INSE6400 – PRINCIPLES OF SYSTEMS

ENGINEERING

PRODUCTION

Instructor: Dr. Ayda Basyouni

Office: EV 7.648

Email: abasyoun@ciise.concordia.ca

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Course Outline

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Principles of Systems Engineerin

g

Foundations of

Systems Engineerin

gIntroductio

n to Systems

Engineering

Structure of Complex

Systems

Concept developme

nt stage

Needs Analysis

Exploration and

definition

Decision and

analysis

Production

Systems Analysis

and Design Evaluation

Systems of uncertainty

Markov models

ReliabilityQueuing

Theory and Analysis

Game Theory

Topic Areas in Operations Analysis

• Forecasting

• Aggregate Planning

• Inventory Control: Deterministic Environments

• Inventory Control: Stochastic Environments

• Supply Chain Management

• Production Control Systems: MRP and JIT

• Operations Scheduling

• Project Scheduling

• Facilities Planning

• Quality and Assurance

• Maintenance and Reliability

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Operations

Finance

Marketing

Functional Areas of the Firm

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Time Horizons for Strategic Decisions

1. Long Term Decisions

• Locating and Sizing New Facilities

• Finding New Markets for Products

• Mission Statement: meeting quality objectives

2. Intermediate Term Decisions

• Forecasting Product Demand

• Determining Manpower Needs

• Setting Channels of Distribution

• Equipment Purchases and Maintenance

3. Short Term Decisions

• Purchasing

• Shift Scheduling

• Inventory Control

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The Elements of Production and

Operations Strategy

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Hierarchy of Production Decisions

Long-range Capacity Planning

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Planning Horizon

Aggregate planning: Intermediate-

range capacity planning, usually

covering 2 to 12 months.

Short

range

Intermediate

range

Long range

Now 2 months 1 Year

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Aggregate planning

• Aggregate planning is intermediate-range capacity

planning used to establish employment levels, output

rates, inventory levels, subcontracting, and backorders for

products that are aggregated, i.e., grouped or brought

together. It does not specifically focus on individual

products but deals with the products in the aggregate.

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Concept of Aggregate Product

• For example, imagine a paint company that produces

blue, brown, and pink paints; the aggregate plan in this

case would be expressed as the total amount of the

paint without specifying how much of it would be blue,

brown or pink.

• Such an aggregate plan may dictate, for example, the

production of 100,000 gallons of paint during an

intermediate-range planning horizon, say during the

whole year. The plan can later be disaggregated as to

how much blue, brown, or pink paint to produce every

specific time period, say every month.

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Why Aggregate Planning Is Necessary

• Make sure enough capacity available to satisfy expected

demand

• Plan for the orderly and systematic change of production

capacity to meet the peaks and valleys of expected

customer demand

• Get the most output for the amount of resources available

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Introduction to Aggregate Planning

• Goal: To plan gross work force levels and set firm-wide production plans so that predicted demand for aggregated units can be met.

Concept is predicated on the idea of an “aggregate unit” of production. May be actual units, or may be measured in weight (tons of steel), volume (gallons of gasoline), time (worker-hours), or dollars of sales. Can even be a fictitious quantity.

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Aggregate Units

The method is based on notion of aggregate units. They

may be

• Actual units of production

• Weight (tons of steel)

• Dollars (Value of sales)

• Fictitious aggregate units(See example 3.1)

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Example of fictitious aggregate units.

One plant produced 6 models of washing machines:

Model # hrs. Price % sales

A 5532 4.2 285 32

K 4242 4.9 345 21

L 9898 5.1 395 17

L 3800 5.2 425 14

M 2624 5.4 525 10

M 3880 5.8 725 06

Question: How do we define an aggregate unit here?

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Example continued

• Notice: Price is not necessarily proportional to worker

hours (i.e., cost): why?

One method for defining an aggregate unit: requires:

.32(4.2) + .21(4.9) + . . . + .06(5.8) = 4.8644 worker hours.

This approach for this example is reasonable since

products produced are similar. When products produced

are heterogeneous, a natural aggregate unit is sales

dollars.

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Aggregate Planning

• Aggregate planning might also be called macroproduction planning.

• Whether a company provides a service orproduct, macro planning begins with the forecastof demand.

• Aggregate planning methodology is designed totranslate demand forecasts into a blueprint forplanning :

- staffing and

- production levels

for the firm over a predetermined planninghorizon.

