Aggregate Production Planning

Aggregate Production Planning (APP)

Why aggregate planning

w Details are hard to gather for longer horizons

n Demand for Christmas turkeys at Tom Thumb’s vs Thanksgiving turkeys

w Details carry a lot of uncertainty: aggregation reduces variability

n Demand for meat during Christmas has less variability than the total variability in the demand for chicken, turkey, beef, etc.

w If there is variability why bother making detailed plans, inputs will change anyway

n Instead make plans that carry a lot of flexibility

n Flexibility and aggregation go hand in hand

Aggregate Planningw Aggregate planning: General plan

n Combined products = aggregate product

l Short and long sleeve shirts = shirt

w Single product

n Pooled capacities = aggregated capacity

l Dedicated machine and general machine = machine

w Single capacity

n Time periods = time buckets

l Consider all the demand and production of a given month together

w Quite a few time buckets [Jan/Feb… or IQ/IIQ/…]

refers to intermediate range planning covering 2 to 24 months … a “big picture” look at planning aimed at balancing capacity and demand


Forecast, Production Plan and Inventory

Recall from the forecasting presentation, future demand is forecasted,

6 Month Forecast1 2 3 4 5 6

Forecast Demand 10 8 12 14 10 8

Production Plan 10 10 10 12 12 10then a manufacturing production plan is developed,

Inventory 10 10 12 10 8 10 12resulting in an inventory plan

which can be evaluated against financial objectives.

Aggregate Production Planning Horizon

Group level forecast

Decision Areas

Staff Planning

Production planning

Master production scheduling

Purchasing (material and equipment)

Distribution

Short Range Intermediate Range Long Range

Now 2 months - 2 years

APP

Planning Sequence

Master scheduleEstablishes short range schedules for specific

products

Aggregate Production PlanEstablishes intermediate

range production capacity for product groups

Corporatestrategies

and policies

Economic,competitive,and political conditions

Aggregatedemand

forecasts

Business PlanEstablishes long range production and capacity strategies

Overview of Manufacturing

Planning Activities

Month J F M A M J J A S

# motors 40 25 50 30 30 50 30 40 40

Month J F M A M J J A S

# AC Motors

5 hp 15 - 30 - - 30 - - 10

25 hp 20 25 20 15 15 15 20 20 20

# DC Motors

20 hp - - - - - - 10 10 -

# WR motors

10 hp 5 - - 15 15 5 - 10 10

Master Schedule

Aggregate Plan

Note: Aggregate plan expresses the end product as “motors”

Note: Master schedule specifies precisely how many of which type (or size) of motors will be produced, and when – to plan for the material and capacity requirements

Example

Aggregate Production Planning is a planning process which establishes a company-wide game plan for allocating resources (people, equipment, etc.) and economically meeting demand. APP

. Matches market demand to company resources

. Expresses intermediate range demand, resources, and capacity in general terms – product groups or families of products rather than at the detail product level (e.g. televisions vs 21”, 27”, 32”, etc.)

. Allows planners more time to deal with short range and day-to-day issues

. Provides information to allow for flexibility … because of forecast inaccuracy intermediate plans do not have to be “locked in” too soon

Aggregate Production Planning

Supplier capabilities Storage capacity Materials availability

Materials

Current machine capacities Plans for future capacities Work-force capacities Current staffing level

Operations

New products Product design changes Machine standards

EngineeringLabor-market conditions Training capacity

Human Resources

Cost data Financial condition of firm

Accounting & Finance

APP

Customer needs Demand forecasts Competition behavior

Distribution & Marketing

Managerial Inputs to APP

The Process of APP:

. Use the company forecast to determine demand for each period

. Determine capacities (regular time, overtime, subcontracting, etc) for each period

. Identify company or departmental policies that are pertinent(employment policies, safety stock policies, etc.)

. Determine unit costs for regular time, overtime, subcontracting, holding inventories, layoffs, and other relevant costs

. Develop alternatives with cost for each

. If satisfactory plans emerge select the one that best satisfies objectives; otherwise, continue with the previous step.

Aggregate Production Planning Process

PRODUCTIONPLANNING

CAPACITY

WORK FORCE

PRODUCTION

INVENTORY

INTERNAL

EXTERNAL

EXTERNALCAPACITY

COMPETITIONRAW MATERIAL

SUPPLYDEMAND

ECONOMICCONDITIONS

Production Planning Environment

Aggregate Planning ProcessAggregate Planning Process

No

APP Process

Determine requirements for planning horizon

Identify alternatives, constraints and costs

Prepare prospective plan for planning

horizon

Is the plan acceptable?

