2. AP_Methods.ppt

The Graphical The Graphical Method to Aggregate Method to Aggregate PlanningPlanning

11ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

Aggregate Planning -- RECAPAggregate Planning -- RECAP Aggregate PlanningAggregate Planning: Intermediate-range : Intermediate-range

capacity planning, usually covering 3 to 18 capacity planning, usually covering 3 to 18 months.months.

The The GoalGoal of aggregate planning is to of aggregate planning is to achieve achieve a production plana production plan that will effectively utilize that will effectively utilize the organization’s resources to satisfy the the organization’s resources to satisfy the expected demand and Inventory expected demand and Inventory requirements, while requirements, while minimizingminimizing the sum of the sum of costs related to regular labor time, overtime, costs related to regular labor time, overtime, subcontracting, inventory holding costs, and subcontracting, inventory holding costs, and costs associated with changing the size of the costs associated with changing the size of the workforce.workforce.

Constraints Constraints involve the maximums of the involve the maximums of the number of workforce, inventories, overtime, number of workforce, inventories, overtime, and subcontracting.and subcontracting.


The Graphical Approach The Graphical Approach to Aggregate Planning to Aggregate Planning

Forecast the demand for each periodForecast the demand for each period Determine the capacity for regular Determine the capacity for regular

time, overtime, and subcontractingtime, overtime, and subcontracting Determine labor costs, hiring and firing Determine labor costs, hiring and firing

costs, and inventory holding costscosts, and inventory holding costs Consider company policies that may Consider company policies that may

apply to the worker or the stock levelsapply to the worker or the stock levels Develop alternative plans, and Develop alternative plans, and

examine their total costsexamine their total costs33ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

Determining the Determining the Aggregate Plan: Example Aggregate Plan: Example 11 Step #1: Collect relevant data:Step #1: Collect relevant data:

– Forecasts, inventory levels, desired Forecasts, inventory levels, desired final inventory levels, current and final inventory levels, current and future resource availability, future resource availability, production times and costs.production times and costs.


Example 1-Relevant Data: collect of the forecasts and capacity

Month Forecasted DemandJanuary 1100February 1500March 1800April 1600May 900June 1100

8000Total

Capacity: 27 employees @ 21 days/month @ 8 hours/day55

ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

Example 1: Beginning inventory levels, Production time and relevant costs

• Relevant costs:– Raw materials $100/unit– Inventory $12/unit/month– Backlogs $20/unit/month– Sub-contracting $45/unit– Hiring $200– Firing $250– Regular cost $12/hr (8 hrs/day)– OT cost $18/hr

• Production hours 3hrs/unit• Inventory:

– beg. inventory 400 units– safety stock 25% of demand 66

Example 1-Relevant Data: Production Requirements and Inventory levels

(1) (2)(3)=0.25*(2)

(4)=(2)+(3)-(1)(5)=(1)+(4)-(2)

Month BegDem.

Safety Quantity EndInv Stock produced Inventory

January 1100 975February 1500 1600

March 1800 1875April 1600 1550May 900 725

June 1100 11508000

275375

400225275

450

275375

400225275

450

400275

450400225

375

7875

P.S.: The Quantity Produced to meet the monthly requirement includes the forecasted demand and Safety Stock.Total Production Quantity= 7875 units

2000

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Determining the Aggregate Plan for Example1-- Next Step

Step # 2: Analyze per unit costs for each of the strategies:

– Determine the preference thresholds Estimates the cost of each option on a homogeneous

unit of measure (e.g. $/hr, $/month, $/unit) Compare between options using this unit cost to

determine at what moment an option becomes preferable over another (refer to Example 2 and Example 4 on how to compute Preference Thresholds)



Example:- Overtime (unit cost $6/hr {$18/hr – $12/hr})

Versus hire/fire ($450 = Cost of Hiring + Cost of Firing = $200 + $250 )

- Overtime (unit cost $54/unit{ $18/hr*3hr/unit} Versus Sub-Contracting (unit cost $45/unit)

- Idle time (unit cost $12/hr) Versus fire/hire ($450)

- Sub-contracting (unit cost $45/unit) versus Backlogs ($56/unit {$20/unit + ($12/hr*3hr)} 99


Step # 3: Develop and evaluate alternative plans:– Development of plans corresponding to dominant

strategies and evaluation of total costFor Example 1:

– The dominant strategies are: Chase Strategy and Level Strategy

– The Graphical method is used for the evaluation of total cost of the aggregate plan 1 using the Chase strategy and the aggregate plan 2 using Level Strategy

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Example 1: Chase Strategy

A possible option:Hire and layoff workers as needed to produce exact quantity to meet the monthly requirement (forecasted demand and Safety Stock). Inventory is not used to absorb demand fluctuations.

Prepare an aggregate Production plan using this option and determine its cost using the graphical method 1111


Example 1: Development and evaluation of aggregate plan 1 using the Chase Strategy

January February March April May June TotalProduction required (1) 975 1600 1875 1550 725 1150Hours of Prod. required (2)=(1)*3/hr/units 2925 4800 5625 4650 2175 3450Employee available (3) 27 18 29 34 28 13Hours/month/empl (4)=21day*8hr/day 168 168 168 168 168 168Employee required

(5)=(2)/(4) 17.42 28.6 33.5 27.7 12.95 20.54

Employees Hired (7) 0 11 5 0 0 8Cost of Hiring (8)=(7)*$200 -$ -$ 2200 -$ 1000 -$ -$ $ 1600 4,800$ Employees Fired (9) 9 0 6 15 0Cost of Firing (10)=(9)*$250 -$ 2250 -$ -$ 1,500$ -$3750 -$ 7,500$ Cost of Salaries (11)=(6)*(4)* $12/hr 36,288$ 58,464$ 68,544$ 56,448$ 26,208$ 42,336$ 288,288$

Total Cost: 324,588$

0

Total inventory Cost: 2000 units* 12 = $24,000

Employee required (Int.) 18 29 34 28 13 21


Level Strategy Maintain a constant production rate and workforce

level throughout the six month period. Inventory is build up during periods of less than average demand; alternatively, delivery lead time, Backlogs, may be allowed to grow during periods of high demand.

Maintain a Monthly production rate of 1313 units/month (Total Quantity Produced/6 = 7875/6 = 1312.5).

Maintain a constant workforce of 24 employees/month {(1313units * 3hr)/168 = 23.4 employees/month }

Prepare an aggregate plan using this option and determine its cost.


