19,125 $19,375 $19,625 $19,875 $27,340 $33,267 $15,000 $516,447

Unit Inventory Cost per MonthPremium Labor

Hours per Unit

Straight LaborOvertime Labor



• How to avoid solution that has overtime or double time, but not straight time?

• This could happened in an intermediate solution while Excel is searching for a solution, but not in the final solution, when costs are minimized.

• If additional straight-time capacity were available, the model shift overtime or double overtime work and lower costs even further.

• The same logic keeps premium overtime from being used before standard overtime

• When production quantities increase, cost seem to increase in a nonlinear manner


Tradeoffs between Level and Chase Strategies

The Bricks and Tiles Corporation is currently producing at a Level rate to meet current demand, but production has been well automated and workers do not need much training to run the machines.

Management is considering a reduction in capacity when the demand is low, and an expansion when demand is high; that is, management is considering a strategy to chase demand.

Such a strategy will reduce inventory cost, but introduces the the issue of hiring and firing workers

Chase strategy can has a bad effect on the morale of the worker

The corporation want to base their decision on a cost analysis



Bricks and Tiles CorporationCurrent Solution For Tiles

50200$25$10

$100

1 2 3 4 5Production 200 200 200 200 200Demand 50 100 200 300 350Increase Production 0 0 0 0 0Decrease Production 0 0 0 0 0Start Inventory 0 150 250 250 150End Inventory 150 250 250 150 0Cost of Production $10,000 $10,000 $10,000 $10,000 $10,000Cost of Hiring/Firing $0 $0 $0 $0 $0Inventory Cost $7,500 $20,000 $25,000 $20,000 $7,500Monthly Cost $17,500 $30,000 $35,000 $30,000 $17,500Total Cost $380,000

Inventory Cost per Tile

Cost per TileStarting Production LevelHiring Cost per TileFiring Cost per Tile

8 9 10 11 12 Totals200 200 200 200 200 2,400

50 50 500 250 400 2,4000 0 0 0 00 0 0 0 0

250 400 550 250 200400 550 250 200 0

$10,000 $10,000 $10,000 $10,000 $10,000 $120,000$0 $0 $0 $0 $0 $0

$32,500 $47,500 $40,000 $22,500 $10,000 $260,000$42,500 $57,500 $50,000 $32,500 $20,000 $380,000

• The yearly demand is 2,400 million tiles, and 200 million are produced each month.

• The current approach does not allow for hiring and firing

• As a result, inventories balloon during the year, and inventory costs are more than twice the actual cost of production



The problem is to minimize the total cost under the constraints, including the constraint of hiring and firing

Since production exactly matches demand, there is no inventory cost.

Modification on the model involve lumps hiring and firing into one categories

This solution allows for too many firings in any one period, so the model has to modify

Bricks and Tiles CorporationUnlimited Hiring and Firing

50200$25$10

$100

1 2 3 9 10 11 12 TotalsProduction 50 100 200 50 500 250 400 2,400Demand 50 100 200 50 500 250 400 2,400Increase Production 0 50 100 0 450 0 150Decrease Production 150 0 0 0 0 250 0Start Inventory 0 0 0 0 0 0 0End Inventory 0 0 0 0 0 0 0Cost of Production $2,500 $5,000 $10,000 $2,500 $25,000 $12,500 $20,000 $120,000Cost of Hiring/Firing $1,500 $1,250 $2,500 $0 $11,250 $2,500 $3,750 $31,250Inventory Cost $0 $0 $0 $0 $0 $0 $0 $0Monthly Cost $4,000 $6,250 $12,500 $2,500 $36,250 $15,000 $23,750 $151,250Total Cost $151,250





Modification on the the following model involve place a limit on firings only because the management do not desire to limit hiring.

Bricks and Tiles CorporationLimited Firing

50200$25$10

$100

1 2 3 4 9 10 11 12 TotalsProduction 150 250 250 200 175 375 325 325 2,400Demand 50 100 200 300 50 500 250 400 2,400Increase Production 0 100 0 0 125 200 0 0Decrease Production 50 0 0 50 0 0 50 0Start Inventory 0 100 250 300 0 125 0 75End Inventory 100 250 300 200 125 0 75 0Cost of Production $7,500 $12,500 $12,500 $10,000 $8,750 $18,750 $16,250 $16,250 $120,000Cost of Firing $500 $0 $0 $500 $0 $0 $500 $0 $3,000Cost of Hiring $0 $2,500 $0 $0 $3,125 $5,000 $0 $0 $10,625Inventory Cost $5,000 $17,500 $27,500 $25,000 $6,250 $6,250 $3,750 $3,750 $110,000Monthly Cost $13,000 $32,500 $40,000 $35,500 $18,125 $30,000 $20,500 $20,000 $243,625Total Cost $243,625





Here, cost of firing is limited to $500, which corresponds to ten firings. The results can be summarized as follows:

Aggregate Plan Cost

Steady Production $380,000

Unlimited Firing $151,250

Limited Firing $243,625

___________________________________________________________________


Learning Curves

The general concept of learning curve theory is that the time required to produce a second units of product is less then that required for the first unit, the third unit can be produced faster than the second, and so on.