Yes

Implement and update the plan

Move ahead to the next planning session

Aggregate Planning Objectives

The overriding objective of Aggregate Production Planning is to consider company policies and management inputs related to operations, distribution & marketing, materials, accounting & finance, engineering and human resources to

. Minimize costs & maximize profits

. Maximize customer service

. Minimize inventory investment

. Minimize changes in production rates

. Minimize changes in work-force levels

. Maximize utilization of plant and equipment


Operations Managers try to determine the best way to meet forecasted demand by adjusting various capacity.

Strategies for meeting uneven supply & demand

Level capacity - maintain a level (steady rate) of production output while meeting variations in demand – [that is, use inventory to absorb fluctuations in demand]

Aggregate Planning … balancing demand/capacity

Time

Level production capacity

Demand

Uni

ts

Effect Of “Level Output Strategy”

a level output strategy – make the same amount each period

6 Month ForecastPlanning Period 1 2 3 4 5 6Forecasted Demand 10 8 12 14 10 8

Production Plan 10 10 10 10 10 10

inventory is used to “buffer” the difference in capacity and demand

Inventory Position 10 10 12 10 6 6 8

Leveling strategies try to keep output (production levels) constant and use other methods for dealing with the fluctuating demand. These strategies may be either aggressive or reactive, or a combination of both.

One popular way is to build inventory in low demand times and draw it down in high demand times.

Extreme AP Strategies- Constant Output and Constant Capacity

Inventory

DemandCapacity = Output

Cost Increased

Inventory Holding Cost/ Back-Order Cost

Costs Minimized

Hiring & Firing Cost/ Subcontracting CostOvertime- Idle Time Cost

Use When Inventory Holding Cost is LowFor High Capital Intensive Operations

Examples Water Purification Plant

Extreme AP Strategy- Variable Output and Constant Capacity

Idle TimeOvertime

Output Capacity

Demand

Cost Increase

Overtime and Idle Time CostSubcontracting Cost

Costs Minimized

Inventory Holding CostHiring/ Firing Cost

Use When Inventory is Impossible or ExpensiveFor High Skilled Labor Intensive Operations

Examples Law Firms, Accounting Service


Chase demand - match production capacity to demand by adjusting capacity to the demand for the period


Time

Uni

ts

Production chases demand

Demand

Effect Of “Chase Demand Strategy”

a chase demand strategy – production is adjusted to meet demand

6 Month ForecastPlanning Period 1 2 3 4 5 6Forecasted Demand 10 8 12 14 10 8

Production Plan 10 8 12 14 10 8

inventory remains constant

Inventory Position 10 10 10 10 10 10 10

Cost Increase

Hiring & Firing Cost/ Idle Capacity Cost

Costs Minimized

Inventory Holding Cost/ Subcontracting Cost

Overtime and Idle Time Cost

Use Inventory is Impossible or Expensive

Low Skilled Labor Operations

There is a match between Labor Availability and the Need for Labor

Examples Entertainment Center (Disney World), Farm Workers

Chase demand (Ideal Case)- change workforce levels so that production matches demand


Demand Options … when capacity and demand are not the same

. Pricing can be adjusted to affect demand (e.g. lower rates in off season)

. Promotions (e.g. advertising, consumer marketing campaigns)

. Back Orders - shift demand to another period by taking orders in one period and promising deliver in a future period when capacity is available (may not create a satisfied customer)

. New demand - create a new need for capacity by producing a product during slack times to utilize resources (e.g. snow blower company produces leaf blowers in off season) .



Capacity Options … when capacity and demand are not the same

. Hire or lay-off workers (may create morale and employment problems

. Use overtime or under-time

. Part-time workers

. Manage capacity with inventory (e.g. let inventories build during periods of low demand or deplete during periods of high demand)

. Subcontract temporary capacity


Level Strategy

Chase Strategy

Production equals

demand

Production rate is constant

Strategy Details

APP Strategies - Pure StrategiesCapacity Options — Change Capacity [Reactive Strategies]

1) changing inventory levels

2) varying work force size by hiring or layoffs

3) varying production capacity through overtime or idle time

4) subcontracting

5) using part-time workers

The above five pure strategies are called “passive strategies” because they do not try to change demand but attempt to absorb the fluctuations in it.

Reactive Strategy ExamplesReactive Strategy Examples

w Anticipation inventory is a reactive strategy. It can absorb uneven rates of demand or supply. Thus it is also a leveling strategy .

w Workforce adjustment (use of overtime, under-time or subcontracting) is reactive.

n If you are varying your workforce it is also chase. If you subcontract, it is leveling.

w Scheduling employee vacations for low demand times is a reactive strategy.

w Using backorders in high-demand times is a leveling and a reactive strategy.