Example 1: Development and evaluation of aggregate plan 2 using the Level Strategy

January February March April May June Total

Demand 1100 1500 1800 1600 900 1100Production 1313 1313 1313 1313 1313 1310Ending Inventory 613 426 -61 -348 65 275Beginning Inventory 400 613 426 -61 -348 65Inventory 613 426 0 0 65 275Backlog 0 0 61 348 0 0Firing 3 0 0 0 0 0Cost Salaries $48,384 $48,384 $48,384 $48,384 $48,384 $48,384 $290,304Cost Firing $750 $0 $0 $0 $0 $0 $750Cost Inventory $7,356 $5,112 $0 $0 $780 $3,300 $16,548Cost Backlog $0 $0 $1,220 $6,960 $0 $0 $8,180

Total $315,782


Comments on Comments on Aggregate Plan 2 Aggregate Plan 2 using the Level Strategyusing the Level Strategy

In the “In the “ProductionProduction” Row- ” Row- June June “Column” you can “Column” you can have the following 2 options:have the following 2 options:

1.1. The quantity produced to be 1310 unitsThe quantity produced to be 1310 units (7875units – (1313units*5month))(7875units – (1313units*5month))

Then there is no need to compute the Cost of Raw Then there is no need to compute the Cost of Raw Materials, which is $787,500( 7875 units * Materials, which is $787,500( 7875 units * $100/units), cause it is a fixed cost for both plan 1 $100/units), cause it is a fixed cost for both plan 1 and plan 2 and plan 2

2.2. The quantity producedThe quantity produced is similar to other months, is similar to other months, and thus and thus 1313 units1313 units..Then you have to include the Cost of Raw materials Then you have to include the Cost of Raw materials in plan 1, which is $787,500; and the Cost of Raw in plan 1, which is $787,500; and the Cost of Raw material in plan 2, which is $787,800; cause the total material in plan 2, which is $787,800; cause the total number of units produced in each plan is variable.number of units produced in each plan is variable.1515

Comments on Comments on Aggregate Plan 2 using Aggregate Plan 2 using the Level Strategythe Level Strategy

Notice the followingNotice the following

Final Inventory (1) 613 426 -61 -348 65 275

Safety Stock (2)

275 375 450 400 225 275

Excess units in Safety Stock

(3)=max{ (1)-(2), 0}

338 51 0 0 0 0

January February March April May June


Determining the Aggregate Plan for Example 1- Last Step

• Choose the aggregate plan:– The best plan is chosen and implemented.

The Total Cost of aggregate plan 1 (Chase Strategy) = $324,588

The Total Cost of aggregate plan 2 (Level Strategy) = $315,782

Given these two options the plan to be implemented is the one with them minimum cost Aggregate plan 2 using the Level Strategy.


Example 2Example 2 Consider a company that experiences seasonal Consider a company that experiences seasonal

demand for its product family. demand for its product family. The company estimates that the typical unit of its The company estimates that the typical unit of its

product requires 20 hours to produce. Each product requires 20 hours to produce. Each employee is estimated to contribute 162 hours employee is estimated to contribute 162 hours per month, so each employee can produce about per month, so each employee can produce about

162 / 20 = 8.1 units per month on average. 162 / 20 = 8.1 units per month on average. Estimates indicate that it costs $300 to hire an Estimates indicate that it costs $300 to hire an

employee and $400 to lay off an employee. employee and $400 to lay off an employee. At least 1000 units should be available as work-in-At least 1000 units should be available as work-in-

process inventory and safety stock, and this process inventory and safety stock, and this amount will be on hand at the start of the amount will be on hand at the start of the planning horizon. It costs $6 per month to hold a planning horizon. It costs $6 per month to hold a unit in inventory. unit in inventory.

The demand for the next twelve months is given The demand for the next twelve months is given in the following table.in the following table. 1818ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

Example 2: DemandExample 2: Demand Month Forecast 1

2 3 4 5 6 7 8 9 0

11 12

1,600 1,400 1,200 1,000 1,500 2,000 2,500 2,500 3,000 3,000 2,500 2,100


Forecasted Demand Forecasted Demand

121110987654321

3000

2025

0

MONTH

F

OREC

AST


Example 2Example 2 Assume that the company begins Assume that the company begins

the planning year with a work-the planning year with a work-force of 250, and that employees force of 250, and that employees are paid $18 per hourare paid $18 per hour


Step # 2: Preference Step # 2: Preference ThresholdsThresholds If the demand is more than what you can satisfy If the demand is more than what you can satisfy

with your present work-force, is it more with your present work-force, is it more economical to use:economical to use:– Overtime? Overtime? – Part-time employees?Part-time employees?– Subcontracting?Subcontracting?– Increased inventory levels?Increased inventory levels?– Stockouts or backlogs?Stockouts or backlogs?

How long should you be able to use a new How long should you be able to use a new employee so that the cost of hiring is offset?employee so that the cost of hiring is offset?

If your work-force is larger than what the demand If your work-force is larger than what the demand requires, how much idle time can you tolerate requires, how much idle time can you tolerate before it is more economical to fire part of it?before it is more economical to fire part of it?

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Step # 2: Preference Step # 2: Preference ThresholdsThresholds At the beginning of month 1, our work-At the beginning of month 1, our work-

force is larger than needed. We can:force is larger than needed. We can:– Tolerate idle time (at a cost of $18 per Tolerate idle time (at a cost of $18 per

employee per hour or $2,916 per employee per hour or $2,916 per employee per month);employee per month);

– Fire some employees (and hire more Fire some employees (and hire more later);later);

– Build inventory for later use.Build inventory for later use. For idle time to be preferable over firing For idle time to be preferable over firing

then Hiring, the number of hours we keep then Hiring, the number of hours we keep an employee idle has to be less than:an employee idle has to be less than:.39

18700

hourper employeeper cost idlefiring ofcost + hiring ofcost

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Idle Time Versus Inventory Idle Time Versus Inventory BuildingBuildingIdle cost: $2,916/month per employeeIdle cost: $2,916/month per employee

Inventory cost: $48.6/month’s production per Inventory cost: $48.6/month’s production per employeeemployee

– The cost of one employee building inventory for one The cost of one employee building inventory for one month is $6 month is $6 8.1 = $48.6;8.1 = $48.6;

– The cost of one employee building inventory for two The cost of one employee building inventory for two months is $6 months is $6 8.1 8.1 2) = $48.6 2) = $48.6 2);2);

– The cost of one employee building inventory for n The cost of one employee building inventory for n months is $6 months is $6 8.1 8.1 2 + ... + n) = $48.6 2 + ... + n) = $48.6 2 + ... + n) = 2 + ... + n) = $48.6 x [($48.6 x [(n+1)*nn+1)*n]/2;]/2;