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Aggregate Planning

• The aggregate planning methodology discussed in this

chapter assumes that the demand is deterministic and

dynamic.

• This assumption is made to simplify the analysis and

allow us to focus on the systematic and predictable

changes in the demand pattern.

• Aggregate planning involves competing objectives:

- react quickly to anticipated changes in demand

- retain a stable workforce

- develop a production plan that maximizes profit

over the planning horizon subject to

constraints on capacity

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Nature of Demand

• Demand

I. Deterministic

Static

Dynamic

II. Probabilistic

Stationary

Non-Stationary

In aggregate production planning, we assume

that demand is deterministic and dynamic.

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Costs in Aggregate Planning

• Smoothing Costs

• changing size of the work force

• changing number of units produced

• Holding Costs

• primary component: opportunity cost of

investment in inventory

• Shortage Costs

• Cost of demand exceeding stock on hand.

Other Costs: payroll, overtime, idle cost,

subcontracting.

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Cost of Changing the Size of the Workforce

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Holding and Back-Order Costs

Back-orders Positive inventory

Slope = CP Slope = Ci$ C

ost

Inventory

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Overview of the Aggregate Production

ProblemSuppose that D1, D2, . . . , DT are the forecasts of demand

for aggregate units over the planning horizon (T periods.)

The problem is to determine both work force levels (Wt)

and production levels (Pt ) to minimize total costs over the

T period planning horizon.

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Prototype Aggregate Planning Example

The washing machine plant is interested in determining

work force and production levels for the next 8 months.

Forecasted demands for Jan-Aug. are: 420, 280, 460,

190, 310, 145, 110, 125. Starting inventory at the end of

December is 200 and the company would like to have 100

units on hand at the end of August. Find monthly

production levels.

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Step 1: Determine “net” demand.

(subtract starting inventory from period 1 forecast and add

ending inventory to period 8 forecast.)

Month Net Predicted Cum. Net

Demand Demand

1(Jan) 220(420-200) 220

2(Feb) 280 500

3(Mar) 460 960

4(Apr) 190 1150

5(May) 310 1460

6(June) 145 1605

7(July) 110 1715

8(Aug) 225(125+100) 1940

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Basic Strategies

• Constant Workforce (Level Capacity)strategy:

• Maintaining a steady rate of regular-time output while meeting variations in demand by a combination of options.

• Zero Inventory (Matching Demand, Chase) strategy:

• Matching capacity to demand; the planned output for a period is set at the expected demand for that period.

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Level vs. Chase Strategy

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Advantages and Disadvantages

• Chase Strategy

• Reduced inventory costs.

• High levels of worker utilization.

• Cost of fluctuating workforce levels.

• Potential damage to employee morale.

• Level Strategy

• Worker levels and production output are stable.

• High inventory costs.

• Increased labor costs.

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Constant Work Force Plan

Suppose that we are interested in determining a

production plan that doesn’t change the size of the

workforce over the planning horizon. How would we do

that?

One method:

Monthly Production = 1940/8 = 242.2 or rounded to

243/month.

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Step 1: Determine “net” demand.

(subtract starting inventory from period 1 forecast and add

ending inventory to period 8 forecast.)

Month Net Predicted Cum. Net

Demand Demand

1(Jan) 220(420-200) 220

2(Feb) 280 500

3(Mar) 460 960

4(Apr) 190 1150

5(May) 310 1460

6(June) 145 1605

7(July) 110 1715

8(Aug) 225(125+100) 1940

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To match net demand at period 3, so that monthly production is

960/3 = 320. Ending inventory each month is found from:

Month Cum. Net. Dem. Cum. Prod. Invent.

1(Jan) 220 320 100

2(Feb) 500 640 140

3(Mar) 960 960 0

4(Apr.) 1150 1280 130

5(May) 1460 1600 140

6(June) 1605 1920 315

7(July) 1715 2240 525

8(Aug) 1940 2560 620

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But - may not be realistic for several reasons:

•Since all months do not have the

same number of workdays, a constant

production level may not translate to

the same number of workers each

month.

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To Overcome These Shortcomings:

•Assume number of workdays per

month is given (reasonable!)

•Compute a “K factor” given by:K = number of aggregate units produced by one worker in one day

Finding K

• Suppose we are told that over a period of 40 days, 520

units were produced with 38 workers. It follows that:

• K= 520/(38*40) = .3421 average number of units

produced by one worker in one day.