¨ Demand Options — change demand [Proactive Strategies]

6) influencing demand

7) backordering during high demand periods

8) Counter seasonal product mixing

APP Strategies - Pure Strategies

The above three pure strategies are called “active strategies” through which firms try to influence the demand pattern to smooth out its changes over the planning period.

ww The purpose of aggressive strategies is to influence The purpose of aggressive strategies is to influence demand in order to smooth out (demand in order to smooth out (levellevel) production or ) production or service flow. service flow. ((All aggressive strategies are All aggressive strategies are levelingleveling.).)

ww Product Promotions Product Promotions are designed to increase sales using are designed to increase sales using creative pricing. Doing so in a low demand period is a creative pricing. Doing so in a low demand period is a leveling leveling strategy.strategy.

nn OffOff--season rates: (January retail sales) (slowseason rates: (January retail sales) (slow--season season resort rates)resort rates)

ww Complementary productsComplementary products: Services or products that have : Services or products that have similar resource requirements but different demand cycles similar resource requirements but different demand cycles allow allow leveling leveling of output.of output.

nn EG: counterEG: counter--seasonal products or services such as seasonal products or services such as seasonal clothing.seasonal clothing.

Aggressive StrategiesAggressive Strategies

Planning Strategies SummarizedPlanning Strategies SummarizedReactive Strategies

w Hiring & Layoffs (Chase)

w Overtime & Idle time (Chase)

w Subcontracting (Leveling)

w Back Orders (Leveling)

w Inventory Levels (Leveling) (Creating more inventory in slow periods and using it to meet excess demand in high demand periods.)

Aggressive Strategies

w Pricing (Leveling)

w Promotion (Leveling)

w Complementary (counter-seasonal) Products(Leveling)

Most planning strategies are not Pure (one kind). They are usually Hybrid Strategies with a combination of techniques, often using leveling and chase.

Aggregate Scheduling Options/Strategies :Advantages & Disadvantages

Option Advantage Disadvantage SomeComments

Changinginventory levels

Changes inhuman resourcesare gradual, notabruptproductionchanges

Inventoryholding costs;Shortages mayresult in lostsales

Applies mainlyto production,not service,operations

Varyingworkforce sizeby hiring orlayoffs

Avoids use ofother alternatives

Hiring, layoff,and trainingcosts

Used where sizeof labor pool islarge



Varyingproduction ratesthrough overtimeor idle time

Matches seasonalfluctuationswithouthiring/trainingcosts

Overtimepremiums, tiredworkers, may notmeet demand

Allowsflexibility withinthe aggregateplan

Subcontracting Permitsflexibility andsmoothing of thefirm's output

Loss of qualitycontrol; reducedprofits; loss offuture business

Applies mainlyin productionsettings



Using part-timeworkers

Less costly andmore flexiblethan full-timeworkers

Highturnover/trainingcosts; qualitysuffers;schedulingdifficult

Good forunskilled jobs inareas with largetemporary laborpools

Influencingdemand

Tries to useexcess capacity.Discounts drawnew customers.

Uncertainty indemand. Hard tomatch demand tosupply exactly.

Createsmarketing ideas.Overbookingused in somebusinesses.



Back orderingduring high-demand periods

May avoidovertime. Keepscapacity constant

Customer mustbe willing towait, butgoodwill is lost.

Many companiesbackorder.

Counterseasonalproducts andservice mixing

Fully utilizesresources; allowsstable workforce.

May requireskills orequipmentoutside a firm'sareas ofexpertise.

Risky findingproducts orservices withopposite demandpatterns.

The Reality of Planning StrategyThe Reality of Planning Strategyw Most Aggregate Planning (Production and Staffing) is

Trial and Error planning.

w Process-Focused firms are more apt to use Chasestrategies. (Chasing/reacting to demand)

n Process-focused firms are smaller and more adaptable to changing demand and more flexible in making capacity change. (Wait-and-see capacity planning)

w Product-Focused Firms are more apt to use Levelingstrategies. (Keeping output level)

n High volume, lower inventories, lower margins and higher equipment-utilization needs make it more difficult and costly to vary production rates.

No allowances are made for holidays, different number of workdays

Cost is a linear function composed of unit cost & number of units

Plans are feasible (e.g. sufficient inventory storage space is available, subcontractors are available to produce quantity and quality of products, changes in output can be made as needed)

Cost figures can be reasonably estimated and are constant for the planning horizon

Inventories are built and drawn down at a uniform rate and output occurs at a uniform rate though out

Aggregate Planning assumptions

1. Informal, trial and error methods. In practice, these techniques are more commonly used.

2. Mathematical techniques - such as linear programming, linear decision rules or simulation. Although not widely used, they serve as a basis for comparing the effectiveness of alternative techniques for aggregate planning.