– For idle time to be preferable, the number n of months For idle time to be preferable, the number n of months we have one employee working to build it has to be we have one employee working to build it has to be such that such that $2,916$2,916n n $48.6 $48.6 2 + ... + n) 2 + ... + n)

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Idle Time Versus Inventory Idle Time Versus Inventory BuildingBuilding

# months# months Idle costIdle cost Inventory costInventory cost 11 $ 2,916 $ 2,916 $ 48.6*$ 48.6* 22 $ 5,832 $ 5,832 $ 145.8*$ 145.8* 33 $ 8,748 $ 8,748 $ 291.6*$ 291.6* 44 $ 11,664 $ 11,664 $ 486*$ 486* 55 $ 14,580 $ 14,580 $ 729*$ 729* 66 $ 17,496 $ 17,496 $ 1,020.6*$ 1,020.6* etc.etc. etc.etc. etc. etc. 119119 $347,004* $347,004* $347,004* $347,004* 120120 $349,920* $349,920* $352,836 $352,836

Idle time is preferable if an employee has to build up inventory Idle time is preferable if an employee has to build up inventory for more than 120 months (10 years)!! for more than 120 months (10 years)!!

Thus Inventory building is always better during the planning Thus Inventory building is always better during the planning period.period.


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Inventory building versus firing and Inventory building versus firing and hiringhiring

Inventory cost =$6/unit =$48.6/month’s Inventory cost =$6/unit =$48.6/month’s production per employeeproduction per employee

Firing and hiring cost = $700Firing and hiring cost = $700# months# months Inventory costInventory cost 11 $ 48.6*$ 48.6* 22 $ 145.8*$ 145.8* 33 $ 291.6*$ 291.6* 44 $ 486*$ 486* 55 $ 729$ 729

it is better to fire an employee if he has to be kept it is better to fire an employee if he has to be kept building inventory for 5 months or more.building inventory for 5 months or more.

Similarly, at the beginning of month 5, the Similarly, at the beginning of month 5, the demand begins to rise, and we can:demand begins to rise, and we can:– Use overtime or subcontracting;Use overtime or subcontracting;– Hire some new employees (and fire more Hire some new employees (and fire more

later);later);– Accept shortages or backlogs.Accept shortages or backlogs.

The cost of any two options can be The cost of any two options can be compared to come up quickly with an compared to come up quickly with an economical (maybe not optimal) aggregate economical (maybe not optimal) aggregate plan. plan.


Step # 2: Preference Step # 2: Preference ThresholdsThresholds

Example 2: Step # 3Example 2: Step # 3

We consider the three strategies:We consider the three strategies:– A chase strategy;A chase strategy;– A level strategy with a work-force A level strategy with a work-force

level of 250;level of 250;– A mixed strategy with a work-force A mixed strategy with a work-force

level of 201 employees for the first level of 201 employees for the first five months, and 285 employees five months, and 285 employees afterwards.afterwards.


Example 2: Chase Strategy Example 2: Chase Strategy

Month

Prod. Req.

WF Req.

WF

Change

Ending

Inv.

Inv. Cost

HR Cost

1 2 3 4 5 6 7 8 9

10 11 12

1,600 1,400 1,200 1,000 1,500 2,000 2,500 2,500 3,000 3,000 2,500 2,100

198 173 148 123 186 247 308 309 370 371 308 259

-52 -25 -25 -25 63 61 61 1

61 1

-63 -49 -9

1,003.8 1,005.1 1,003.9 1,000.2 1,006.8 1,007.5 1,002.3 1,005.2 1,002.2 1,007.3 1,002.1 1,000.0

$6,022.8 $6,030.6 $6,023.4 $6,001.2 $6,040.8 $6,045.0 $6,013.8 $6,031.2 $6,013.2 $6,043.8 $6,012.6 $6,000.0

$20,800 $10,000 $10,000 $10,000 $18,900 $18,300 $18,300 $300 $18,300 $300 $25,200 $19,600

$3,600 24,300 3,000 12,046.4 $72,278.4 $173,600

Example 2: Level Strategy Example 2: Level Strategy

Month

Demand

Production Ending

Inventory Holding

Cost 1 2 3 4 5 6 7 8 9 10 11 12

1,600 1,400 1,200 1,000 1,500 2,000 2,500 2,500 3,000 3,000 2,500 2,100

2,025 2,025 2,025 2,025 2,025 2,025 2,025 2,025 2,025 2,025 2,025 2,025

1,425 2,050 2,875 3,900 4,425 4,450 3,975 3,500 2,525 1,550 1,075 1,000

$8,550 $12,300 $17,250 $23,400 $26,550 $26,700 $23,850 $21,000 $15,150 $9,300 $6,450 $6,000

24,300 24,300 32,750 $196,500

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Example 2: Mixed StrategyExample 2: Mixed Strategy

Month

Employees

Monthly

Production

Demand

Ending Inventory

Inventory Holding

Cost

Cost of Changing Workforce

1 2 3 4 5 6 7 8 9

10 11 12

201 201 201 201 201 285 285 285 285 285 285 285

1,628.1 1,628.1 1,628.1 1,628.1 1,628.1 2,308.5 2,308.5 2,308.5 2,308.5 2,308.5 2,308.5 2,308.5

1,600 1,400 1,200 1,000 1,500 2,000 2,500 2,500 3,000 3,000 2,500 2,100

1,028.1 1,256.2 1,684.3 2,312.4 2,440.5 2,749.0 2,557.5 2,366.0 1,674.5 983.0 791.5 1,000.0

$6,168.6 $7,537.2 $10,105.8 $13,874.4 $14,643.0 $16,494.0 $15,345.0 $14,196.0 $10,047.0 $5,898.0 $4,749.0 $6,000.0

$19,600

$25,200

$14,000 3,000 24,300 24,300 19,814.9 $125,058 $58,800

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Example 2: SummaryExample 2: Summary

Chase Strategy

Level Strategy

Mixed Strategy

Inventory Cost WF Change Cost Labour Cost

$72,278.4 $173,600.0

$8,748,000.0

$196,500.0

$8,748,000.0

$125,058.0 $58,800.0

$8,748,000.0 Total Cost $8,993,878.4 $8,944,500.0 $8,931,858.0

32ADM 3301 ~ Rim Jaber

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The Transportation The Transportation MethodMethod


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The Transportation The Transportation MethodMethod

The transportation problems involve The transportation problems involve finding the lowest-cost plan for distributing finding the lowest-cost plan for distributing goods and services from a number of goods and services from a number of sources (supply points) to a number of sources (supply points) to a number of destinations (demand points).destinations (demand points).