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Computing Constant Work Force --

Realistically

• Assume we are given the following # of working days per month: 22, 16, 23, 20, 21, 22, 21, 22. • March is still the critical month.

• Cum. net demand thru March = 960.

• Cum # working days = 22+16+23 = 61.

• We find that:

• 960/61 = 15.7377 units/day

• 15.7377/.3421 = 46 workers required

• Actually 46.003 – here we truncate because we are set to build inventory so the low number should work (check for March stock out) – however we must use care and typically ‘round up’ any fractional worker calculations thus building more inventory

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Tabulate Days/Production Per Worker Versus

Demand To Find Minimum Numbers

Month # Work Days #Units/worker Forecast Demand net

Cum. Net

Demand

Cum.Units/

Worker

Min #

Workers

Jan 22.00 7.53 220.00 220.00 7.53 29.23

Feb 16.00 5.47 280.00 500.00 13.00 38.46

Mar 23.00 7.87 460.00 960.00 20.87 46.00

Apr 20.00 6.84 190.00 1150.00 27.71 41.50

May 21.00 7.18 310.00 1460.00 34.89 41.84

Jun 22.00 7.53 145.00 1605.00 42.42 37.84

Jul 21.00 7.18 110.00 1715.00 49.60 34.57

Aug 22.00 7.53 225.00 1940.00 57.13 33.96

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What Should We Look At?

• Cumulative Demand says March needs most workers –

this can be interpretted as building inventories in Jan +

Feb to fulfill the greater March demand

• However, if we keep this number of workers we will

continue to build inventory through the rest of the plan!

Constant Work Force Production Plan

Mo # wk days Prod. Cum Cum Nt End Inv

Level Prod Dem

Jan 22 346 346 220 126

Feb 16 252 598 500 98

Mar 23 362 960 960 0

Apr 20 315 1275 1150 125

May 21 330 1605 1460 145

Jun 22 346 1951 1605 346

Jul 21 330 2281 1715 566

Aug 22 346 2627 1940 687

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Addition of Costs

• Holding Cost (per unit per month): $8.50

• Hiring Cost per worker: $800

• Firing Cost per worker: $1,250

• Payroll Cost: $75/worker/day

• Shortage Cost: $50 unit short/month

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Cost Evaluation of Constant Work Force Plan

• Assume that the work force at the end of Dec.

was 40.

• Cost to hire 6 workers: 6*800 = $4800

• Inventory Cost: accumulate ending inventory:

(126+98+0+. . .+687) = 2093. Add in 100 units

netted out in Aug = 2193.

• Hence Inv. Cost = 2193*8.5=$18,640.50

• Payroll cost:

($75/worker/day)(46 workers )(167days) = $576,150

• Cost of plan: $576,150 + $18,640.50 + $4800 =

$599,590.50

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Cost Reduction in Constant Work Force Plan

(Mixed Strategy)

In the original cum net demand curve, consider making

reductions in the work force one or more times over

the planning horizon to decrease inventory investment.

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Zero Inventory Plan (Chase Strategy)

• Here the idea is to change the workforce each

month in order to reduce ending inventory to

nearly zero by matching the workforce with

monthly demand as closely as possible. This is

accomplished by computing the # of units

produced by one worker each month (by

multiplying K by #days per month) and then

taking net demand each month and dividing by

this quantity. The resulting ratio is rounded up to

avoid shortages.

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An Alternative is called the “Chase Plan”

• Here, we hire and fire (layoff) workers to keep inventory low!

• We would employ only the number of workers needed each month to meet the demand

• Examining our chart (earlier) we need:• Jan: 30; Feb: 51; Mar: 59; Apr: 27; May: 43 Jun: 20; Jul: 15; Aug:

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• Found by: (monthly demand) (monthly production/worker), forJan= 220/(22*.3425)

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Tabulate Days/Production Per Worker Versus