General Procedure for Aggregate Planning

1. Determine demand and production requirements for each period.

2. Determine production capacity (regular time, overtime, subcontracting) for each period.

3. Determine company or departmental policies that are pertinent.

For example, maintain a safety stock of 5 percent of demand, or maintain a reasonably stable work force.

4. Determine unit costs for regular time, overtime, subcontracting, holding inventories, back orders and other relevant costs.

5. Develop alternative plans and compute the cost of each.

6. If satisfactory plans emerge, select the one that best satisfies objectives (such as cost minimization). Otherwise, return to step 5.

Techniques for Aggregate Production Planning

Simple tables or worksheets can be developed to evaluate demand, aggregate group level production plans and inventory. We will look at some examples to illustrate the concept of aggregate planning. The assumptions for these examples simplify the computations but can be easily modified to “real situations”.

Aggregate Planning – Informal Techniques

Aggregate Planning – Informal Techniques

Aggregate Planning - formula’s

Number of workers in period = Number of workers at end of the previous period + Number of new workers at the start of a period - Number of laid-off workers at the start of a period

Inventory at the end of a period = Inventory at the end of the previous period + Production in the current period - Amount used to satisfy demand in the

current period

Average Inventory for a period = (Beginning Inventory + Ending Inventory) / 2

Cost for a period = Output Cost + Hire/Lay-off Cost + Inventory Cost + Backorder Cost where Output Cost = Regular Time Cost + Overtime Cost + Subcontractor Cost

How To Calculate Costs …

Regular Costs. Output cost = Regular cost per unit * Quantity of regular output. Overtime cost = Overtime cost per unit * Overtime quantity. Subcontract cost = Subcontract cost per unit * Subcontract quantity

Hire-Layoff Costs. Hire cost = Cost per hire * Number hired. Lay-off cost = Cost per lay-off * Number laid off

Inventory Costs. Carrying cost per unit * Average inventory

Back Order Costs. Back order cost per unit * Backorder quantity

Aggregate Production Planning Illustration

Given the following information:

6 month production planning period

10 labour-hours per unit required

Labour cost = $10/hour regular= $15/hour overtime

Total unit cost = $200 / unit= $228/unit subcontract

Current workforce = 20 employees

Hiring cost = $500 / employee

Layoff cost = $800 / employee

Safety stock = 20% of monthly forecast

Beginning inventory = 50 units

Inventory carrying cost = $10/unit/month

Stockout cost = $50/unit/month

Additional information available:Sales Work Work Hours

Month Forecast Days at 8 Hrs. / DayJan. 300 22 176Feb. 500 19 152Mar. 400 21 168Apr. 100 21 168May. 200 22 176June 300 20 160

First Step: Calculate Production Requirement

Sales Safety ProductionMonth Forecast Stock RequiredJan. 300 60 300+60-50 = 310Feb. 500 100 500+100-60 = 540 Mar. 400 80 400+80-100 = 380Apr. 100 20 100+20-80 = 40May. 200 40 200+40-20 = 220 June 300 60 300+60-40 = 320

Safety Stock of the period t will be an Beginni9ng Inventory of the period (t+1)

ProductionRequired

31054038040220320

HoursRequired

310054003800400

22003200

Hrs. Avail.per Worker

176152168168176160

WorkersRequired

18362331320

WorkersHired

18

107

WorkersFired

2

1320

Hire/FireCosts

$16009000

10400 16000 50003500

Total Cost = $45,500

ProductionRequired

31054038040220320

HoursRequired

31005400380040022003200

Total Hrs.Available

352030403360336035203200

OvertimeHours

2360440

UndertimeHours420

29601320

OT/ UTCosts$420011800

2200148006600

0

Plan # 2 - Exact Production; Vary Production Rate


MonthJan.Feb.Mar.Apr.MayJune


Plan # 1 - Exact Production; Vary Work Force

Aggregate Production Planning Illustration – Contd.

Cum. Prod.Required

310850

1230127014901810

TotalProduction

352304336336352320

CumulativeProduction

352656992

132816802000

InventoryLevel

42

58190190

StockoutLevel

194238

Inv. / SOCosts$4209700

11900 580

19001900


HoursAvailable

352030403360336035203200

Total Cost = $7,160 + $ 21,000 = $28,160

Cum. Prod.Required

310850

1230127014901810

HoursAvailable3520(20)4560(30)5040(30)1680(10)1760(10)1600(10)

TotalProduction

352456504168176160

Cumulative Production

352808

1312 1480 1656 1816

Inv. / (SO) Level42

(42)82210166

6

Inv. / SOCosts$4202100820

2100 1660

60

Hire/FireCosts

5000

16000

$7,160 $21,000



Plan # 3 - Exact Production; Vary Inventory Level With 20 Employees

Aggregate Production Planning Illustration – Contd.