We can use the transportation method as a We can use the transportation method as a way to obtain aggregate plans that would way to obtain aggregate plans that would match capacity with demand and ending match capacity with demand and ending inventory requirements at minimum costs. inventory requirements at minimum costs.


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The Transportation The Transportation Method –Cont’dMethod –Cont’d

The transportation method starts with the The transportation method starts with the development of a feasible solution, which development of a feasible solution, which is then sequentially tested and improved is then sequentially tested and improved until an optimal solution is obtained. The until an optimal solution is obtained. The major steps in the process are:major steps in the process are:1.1. Obtaining an initial solution/plan Obtaining an initial solution/plan 2.2. Testing for optimality (Stepping stone Method, Testing for optimality (Stepping stone Method,

MODI Method…)MODI Method…)3.3. Improving sub-optimal solutionsImproving sub-optimal solutions

We will discuss step 1 that is often We will discuss step 1 that is often optimal or near optimal, as for the last optimal or near optimal, as for the last two steps they will not be discussed. two steps they will not be discussed. ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

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Obtaining an Initial Obtaining an Initial PlanPlan Different methods are available for Different methods are available for

obtaining such a plan obtaining such a plan Focus on Focus on the intuitive lowest-cost the intuitive lowest-cost

approachapproach– Heuristic approach that yields an initial Heuristic approach that yields an initial

solution that is often optimal.solution that is often optimal. The method requires that the total The method requires that the total

supply is equal to the total demand supply is equal to the total demand – Balanced transportation problemBalanced transportation problem– Total supply > total demandTotal supply > total demand

We need to add an extra column entitled We need to add an extra column entitled “Excess” or “Unused Capacity” to the “Excess” or “Unused Capacity” to the Transportation table. Transportation table.


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Intuitive Lowest-cost Intuitive Lowest-cost ApproachApproach1.1. Identify the cell with the lowest cost.Identify the cell with the lowest cost.2.2. Allocate as many units as possible to Allocate as many units as possible to

that cell, and cross out the row or that cell, and cross out the row or column (or both) that is exhausted by column (or both) that is exhausted by this. Reduce the uncrossed row or this. Reduce the uncrossed row or column’s supply or demand by this column’s supply or demand by this amount.amount.

3.3. Find the cells with the next lowest cost Find the cells with the next lowest cost from among the not crossed out cells.from among the not crossed out cells.

4.4. Repeat steps (2) and (3) until all units Repeat steps (2) and (3) until all units have been allocated.have been allocated.

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Example 3Demand for pencils for the next four months is 560,000, 960,000, 1,140,000 and 700,000, respectively.The production capacity at regular time is 600 boxes (of 1,000 pencils each) for the first month, and 800 boxes for each of the other months. Overtime costs $25 per box more than the regular production cost. The cost of raw materials is $50 per box.The overtime capacity is 150 boxes during the first month and 200 boxes per month for the other months.The cost of holding inventory is $5 per unit per month, and no backlogs are accepted (Demand must be satisfied in the period it occurs; that is, no backordering is allowed.)The inventory at the beginning of month 1 is 200 boxes, and the required final inventory at the end of month 4 is 225 boxes.


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Transportation TableProduction Periods

Sales Periods End Inv

Unu Cap

Tot Cap

1 2 3 4 Beginning Inventory

1 Regular Overtime 2 Regular Overtime 3 Regular Overtime 4 Regular Overtime

Total Req

4040

. . . . . . . . . . . . . .Month 1 Month 2 Month 3 Month 4 Final Excess Capacity

Inventory

BeginningInventory

Month 1 Reg

Month 1 O-T

Month 2 Reg

Month 2 O-T

Month 3 Reg

Month 3 O-T

Month 4 Reg

Month 4 O-T

Demand

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. . . . . . . . . . . . . .Month 1 Month 2 Month 3 Month 4 Final Excess Capacity

Inventory

Beginning 0 5 10 15 20 200Inventory 200

Month 1 Reg 50 55 60 65 70 600360

Month 1 O-T 75 80 85 90 95 150150

Month 2 Reg 50 55 60 65 800

800

Month 2 O-T 75 80 85 90 200

Month 3 Reg800

Month 3 O-T

Month 4 Reg

Month 4 O-T

50 55 60

75 80 85

50 55

75 80

800

200

800

200

Demand 960 1140 700 225 365 3950

160

75

140

0

240

0

0

560360 0 160 0 340

80 080

260

200 0

60

60 140

0

700

0

100100

125

0

125

0

75

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Optimal Production Plan• Regular time production:

– 600 boxes in the first month, and 800 boxes in each of the following months

• Overtime production:– 60 boxes in month 2, 200 in month 3 and 125 in month 4

• Optimal cost:– Sum of the products of the quantities produced by the

unit costs (cost Reg.+ cost of O-T) plus cost of regular time production

– Optimal cost = $152,100 + $29,800 + cost of regular time

– Optimal cost = $181 900 + cost of regular timeADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

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Transportation Method Transportation Method • Variables and assumptions:

Let xijk be the number of units produced in period i to meet the requirements of period j using production type k (e.g. k = regular or overtime production or subcontracting );

Variable costs are linear; Demand is deterministic; Work-force levels are known for each period.

• The "transportation" costs cijk:– Production and inventory holding costs associated with

producing one unit in period i to meet demand of period j using production type k


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Transportation Method Transportation Method The sources (which have a The sources (which have a

certain “capacity”):certain “capacity”):– Initial inventory level;Initial inventory level;– Regular time production for each period; Regular time production for each period; – Overtime production for each period;Overtime production for each period;– Quantity subcontracted for each period.Quantity subcontracted for each period.

The sinks (which have a certain The sinks (which have a certain “demand”):“demand”):– Periods for which there is a demand;Periods for which there is a demand;– Final inventory level.Final inventory level.

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Possible Generalizations Possible Generalizations • Production of n different products: create n

columns per demand period in tableau.• Backlogging accepted: adjust cijk by adding backlog

cost for i > j.• Stockouts (insufficient capacity): add "lost sales"

row to transportation tableau.• Perishability of length t periods: xijk = 0 if j-i > t

(non-feasible boxes).• Subcontracting: add "subcontracting" row to

transportation tableau.• Learning effects: adjust production capacity

accordingly.ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

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Example 4

• Collect relevant data:– Forecasts, inventory levels, desired final

inventory levels, current and future resource availability, production times and costs.