Learning curves apply not only to an individual learning a new task but also to an organization learning to produce a new product or use a new production process


Learning Curves

Learning curve theory provides the formula for any learning rate.

Formula to calculate learning curve:

Exponent = LN(Learning rate)/LN(2)

Time to make the nth unit = (Time to make the first unit) * n Exponent

Example:

If the first unit takes 100 hours with a 90% learning rate, and you want to predict the time it will take to make unit number 4 then:

Exponent = LN(Learning rate)/LN(2) = -0.152

Time to make the 4th unit = 100 * 4 ^-0.152 = 81 hours


Learning Curves

Time for First Unit 100Learning Rate 75%Exponent -0.41504

10 38.455920 28.841930 24.374740 21.631450 19.718060 18.281070 17.148180 16.223690 15.4496

100 14.7885110 14.2150120 13.7108130 13.2628140 12.8610150 12.4980160 12.1677170 11.8653180 11.5872190 11.3300200 11.0914

Learning Curve

0

10

20

30

40

501

0

30

50

70

90

11

0

13

0

15

0

17

0

19

0

The following worksheet calculate any learning curve and display a chart of the

curve


Estimating Learning Curves

Estimated Learning Rate 86.28%Exponent -0.21296

Measured Completion Time (minutes)

ObservationEstimated

CurveSquared

Deviations AverageIndividual

#1Individual

#2Individual

#31 10.83 0.00 10.83 10.65 9.90 11.13

10 6.63 10.65 9.90 10.15 9.37 10.1120 5.72 10.24 8.92 9.13 8.44 9.1430 5.25 7.75 8.03 8.18 7.57 8.2340 4.94 5.18 7.21 7.31 6.80 7.3950 4.71 3.17 6.49 6.59 6.11 6.6760 4.53 1.73 5.85 5.97 5.53 5.9770 4.38 0.75 5.25 5.39 5.01 5.3280 4.26 0.22 4.72 4.88 4.55 4.7590 4.15 0.01 4.24 4.37 4.12 4.24

100 4.06 0.05 3.83 3.92 3.72 3.78110 3.98 0.28 3.45 3.50 3.36 3.35120 3.91 0.65 3.10 3.13 3.02 2.99130 3.84 1.10 2.79 2.83 2.68 2.68140 3.78 1.61 2.51 2.52 2.36 2.44150 3.73 2.13 2.27 2.30 2.13 2.24160 3.68 2.67 2.04 2.12 1.94 2.00170 3.63 3.24 1.83 1.87 1.71 1.76180 3.58 3.73 1.65 1.66 1.51 1.59190 3.54 4.30 1.47 1.45 1.34 1.40200 3.51 4.84 1.31 1.34 1.17 1.28

Total Deviation 64.30

To estimate the learning rate for individuals, the curve-fitting (cubic function), can be applied to existing data for individuals who have previously learned the same task

1- Average the data of a ten individuals to complete a task at various skills levels

2- the curve estimate using observation as x and exponent as coefficient

3- compute the squared deviations and total squared deviation

4- Use the Excel Solver to minimize the total squared deviation by varing the learning rate

Estimating the learning rate for individuals learning a new task


Estimating Learning CurvesEstimating the firm learning rate

• Naturally, the firm does not learn the same task more than once, however, learning rates for similar task can be used

• Since the organization is made up of many individuals, variation in learning tend to average out, so the firm’s learning rate tends to be more consistent over time and tasks than individual learning rates.


Steep Learning Curves

Learning Curve

02468

1012

10 30 50 70 90 110

130

150

170

190

Learning Curve

0

20

40

60

80

10 30 50 70 90 110

130

150

170

190

• A Learning curve for a process with a 50% learning rate

•This process is very easy to learn

•Each time you double production, you cut the production time in half

• The curve is very steep

• A Learning curve for a process with a 90% learning rate

•This process is leaned much more slowly

•Each doubling of production gives only 10% reduction in processing time

•The curve much less steep

Documents

1 BIS APPLICATION 2002-2003 MANAGEMENT INFORMATION SYSTEM Aggregate Planning and learning Curves Chapter outline: 1.The Nature of Aggregate Planning 2.Tradeoffs