Plan # 4 - Exact Production; Vary Workforce Level; Vary Inventory Level

PlanCosts

45,50061,00026,40028,160

Plan1234

ProductionCosts

362,000362,000400,000363,200

TotalCosts

407,500446,500426,400391,360

UnitsProduced

1810181020001816

Costper Unit$225.14$233.70$213.20$215.51

Final Cost Analysis:

Decision: Go with Plan # 3 on the basis of lowest cost per unit.

Aggregate Production Planning Illustration - Contd.

Example 2: Planners for a company that makes several models of tractors are about to prepare an aggregate plan that will cover 6 periods. The have assembled the following cost information ($):

Output CostsRegular time 2 per tractorOvertime 3 per tractorSubcontract 6 per tractor

Inventory Costs1 per tractor on average inventory Back Order Costs 5 per tractor per period

The forecasted demand by period is:

Aggregate Planning – Example 2

Planning Period 1 2 3 4 5 6 TotalForecasted Demand 200 200 300 400 500 200 1800

They now want to evaluate a plan that calls for a steady rate of regular-time output.

They intend to start with 0 inventory on hand in the first period.

Prepare an aggregate plan and determine its cost for a level output rate of 300 units per period with 15 workers.


Aggregate Planning

Total cost of plan is $4,700

Inventory

Backorder

Costs

Production Schedule

Cumulative Forecast & Production

Cost Components Notice the backorder

cost in period 5

Example 2: After reviewing the plan the planners need to develop an alternative based on the news that one of the regular time workers has decided to retire.

Rather than replace that person they would rather stay with a smaller work force and use overtime to make up for the lost output.

The maximum overtime output is 40 units.


First the regular time output of 300 units per 15 people must be adjusted for 14 people. Therefore 300/15*14 = 280 = adjusted regular time output for 14 people.

We are 120 tractors short.

Where do we manufacture them?

Aggregate Planning

Why did we put manufacture them here?

Does manufacturing them in other periods produce a lower cost?


Aggregate Planning

Notice the backorder cost in period 5

Example 3: A third option is to use temporary workers rather than overtime to fill in for the retiring worker.

Suppose that it costs an additional $100 to hire and train a temporary worker and that a temporary worker can produce 15 tractors per period.


First of all 120 units are needed to replace the retired worker’s output (see output from Example 2).

Therefore 120/15 = 8 means that 8 temporary worker periods are needed to create the 120 units.

Noting that periods 4 and 5 have the heaviest demand, using 4 temporary workers during those periods seems reasonable. This means that we only have to hire 4 temporary workers for two months.

Why is the hire/train cost only $400?


Aggregate Planning

Notice the backorder cost in period 5

Notice the Hire/Layoff cost in period 4

Pure Strategies

Hiring costHiring cost = $100 per worker= $100 per workerFiring costFiring cost = $500 per worker= $500 per worker

Regular production cost per pound = $2.00Regular production cost per pound = $2.00Inventory carrying costInventory carrying cost = $0.50 pound per quarter= $0.50 pound per quarter

Production per employeeProduction per employee = 1,000 pounds per quarter= 1,000 pounds per quarterBeginning work forceBeginning work force = 100 workers= 100 workers

QUARTERQUARTER SALES FORECAST (LB)SALES FORECAST (LB)

SpringSpring 80,00080,000SummerSummer 50,00050,000FallFall 120,000120,000WinterWinter 150,000150,000

Example:Example:

Level Production Strategy

Level production

= 100,000 pounds(80,000 + 50,000 + 120,000 + 150,000)

4

SpringSpring 80,00080,000 100,000100,000 20,00020,000SummerSummer 50,00050,000 100,000100,000 70,00070,000FallFall 120,000120,000 100,000100,000 50,00050,000WinterWinter 150,000150,000 100,000100,000 00

400,000400,000 140,000140,000

Cost of Level Production Strategy:

(400,000 X $2.00) + (140,00 X $.50) = $870,000

SALESSALES PRODUCTIONPRODUCTIONQUARTERQUARTER FORECASTFORECAST PLANPLAN INVENTORYINVENTORY

Chase Demand Strategy

SpringSpring 80,00080,000 80,00080,000 8080 00 2020SummerSummer 50,00050,000 50,00050,000 5050 00 3030FallFall 120,000120,000 120,000120,000 120120 7070 00WinterWinter 150,000150,000 150,000150,000 150150 3030 00