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Example 4 – Relevant DataExample 4 – Relevant Data DemandDemand for product A for the next four months is for product A for the next four months is

255255, , 294294, , 321321 and and 301 units301 units. . The company has The company has 30 employees30 employees who work an who work an

average of average of 20 days per month20 days per month, , 8 hours a day8 hours a day, at , at a rate of a rate of $$20 per hour20 per hour. However, due to a 1-week . However, due to a 1-week lead time in the production process, there are only lead time in the production process, there are only 15 15 production daysproduction days left in left in Month 1Month 1. It is possible to hire . It is possible to hire more, or to lay off some workers, and these decisions more, or to lay off some workers, and these decisions are implemented at the beginning of each month. are implemented at the beginning of each month.

Each Each unitunit requires requires 20 hours20 hours of labour, and of labour, and overtimeovertime is limited to no more than is limited to no more than 40 hours per 40 hours per employee per monthemployee per month ( (30 hours for Month 130 hours for Month 1) and ) and costs costs $30 per hour$30 per hour. Initial inventory is . Initial inventory is 85 units85 units and the company wishes to have a final inventory of and the company wishes to have a final inventory of 50 units50 units at the end of the fourth month. at the end of the fourth month.

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Subcontracting (the work only: the company will provide the raw materials) is possible, but external capacity is limited to 12, 15, 15 and 17 units for the next four months respectively.

Costs for this problem are: Subcontracting: $650 per unit Inventory holding: $125 per unit per month Backlog: $250 per unit per month

(one month maximum)

Hiring: $500 per worker Laying off: $750 per worker


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Example 4: The Example 4: The Transportation MethodTransportation Method

Develop and evaluate Develop and evaluate alternative plans:alternative plans:– The Transportation methodThe Transportation method is used is used

for the evaluation of total cost of the for the evaluation of total cost of the aggregate production plan (Note that aggregate production plan (Note that hiring and firing is not an option in this hiring and firing is not an option in this plan)plan)


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. . . . . . . . . . . . . .Month 1 Month 2 Month 3 Month 4 Ending Excess Capacity

Inventory

0 125 250 375 500Begin. Inv. 85

REG. 0 125 250 375 500180

Month 1 O-T 600 725 850 975 110045

Sub-C 650 775 900 1025 115012

REG. 250 0 125 250 375240

Month 2 O -T 850 600 725 850 97560

Sub-C 900 650 775 900 102515

REG. 250 0 125 250240

Month 3 O - T 850 600 725 85060

Sub-C 900 650 775 90015

REG. 250 0 125240

Month 4 O -T 850 600 72560

Sub-C 900 650 77517

DEMAND255 294 321 301 50

1269

5151

. . . . . . . . . . . . . .Month 1 Month 2 Month 3 Month 4 Ending Excess Capacity

Inventory

0 125 250 375 500Begin. Inv. 85

REG. 0 125 250 375 500180

Month 1 O - T 600 725 850 975 110036 45

Sub-C 650 775 900 1025 115012 12

REG. 250 0 125 250 375240

Month 2 O - T 850 600 725 850 97560

Sub-C 900 650 775 900 102515

REG. 250 0 125 250240

Month 3 O - T 850 600 725 85060

Sub-C 900 650 775 90015

REG. 250 0 125240

Month 4 O - T 850 600 72560

Sub-C 900 650 77517

DEMAND255 294 321 301 50 48

1269

85 0

170

170 10

0

240 0

54

240 0

81

240 0

61

10

44

0

44 16

0

60

21

0

60

1

0

15

6

0

1

0

16

34

160

0

610

15

9

0

9 36

0

10

24

0

5252

Optimal Production Optimal Production PlanPlan(30 employees)(30 employees) Regular time: Regular time:

– Produce to full capacity each monthProduce to full capacity each month Overtime: Overtime:

– Produce 9 units in month 1 and 60 units Produce 9 units in month 1 and 60 units each subsequent month.each subsequent month.

Subcontracting: Subcontracting: – Do not subcontract in month 1, but use Do not subcontract in month 1, but use

the whole allowance in months 2 to 4.the whole allowance in months 2 to 4. Backlogs: Backlogs:

– Do not backlog.Do not backlog.ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

5353

The Cost of the Production The Cost of the Production Plan Plan

Optimal cost=Variable Costs+ workforce Optimal cost=Variable Costs+ workforce costcost

Workforce CostWorkforce Cost = 30*($20*8*20)*4 = = 30*($20*8*20)*4 = = = $384,000

Variable Costs is determined directly from Variable Costs is determined directly from the transportation table the transportation table

= 10*125 +Overtime cost + Subcontracting cost = 10*125 +Overtime cost + Subcontracting cost = $1250 + $122,400 + $38,175 = $161,825 = $1250 + $122,400 + $38,175 = $161,825

Optimal Cost = $161,825 Optimal Cost = $161,825 + $384,000 = $545 825 ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

5454

Example 4: Graphical Example 4: Graphical Method- Preference Method- Preference ThresholdsThresholds Analyze perAnalyze per unit costs unit costs for each of for each of

the strategiesthe strategies determine thedetermine the preference preference

thresholdsthresholds– Estimates the Estimates the cost of each optioncost of each option

on a on a homogeneous unit of homogeneous unit of measure measure (e.g.(e.g. $ $/hr, $/month, $/unit)/hr, $/month, $/unit)

– Compare between options using this Compare between options using this unit cost to determine at what unit cost to determine at what moment an option becomes moment an option becomes preferable over anotherpreferable over anotherADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

5555

Preference Thresholds: Preference Thresholds: Costs of Different OptionsCosts of Different Options

Idle cost:Idle cost:$3,200/month, $20/hour, or $3,200/month, $20/hour, or $400/unit $400/unit – One employee idle for a month One employee idle for a month Cost is one Cost is one

month salary: $20/hr month salary: $20/hr 8hr/day 8hr/day 20day/month = $3200/month20day/month = $3200/month

– One employee idle for an hour One employee idle for an hour $20/hour$20/hour– One employee idle for the production of one One employee idle for the production of one

unit unit Cost is: 20hr/unit Cost is: 20hr/unit $20/hr = $400/unit $20/hr = $400/unit Inventory cost:Inventory cost: $125/unit/month, or $125/unit/month, or

$1,000/month’s production/employee$1,000/month’s production/employee– Each employee produces 8 units per month Each employee produces 8 units per month

(8hr/day(8hr/day20day/month)/20 hr/unit =20day/month)/20 hr/unit =8 unit/month/employee 8 unit/month/employee 125 125 8 = $10008 = $1000

5656

Firing and hiring: Firing and hiring: ($1,250-$3,200/month)/employee($1,250-$3,200/month)/employee

– Cost of Firing+Cost of Hiring= Cost of Firing+Cost of Hiring= $500/employee +$750/employee = $500/employee +$750/employee = $1250/employee$1250/employee