Demand To Find Required Numbers of workers

Month # Work Days #Units/worker Forecast Demand net

Cum. Net

Demand

Cum.Units/

Worker

Min #

Workers

Jan 22.00 7.53 220.00 220.00 7.53 30

Feb 16.00 5.47 280.00 500.00 13.00 51

Mar 23.00 7.87 460.00 960.00 20.87 59

Apr 20.00 6.84 190.00 1150.00 27.71 27

May 21.00 7.18 310.00 1460.00 34.89 43

Jun 22.00 7.53 145.00 1605.00 42.42 20

Jul 21.00 7.18 110.00 1715.00 49.60 15

Aug 22.00 7.53 225.00 1940.00 57.13 30

Changing the Level of Work Force

Period # hired #fired

1 10

2 21

3 8

4 31

5 15

6 23

7 5

8 15

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An Alternative is called the “Chase Plan”

• So we hire or Fire (lay-off) monthly• Jan (starts with 40 workers): Fire 10 (cost $8000)

• Feb: Hire 21 (cost $16800)

• Mar: Hire 8 (cost $6400)

• Apr: Fire 31 (cost $38750)

• May: Hire 15 (cost $12000)

• Jun: Fire 23 (cost $28750)

• Jul: Fire 5 (cost $6250)

• Aug: Hire 15 (cost $12000)

• Total Personnel Costs: $128950

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An Alternative is called the “Chase Plan”

• Inventory cost is essentially 165*8.5 = $1402.50

• Employment costs: $428325

• Chase Plan Total: $558677.50

• It is better than the “Constant Workforce Plan” by:• 599590.50 – 558677.50 = 40913

• But will this be good for your image?

• Can we find a better plan?

Example

MONTH DEMAND (CASES) MONTH DEMAND (CASES)

January 1000 July 500

February 400 August 500

March 400 September 1000

April 400 October 1500

May 400 November 2500

June 400 December 3000

Demand for Quantum Corporation’s action toy series follows a seasonal pattern –

growing through the fall months and culminating in December, with smaller peaks

in January (for after-season markdowns, exchanges, and accessory purchases) and

July (for Christmas-in-July specials).

Each worker can produce on average 100 cases of action toys each month. Overtime is

limited to 300 cases, and subcontracting is unlimited. No action toys are currently in

inventory. The wage rate is $10 per case for regular production, $15 for overtime

production, and $25 for subcontracting. No stockouts are allowed. Holding cost is $1

per case per month. Increasing the workforce costs approximately $1,000 per worker.

Decreasing the workforce costs $500 per worker.

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Example – Level Production

Month Demand Reg OT Subk Inv #Wkrs #Hired #Fired

Jan 1000 1,000 0 0 0 10 0 0

Feb 400 1,000 0 0 600 10 0 0

Mar 400 1,000 0 0 1,200 10 0 0

Apr 400 1,000 0 0 1,800 10 0 0

May 400 1,000 0 0 2,400 10 0 0

Jun 400 1,000 0 0 3,000 10 0 0

Jul 500 1,000 0 0 3,500 10 0 0

Aug 500 1,000 0 0 4,000 10 0 0

Sept 1000 1,000 0 0 4,000 10 0 0

Oct 1500 1,000 0 0 3,500 10 0 0

Nov 2500 1,000 0 0 2,000 10 0 0

Dec 3000 1,000 0 0 0 10 0 0

Total 12,000 12,000 0 0 26,000 0 0

Input: Beg. Wkrs 10 Regular $10 Hiring $1,000

Units/Wkr 100 Overtime $15 Firing $500 Cost: $146,000

Beg. Inv. 0 Subk $25 Inventory $1

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Example – Chase Demand

Month Demand Reg OT Subk Inv #Wkrs #Hired #Fired

Jan 1000 1000 0 0 0 10 0 0

Feb 400 400 0 0 0 4 0 6

Mar 400 400 0 0 0 4 0 0

Apr 400 400 0 0 0 4 0 0

May 400 400 0 0 0 4 0 0

Jun 400 400 0 0 0 4 0 0

Jul 500 500 0 0 0 5 1 0

Aug 500 500 0 0 0 5 0 0

Sept 1000 1000 0 0 0 10 5 0

Oct 1500 1500 0 0 0 15 5 0

Nov 2500 2500 0 0 0 25 10 0

Dec 3000 3000 0 0 0 30 5 0

Total 12,000 12,000 0 0 0 26 6

Input: Beg. Wkrs 10 Regular $10 Hiring $1,000

Units/Wkr 100 Overtime $15 Firing $500 Cost: $149,000

Beg. Inv. 0 Subk $25 Inventory $1

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References

• Production and Operation Analysis, fifth edition, Steven

Nahmias, McGraw Hill

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