100100 5050

SALESSALES PRODUCTIONPRODUCTION WORKERSWORKERS WORKERSWORKERS WORKERSWORKERSQUARTERQUARTER FORECASTFORECAST PLANPLAN NEEDEDNEEDED HIREDHIRED FIREDFIRED

Cost of Chase Demand Strategy

(400,000 X $2.00) + (100 x $100) + (50 x $500) = $835,000

Previous Spring Summer Fall WinterBeginning Inventory 0 10,000 40,000 30,000Demand Forecast 80,000 50,000 120,000 150,000Production Plan 90,000 80,000 110,000 120,000Ending Inventory 0 10,000 40,000 30,000 0Work-force Size 100 90 80 110 120

Total Demand Forecast= 400,000Total Production Plan= 400,000

Inventory Cost (.50/lb) $5,000 $20,000 $15,000 $0Work-force Cost $5,000 $5,000 $3,000 $1,000Total Cost $54,000

Quarter

Mixed Strategy

Initial Inv (t) = End Inv (t-1)

Mixed Strategy• Combination of Level Production and Chase

Demand strategies

• Examples of management policies

– no more than x% of the workforce can be laid off in one quarter

– inventory levels cannot exceed x dollars

• Many industries may simply shut down manufacturing during the low demand season and schedule employee vacations during that time

APP Using Mixed Strategies - Exercise

Production per employee= 100 cases per monthWage rate = $10 per case for regular production

= $15 per case for overtime= $25 for subcontracting

Hiring cost = $1000 per workerFiring cost = $500 per worker

Inventory carrying cost = $1.00 case per monthBeginning work force = 10 workers

January 1000 July 500February 400 August 500March 400 September 1000April 400 October 1500May 400 November 2500June 400 December 3000

MONTH DEMAND (CASES) MONTH DEMAND (CASES)

Mathematical Model

u Data:

– Starting inventory in January: 1,000 units

– Selling price to the retailer: Rs.40/unit

– Workforce at the beginning of January: 80

– # of working days per month: 20

– Regular work per day per employee: 8 hours

– Maximum overtime allowed per employee per month: 10 hours

– Ending inventory required (at end of June): Minimum 500 units

– Demand forecast:

Month January February March April May June

Demand 1,600 3,000 3,200 3,800 2,200 2,200

Numerical Example

Item Cost Materials Rs.10/unit Inventory holding cost Rs.2/unit/month Marginal cost of a stockout Rs.5/unit/month Hiring and training costs Rs.300/worker Layoff cost Rs.500/worker Labor hours required 4/unit Regular time cost Rs.4/hour Over time cost Rs.6/hour Cost of subcontracting Rs.30/unit

(cont…)

u Cost Data:

Numerical Example (Define Decision Variables)

• The decision variables are as follows:

– Wt = Workforce size for month t

– Ht = Number of employees hired at the beginning of month t

– Lt = Number of employees laid off at the beginning of month t

– Pt = Production in month t

– It = Inventory at the end of month t

– St = Number of units stocked out at the end of month t

– Ct = Number of units subcontracted for month t

– Ot = Number of overtime hours worked in month t

(combined for all employees)

Note: For all the above variables, t = 1, 2, …, 6 giving a total of

48 decision variables.

Numerical Example (Components of Objective Function)

• Regular time labor cost

Rs. 4/hour * 8 hr/day * 20 day/month = Rs.640/month

Therefore, regular time labor cost per month:

• Overtime labor cost

Overtime labor cost is Rs.6/hour and Ot represents the number of overtime hours worked in month t (combined for all employees)

Therefore, overtime time labor cost per month:

• Cost of hiring and layoff

This cost is calculated as:

• Cost of holding inventory and stocking out

This cost is calculated as:

• Cost of materials and subcontracting out

This cost is calculated as: 15

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Numerical Example(Objective Function)

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u The objective function is:

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Numerical Example (Define Constraints Linking Variables)

• Workforce size, hiring and layoff constraints:

or

where t = 1, 2, …, 6 and W0 = 80

• Capacity constraints:

or

where t = 1, 2, …, 6

0LHWW tt1tt =++- -

tt1tt LHWW -+= -

ttt O)4/1(W40P +£

0PO)4/1(W40 ttt ³-+

• Inventory balance constraints:

or

where t = 1, 2, …, 6 and I0 = 1,000, I6 >= 500, and S0 = 0,

• Overtime limit constraints:

or

where t = 1, 2, …, 6

tt1tttt1-t SISDCPI -++=++ -

0SISDCPI tt1tttt1-t =+---++ -

tt W10O £

0W10O tt £-

Numerical Example (Define Constraints Linking Variables) (cont…)

Average Inventory and Average Flow Time

• Average inventory for a period t:

• Average inventory over the planning horizon:

i.e.