– One month Salary is $3200/month/employeeOne month Salary is $3200/month/employee– Firing means saving one month salary, thus Firing means saving one month salary, thus

one way to look at Firing and hiring Cost is: one way to look at Firing and hiring Cost is: ($1,250-$3,200/month)/employee($1,250-$3,200/month)/employee

Hiring and firing: Hiring and firing: ($1,250+$3,200/month)/employee($1,250+$3,200/month)/employee– Hiring means paying one month salary as Hiring means paying one month salary as

well, which is an additional $3200/monthwell, which is an additional $3200/month

5757

Overtime cost: Overtime cost: $600/unit $600/unit – 20hr/unit 20hr/unit $30/hr = $600/unit $30/hr = $600/unit

Sub-contracting cost:Sub-contracting cost: $650/unit $650/unit Backlog cost:Backlog cost: $250/unit/month, or $250/unit/month, or

$2,000/month’s production/employee$2,000/month’s production/employee– Each employee produces 8 units per Each employee produces 8 units per

month month 8 unit/employee 8 unit/employee $250/unit/month = $250/unit/month = $2000/month’s production/employee$2000/month’s production/employee

Preference Thresholds: Preference Thresholds: Costs of Different Options Costs of Different Options – Cont’d – Cont’d

5858

Preferences Thresholds: Preferences Thresholds: Comparing Between Two Comparing Between Two OptionsOptions

Idle Time Versus Inventory BuildingIdle Time Versus Inventory Building Idle cost: $3,200/monthIdle cost: $3,200/month Inventory cost: $1,000/month’s productionInventory cost: $1,000/month’s production

– The cost of one employee building inventory for one The cost of one employee building inventory for one month is $125 month is $125 8 = $10008 = $1000

– The cost of one employee building inventory for two The cost of one employee building inventory for two months is $125months is $125882) = $10002) = $10002);2);

– The cost of one employee building inventory for n The cost of one employee building inventory for n months is $1000months is $10002+...+ n) = 2+...+ n) = $1000 $1000 x [(x [(n+1)*nn+1)*n]/2]/2;;

– For idle time to be preferable, the number n of months For idle time to be preferable, the number n of months we have one employee working to build it has to be we have one employee working to build it has to be such that such that $3200$3200n n $1000 $1000 2 + ... + n) 2 + ... + n)

5959

Idle Time Versus Idle Time Versus Inventory BuildingInventory Building

# months# months Idle costIdle cost Inventory costInventory cost 11 $3,200 $3,200 $ 1,000*$ 1,000* 22 $6,400 $6,400 $ 3,000*$ 3,000* 33 $9,600 $9,600 $ 6,000*$ 6,000* 44 $12,800 $12,800 $10,000*$10,000* 55 $16,000 $16,000 $15,000*$15,000* 66 $19,200* $19,200* $21,000$21,000Idle time is preferable if an employee has to Idle time is preferable if an employee has to build up inventory for more than 5 monthsbuild up inventory for more than 5 months


6060

Preferences Thresholds: Preferences Thresholds: Comparing Between Two Comparing Between Two OptionsOptions

Idle time versus firing and hiring:Idle time versus firing and hiring:– Idle cost: $20/hourIdle cost: $20/hour– Firing and hiring cost: $1,250Firing and hiring cost: $1,2501,250/20 = 62.5 hours1,250/20 = 62.5 hours

Firing and hiring is better if an employee Firing and hiring is better if an employee has to stay idle for more than 62.5 has to stay idle for more than 62.5 hourshours..

For idle time to be preferable, the number For idle time to be preferable, the number of hours we keep an employee idle has of hours we keep an employee idle has to be less than 62.5 hoursto be less than 62.5 hours

6161

Inventory building Inventory building versus firing and hiringversus firing and hiring Inventory cost =$125/unit Inventory cost =$125/unit

=$1,000/month’s prod=$1,000/month’s prod Firing and hiring cost = $1,250Firing and hiring cost = $1,250

# months# months Inventory costInventory cost 11 $1,000$1,000 22 $3,000$3,000

It is better to fire and then hire an It is better to fire and then hire an employee when needed, if he has to employee when needed, if he has to be kept building inventory for more be kept building inventory for more than 1 month.than 1 month.


6262

Preferences Thresholds: Preferences Thresholds: Comparing Between Two Comparing Between Two OptionsOptions Overtime versus sub-contractingOvertime versus sub-contracting

– Overtime cost = $600/unit Overtime cost = $600/unit – Sub-contracting cost = $650/unitSub-contracting cost = $650/unit

Overtime is always better.Overtime is always better. Overtime versus backlogsOvertime versus backlogs

– Overtime cost = $600/unitOvertime cost = $600/unit– Backlog cost = $250 + $400 = $650/unitBacklog cost = $250 + $400 = $650/unit

Overtime is always better.Overtime is always better.ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

6363

Overtime versus hiring and Overtime versus hiring and firingfiring

Overtime at $30/hr versus Hiring an Overtime at $30/hr versus Hiring an employee at $20/hr when needed than fire employee at $20/hr when needed than fire him later on.him later on. – Incremental overtime cost: $30/hour - Incremental overtime cost: $30/hour -

$20/hour = $10/hour$20/hour = $10/hour– Hiring and firing cost: $1,250Hiring and firing cost: $1,250– 1,250/10 = 125 hours1,250/10 = 125 hours

It is better to hire and fire if more than 125 It is better to hire and fire if more than 125 hours of overtime are neededhours of overtime are needed

For overtime to be preferable, the number of For overtime to be preferable, the number of hours of overtime has to be less than 125 hours of overtime has to be less than 125 hourshours ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

6464

Sub-contracting versus Sub-contracting versus backlogsbacklogs

Sub-contracting Sub-contracting to produce one unitto produce one unit versus backlogs versus backlogs by allowingby allowing back back orders (orders are taken in one period orders (orders are taken in one period and deliveries in the next month)and deliveries in the next month)

Sub-contracting cost: $650/unitSub-contracting cost: $650/unitBacklog cost: $250 + $400 = $650/unitBacklog cost: $250 + $400 = $650/unit Neither is better than the otherNeither is better than the other


6565

Sub-contracting versus hiring and Sub-contracting versus hiring and firingfiring

Sub-contracting Sub-contracting to produce one unitto produce one unit versus hiring versus hiring an employee to an employee to produce that unitproduce that unit and firing and firing him laterhim later– Hiring and firing cost = $1,250Hiring and firing cost = $1,250– The cost to produce one unit using The cost to produce one unit using

regular time is $400/unit, thus regular time is $400/unit, thus – Incremental cost of sub-contracting =Incremental cost of sub-contracting =$650-$400 = $250/unit$650-$400 = $250/unit– 1,250/250 = 5 units1,250/250 = 5 units

It is better to hire and fire if more than It is better to hire and fire if more than 5 units have to be sub-contracted.5 units have to be sub-contracted.


6666

Backlog versus hiring and Backlog versus hiring and firingfiring Backlog Backlog to meet unsatisfied demand to meet unsatisfied demand

by allowingby allowing back orders for a given back orders for a given monthmonth versus hiring versus hiring someone during someone during that month that month and firing and firing him later onhim later on– Backlog cost=$250/unit=$2,000/month’s Backlog cost=$250/unit=$2,000/month’s

prodprod– Hiring and firing cost = $1,250Hiring and firing cost = $1,250

It is better to hire and fireIt is better to hire and fireADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

6767

Example 4: Graphical Method Example 4: Graphical Method

Develop and evaluate Develop and evaluate alternative plans alternative plans – Development of plans corresponding Development of plans corresponding

to dominant to dominant strategiesstrategies and mixed and mixed strategies.strategies. Use the preferences thresholds as Use the preferences thresholds as

guidelines for mixed strategies.guidelines for mixed strategies.– Evaluate the total cost of each plan.Evaluate the total cost of each plan.– Choose the plan with the lowest cost Choose the plan with the lowest cost

option.option.ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

6868

Linear ProgrammingLinear Programming

xxii:: # of items to produce in regular time in period i,# of items to produce in regular time in period i, yyii:: # of items to produce in overtime in period i, # of items to produce in overtime in period i, zzii:: # of items supplied by subcontractors in period i,# of items supplied by subcontractors in period i, ssii:: # of items in stock at the end of period i, # of items in stock at the end of period i, rrii:: # of items produced late in period i + 1 for # of items produced late in period i + 1 for

demand demand of period i (i = 1, 2, 3),of period i (i = 1, 2, 3), vvii:: # of workers to hire at the beginning of period i,# of workers to hire at the beginning of period i, wwii:: # of workers to fire at the beginning of period i.# of workers to fire at the beginning of period i.


6969

Linear ProgrammingLinear ProgrammingMinimize:Minimize:

600 (y600 (y11 + y + y22 + y + y33 + y + y44) + 650 (z) + 650 (z11 + z + z22 + z + z33 + z + z44) + ) + 125 (s125 (s11 + s + s22 + s + s33 + s + s44) + 250 (r) + 250 (r11 + r + r22 + r + r33) + ) + 500 (v500 (v11 + v + v22 + v + v33 + v + v44) + 750 (w) + 750 (w11 + w + w22 + w + w33 + w + w44) +) +12,800(v12,800(v11-w-w11)+9,600(v)+9,600(v22-w-w22)+6,400(v)+6,400(v33-w-w33)+3,200(v)+3,200(v44-w-w44))

Subject to: Subject to: Capacity constraints (regular time):Capacity constraints (regular time):

xx11 180+6v 180+6v11-6w-6w11

xx22 240+8v 240+8v11+8v+8v22-8w-8w11-8w-8w22

xx33 240+8v 240+8v11+8v+8v22+8v+8v33-8w-8w11-8w-8w22-8w-8w33

xx44 240+8v 240+8v11+8v+8v22+8v+8v33+8v+8v44-8w-8w11-8w-8w22-8w-8w33-8w-8w4 4 ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

7070

Linear ProgrammingLinear Programming

Capacity constraints (overtime):Capacity constraints (overtime):yy11 45+1.5v 45+1.5v11-1.5w-1.5w11

yy22 60+2v 60+2v11+2v+2v22-2w-2w11-2w-2w22

yy33 60+2v 60+2v11+2v+2v22+2v+2v33-2w-2w11-2w-2w22-2w-2w33

yy44 60+2v 60+2v11+2v+2v22+2v+2v33+2v+2v44-2w-2w11-2w-2w22-2w-2w33-2w-2w4 4

Sub-contracting limit constraints:Sub-contracting limit constraints:zz11 12, 12, z z22 15, 15, z z33 15, 15, z z44 17 17


7171

ConstraintsConstraintsDo not fire more employees than you have:Do not fire more employees than you have:

ww11 30 30ww22 30 + v 30 + v11 - w - w11

ww33 30 + v 30 + v11 + v + v2 2 - w- w11 - w - w2 2

ww44 30 + v 30 + v11 + v + v2 2 + v+ v3 3 - w- w11 - w - w22 - w - w3 3

Demand constraints (with inventories and Demand constraints (with inventories and backlogs):backlogs):

xx11 + y + y11 + z + z11 + 85 + r + 85 + r11 = 255 + s = 255 + s11

xx22 + y + y22 + z + z22 + s + s11 + r + r22 = 294 + r = 294 + r11 + s + s22

xx33 + y + y33 + z + z3 3 ++ ss22 + r + r33 = 321 + r = 321 + r22 + s + s33

xx44 + y + y44 + z + z44 + s + s33 = 301 + r = 301 + r33 + s + s44

ss44 = 50 = 50 ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

7272

Optimal SolutionOptimal Solution xx11 = 180, x = 180, x22 = 280, x = 280, x33 = 320, x = 320, x44 = 352, y = 352, y22 = 4, = 4,

ss11 = 10, s = 10, s44 = 50, r = 50, r33 = 1, v = 1, v22 = 5, v = 5, v33 = 5, v = 5, v44 = 4. = 4. Manufacture at regular time 180, 280, 320 and 352 Manufacture at regular time 180, 280, 320 and 352

units in months 1, 2, 3, and 4, respectively, as well units in months 1, 2, 3, and 4, respectively, as well as 4 units at over-time in month 2.as 4 units at over-time in month 2.

Keep in inventory 10 units at the end of month 1 Keep in inventory 10 units at the end of month 1 and 50 units at the end of month 4.and 50 units at the end of month 4.