• Average flow time: (Average inventory)/(Throughput)

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Various Scenarios

• Some of the possible scenarios are:

– Increase in holding cost (from Rs.2 to Rs.6)

– Overtime cost drops to Rs.5 per hour

– Increased demand fluctuation

• Your plan will change with the change in scenarios

Month January February March April May June

Demand 1,000 3,000 3,800 4,800 2,000 1,400

Transportation Tableau forAggregate Planning

• Suppose we have the following information

– Beginning Inventory: I0

– Regular time production cost per unit: r

– Overtime production cost per unit: v

– Subcontract production cost per unit: s

– Holding cost per unit per period: h

– Backorder cost per unit per period: b

– Shortage (unsatisfied order) cost per unit per period: c

– Undertime cost per unit: u

– Desired inventory level at the end of period 3: Ie

– Total unused capacities: U

– Total unsatisfied orders: C

Periods

1 2 3

Demand D1 D2 D3

Regular Capacity R1 R2 R3

Overtime Capacity O1 O2 O3

Subcontract Capacity S1 S2 S3

LINEAR PROGRAMMING(no backorders, supply > demand)

Beg. Inventory

Demand for

Period 1 Period 2 Period 3

TotalCapacity(supply)

UnusedCapacitySupply from

v v + h v + 2h

0 h 2h

s s + h s + 2h

v v + h

r r + h r + 2h

v

r r + h

s s + h

s

r

Regular

Overtime

Subcontract

Regular

Overtime

Subcontract

Regular

Overtime

Subcontract

I0

R1

O1

S1

R2

O2

S2

R3

O3

S3

u

u

u

u

u

u

u

u

u

u

Demand D1 D2 D3 + le U Grand Total

1

2

3

LINEAR PROGRAMMING(backorders, supply > demand)

Beg. Inventory

Demand for



UnusedCapacitySupply from

v v + h v + 2h

0 h 2h

s s + h s + 2h

v + b v v + h

r r + h r + 2h

v + 2b v + b v

r + b r r + h

s + b s s + h

s + 2b s + b s

r + 2b r + b r

Regular

Overtime

Subcontract

Regular

Overtime

Subcontract

Regular

Overtime

Subcontract

I0

R1

O1

S1

R2

O2

S2

R3

O3

S3

u

u

u

u

u

u

u

u

u

u

Demand D1 D2 D3 + le U Grand Total

1

2

3

Beg. Inventory

Demand for



Supply from

Regular

Overtime

Subcontract

Regular

Overtime

Subcontract

Regular

Overtime

Subcontract

I0

R1

O1

S1

R2

O2

S2

R3

O3

S3

C

Demand D1 D2 D3 + le Grand Total

v v + h

0 h 2h

s s + h

r r + h

v v + h v + 2h

s s + h s + 2h

r r + h r + 2h

r

v

s

LINEAR PROGRAMMING(no backorders, demand > supply)

Unsatisfied Demand c c c

1

2

3

Demand1 2 3 4 5 6 7 8 9 Total190 230 260 280 210 170 160 260 180 1940

There are 20 full time employees, each can produce 10 units per period at the cost of $6 per unit. Therefore the supply of full time workers is as follows1 2 3 4 5 6 7 8 9 Total200 200 200 200 200 200 200 200 200 1800

Overtime cost is $13 per unit. Inventory carrying cost $5 per unit per periodBacklog cost $10 per unit per period

Maximum over time production is 20 units per period

Formulated the problem as a Linear Programming model.

Exercise

APP by the Transportation Method

1 900 1000 100 5002 1500 1200 150 5003 1600 1300 200 5004 3000 1300 200 500

Regular production cost per unit $20Overtime production cost per unit $25Subcontracting cost per unit $28Inventory holding cost per unit per period $3Beginning inventory 300 units

EXPECTED REGULAR OVERTIME SUBCONTRACTQUARTER DEMAND CAPACITY CAPACITY CAPACITY

Production Plan for the Example using TP

1 900 1000 100 0 5002 1500 1200 150 250 6003 1600 1300 200 500 10004 3000 1300 200 500 0

Total 7000 4800 650 1250 2100

REGULAR SUB- ENDINGPERIOD DEMAND PRODUCTION OVERTIME CONTRACT INVENTORY

The aggregate plan can not be used for production because it is at the group level rather than the individual product level.

The aggregate plan must be broken down into specific product requirements so that specific labor skills, materials, and inventory plans can be determined. (e.g. 21” TV’s take different parts than 27” TV’s)

We will discuss this more in MPS, but first let’s take a look at some general concepts.

The Production Plan

Because different products require different materials, skills, etc. we must manufacture at the item level rather than the group level. The master schedule (item level) is similar to the aggregate plan (group level).

. Master Schedule - is a detailed plan usually done for weekly periods(sometimes daily) showing the quantity and timing of specific items (e.g. 21” TV’s) for a scheduled horizon and can be used by other functional areas of the organization.

. Rough-Cut Capacity Planning - is an approximate balancing of the detailed master production schedule with capacity to test the feasibility of the master production schedule. It resembles the aggregate planning

process; but, at a detailed product level.

The Production Plan

Masterscheduling

Beginning Inventory

Forecast

Customer Orders

Inputs

3 inputs and 3 outputs

Master Scheduling Process

Outputs

Projected Inventory

Master Production Schedule

Available To Promise

(uncommitted inventory)

Projected demand is calculated based on the customer orders and forecast.

Projected Demand = max (forecast, orders)

Inputs To Master Scheduling

Planning Period 1 2 3 4 5 6 7 8Forecast 30 30 30 30 40 40 40 40

Customer Orders 33 20 10 4 2Projected Demand 33 30 30 30 40 40 40 40

Projected On Hand Inventory 64

How can customer orders be more than forecast?

Therefore, the Projected Inventory Position (previous inventory position - projected demand) without any production can be calculated and is shown below:

Outputs Of Master Scheduling



Projected On Hand Inventory 64 31 1 -29 -59 -99 -139 -179 -219

If the lot size for this item is 70 units, we can now build the Master ProductionSchedule. We add our first lot in week/day 3 because this is the first negative inventory position. We then update our Projected Inventory Position.




Projected On Hand Inventory 64 31 1 41 11 -29 -69 -109 -149Master Production Schedule (MPS) 70


We add our next lot in week/day 5 because this is the next negative inventory position. We then update our Projected Inventory Position.



Projected On Hand Inventory 64 31 1 41 11 41 1 -39 -79Master Production Schedule (MPS) 70 70

We add our next lot in week/day 7 because this is the next negative inventory position. We then update our Projected Inventory Position.




Projected On Hand Inventory 64 31 1 41 11 41 1 31 -9Master Production Schedule (MPS) 70 70 70

We add our next lot in week/day 9 because this is the next negative inventory position. We then update our Projected Inventory Position, and have completed the second output of the master scheduling process, the Master Production Schedule.




Projected On Hand Inventory 64 31 1 41 11 41 1 31 61Master Production Schedule (MPS) 70 70 70 70


We are now ready to compute our final output of the master scheduling process, the Available to Promise (ATP) or uncommitted inventory. This is inventory which is available to sell and is extremely important to customer service. The ATP is calculated for week/day 1, 3, 6, 7 and 8.

Think about how Land’s End may use the ATP!




Available To Promise (ATP)


The ATP is calculated for week/day 1 by the following:Week 1 ATP = Beginning inventory - sum of committed

inventory (customer orders) until the first master scheduled lot

= 64 - (33 + 20) = 11




Available To Promise (ATP) 11

The ATP is calculated for week/day 3 by the following:Week 3 ATP = MPS for week/day 3 - sum of committed

inventory (customer orders)until the next master scheduled lot

= 70 - (10 + 4) = 56




Available To Promise (ATP) 11 56





= 70 - 2 = 68




Available To Promise (ATP) 11 56 68




= 70 - 0 = 70




Available To Promise (ATP) 11 56 68 70




= 70 - 0 = 70




Available To Promise (ATP) 11 56 68 70 70

Master Scheduling

You can see by these calculations that changes to a Master Schedule can be disruptive, particularly those in the first few weeks/days of a schedule.

It is difficult to rearrange schedules, materials plans, and labor plans on a short notice.

For these reasons, many schedules have varying degrees of changes that are allowed. Time fences are created to indicate the level of change if any that will be considered .

Stabilizing The Master Schedule

Planning Period1 2 3 4 5 6 7 8 9 10 11 12

Frozen FullFirm Open

Items

Product lines or families

Individual products

Components

Manufacturing operations

Resource level

Plants

Individual machines

Critical work centers

Production Planning Capacity Planning

Resource Requirements Plan

Rough-Cut Capacity Plan

Capacity Requirements Plan

Input/Output Control

Aggregate Production Plan

Master Production Schedule

Material Requirements Plan

Shop Floor Schedule

All work centers

Hierarchical Planning Process

Aggregate Production Planning

Documents

Transcript of Aggregate Production Planning