Backorder 1 unit in month 3.Backorder 1 unit in month 3. Hire 5 workers in month 2, 5 in month 3 and 4 in Hire 5 workers in month 2, 5 in month 3 and 4 in

month 4.month 4. Minimal variable cost = $109,950,Minimal variable cost = $109,950, Total cost = $109,950 + Total cost = $109,950 + $384,000$384,000 = = $493 950$493 950

Aggregate Planning in Services

Controlling the cost of labor is critical1. Accurate scheduling of labor-hours to

assure quick response to customer demand

2. An on-call labor resource to cover unexpected demand

3. Flexibility of individual worker skills4. Flexibility in rate of output or hours of

work7373


Most services use combination strategies and mixed plans

Five Service ScenariosFive Service Scenarios

RestaurantsRestaurants1.1. Smoothing the production processSmoothing the production process2.2. Determining the optimal workforce sizeDetermining the optimal workforce size

HospitalsHospitals– Responding to patient demandResponding to patient demand

National Chains of Small Service National Chains of Small Service FirmsFirms– Planning done at national level and at Planning done at national level and at

local levellocal level

Five Service ScenariosFive Service Scenarios

Miscellaneous ServicesMiscellaneous Services– Plan human resource requirementsPlan human resource requirements– Manage demandManage demand

Airline industryAirline industry– Extremely complex planning problemExtremely complex planning problem– Involves number of flights, number of Involves number of flights, number of

passengers, air and ground personnel, passengers, air and ground personnel, allocation of seats to fare classesallocation of seats to fare classes

– Resources spread through the entire Resources spread through the entire systemsystem

Law Firm Example

Table 13.9Table 13.9

Labor-Hours Required Capacity Constraints

(2) (3) (4) (5) (6)(1) Forecasts Maximum Number

ofCategory of Best Likely Worst Demand in Qualified

Legal Business (hours) (hours) (hours) People PersonnelTrial work 1,800 1,500 1,200 3.6 4Legal research 4,500 4,000 3,500 9.0 32Corporate law 8,000 7,000 6,500 16.0 15Real estate law 1,700 1,500 1,300 3.4 6Criminal law 3,500 3,000 2,500 7.0 12Total hours 19,500 17,000 15,000Lawyers needed 39 34 30

7676© 2011 Pearson Education, Inc. publishing as Prentice © 2011 Pearson Education, Inc. publishing as Prentice HallHall

Revenue (Yield) Revenue (Yield) ManagementManagementAllocating resources to customers at prices that will maximize yield or revenue

1. Service or product can be sold in advance of consumption

2. Demand fluctuates3. Capacity is relatively fixed4. Demand can be segmented5. Variable costs are low and fixed costs

are high

Demand Curve

Revenue (Yield) Management Revenue (Yield) Management ExampleExample

Figure 13.5

Passed-up contribution

Money left on the table

Potential customers exist who are willing to pay more than the $15 variable cost of the room, but not $150

Some customers who paid $150 were actually willing to pay more for the roomTotal

$ contribution =(Price) x (50rooms)=($150 - $15)x (50)=$6750

Price

Room sales

100

50

$150Price charged

for room

$15Variable cost

of room

Total $ contribution =(1st price) x 30 rooms + (2nd price) x 30 rooms =

($100 - $15) x 30 + ($200 - $15) x 30 =$2550 + $5550 = $8100

Demand Curve

Revenue (Yield) Management Revenue (Yield) Management ExampleExample

Figure 13.6

Price

Room sales

100

60

30

$100Price 1

for room

$200Price 2

for room

$15Variable cost

of room

Revenue (Yield) Revenue (Yield) Management MatrixManagement Matrix

Dura

tion

of u

seUn

pred

ictab

le

Pred

ictab

lePrice

Tend to be fixed Tend to be variableQuadrant 1: Quadrant 2:

Movies HotelsStadiums/arenas Airlines

Convention centers Rental carsHotel meeting space Cruise lines

Quadrant 3: Quadrant 4:Restaurants Continuing careGolf courses hospitals

Internet serviceproviders

Figure 13.7Figure 13.7 8080© 2011 Pearson Education, Inc. publishing as Prentice © 2011 Pearson Education, Inc. publishing as Prentice HallHall

Revenue (Yield) Revenue (Yield) Management ApproachesManagement Approaches▶ Airlines, hotels, rental cars, etc.Airlines, hotels, rental cars, etc.

▶ Tend to have predictable duration of service Tend to have predictable duration of service and use variable pricing to control availability and use variable pricing to control availability and revenueand revenue

▶ Movies, stadiums, performing arts Movies, stadiums, performing arts centerscenters▶ Tend to have predicable duration and fixed Tend to have predicable duration and fixed

prices but use seating locations and times to prices but use seating locations and times to manage revenuemanage revenue

Revenue (Yield) Revenue (Yield) Management ApproachesManagement Approaches▶ Restaurants, golf courses, ISPsRestaurants, golf courses, ISPs

▶ Generally have unpredictable duration of Generally have unpredictable duration of customer use and fixed prices, may use customer use and fixed prices, may use “off-peak” rates to shift demand and “off-peak” rates to shift demand and manage revenuemanage revenue

▶ Health care businesses, etc.Health care businesses, etc.▶ Tend to have unpredictable duration of Tend to have unpredictable duration of

service and variable pricing, often attempt service and variable pricing, often attempt to control duration of service to control duration of service

Making Revenue (Yield) Making Revenue (Yield) Management WorkManagement Work1. Multiple pricing structures must

be feasible and appear logical to the customer

2. Forecasts of the use and duration of use

3. Changes in demand

8484

What’s Needed for What’s Needed for Aggregate PlanningAggregate Planning The development The development andand application application

of any mathematically based of any mathematically based aggregate planning model aggregate planning model requires considerablerequires considerable- Time:- Time:

Problem definition,Problem definition, Model development,Model development, Model verification,Model verification, Model application;Model application;


8585

What’s Needed for What’s Needed for Aggregate PlanningAggregate Planning

– Expertise:Expertise: People who understand the problem,People who understand the problem, People who understand both the People who understand both the

modeling process, and the modeling process, and the specific model;specific model;

– Money:Money: Money to pay for all of the above,Money to pay for all of the above, Often requires funding for several Often requires funding for several

people for several months.people for several months.ADM 3301 ~ Rim JaberADM 3301 ~ Rim Jaber

Summary of Aggregate Planning Methods

TechniquesSolution

Approaches Important AspectsGraphical

methodsTrial and

errorSimple to understand and

easy to use. Many solutions; one chosen may not be optimal.

Transportation method of linear programming

Optimization LP software available; permits sensitivity analysis and new constraints; linear functions may not be realistic.

Table 13.8Table 13.88686© 2011 Pearson Education, Inc. publishing as Prentice © 2011 Pearson Education, Inc. publishing as Prentice HallHall

Summary of Aggregate Planning Methods

TechniquesSolution

Approaches Important AspectsManagement

coefficients model

Heuristic Simple, easy to implement; tries to mimic manager’s decision process; uses regression.

Simulation Change parameters

Complex; may be difficult to build and for managers to understand.

Table 13.8Table 13.88787© 2011 Pearson Education, Inc. publishing as Prentice © 2011 Pearson Education, Inc. publishing as Prentice HallHall

© 2011 Pearson Education, Inc. publishing as Prentice Hall© 2011 Pearson Education, Inc. publishing as Prentice Hall

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,

mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

Printed in the United States of America.

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