Planning Lecture 1

8/9/2019 Planning Lecture 1

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Aggregate Planningin a Supply Chain

Supply Chain Management

Fall, 2004Dr. Lu

Note 7


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Outline

Identify the types of decisions that are best solved

by aggregate planning

Describe the kind of information needed to produce

an aggregate plan

Explain the basic trade-offs a manager makes when

producing an aggregate plan

Formulate and solve aggregate planning problems

using Linear Programming


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Types of Questions in Aggregate Planning

Month Demand Forecast

January 1,000

February 3,000March 3,800

April 4,800

May 2,000June 1,400

Should build a plant with large capacity?

or

Should incur the costs of holding inventory?


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Definition

- Given the demand forecast for each period in the

planning horizon, determine the production level,

inventory level, and the capacity level for each

period that maximize the firms profit over

planning horizon.

Planning horizon

- usually between 3 and 18 months

The Aggregate Planning Problem


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Demand forecast Ft

Production Costs

- Labor costs (regular time & overtime costs ($/hour))

- Cost of subcontracting production ($/unit, $/hour)

- Cost of hiring/laying off workforce ($/worker)

Labor/machine hours required per unit

Inventory holding cost ($/unit/period)

Required Information


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Stockout or backlog cost ($/unit/period)

Constraints

- limits on overtime

-

limits on layoffs- limits on capital available

- limits on stockouts and backlogs

Required Information (continued)


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Production quantity from regular time, overtime and

subcontracted time # of workers and supplier

purchase level.

Inventory held warehouse space and working

capital needed.

Backlog / stockout quantity customer service level

Workforce hired / laid off customer service level

Machine capacity increase / decrease new

production equipment purchased

Decisions to make


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Apooraggregate plan can result in

1. Lost sales and lost profits

- if unable to meet demand

2. A large amount of excess inventory and capacity

- thereby raise costs

Therefore, aggregate planning is a very important

tool in helping a company maximize profitability

The Quality of an Aggregate Plan


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The aggregate planner must make trade-offs

among capacity, inventory and backlog cost

Basic Strategies

1. Chase strategy

2. Time flexibility from workforce or capacity

strategy

3. Level strategy

Aggregate Planning Strategies


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2. Time flexibility from workforce strategy

lever : utilization

The workforce is kept stable but the number of hours

worked is varied over time to synchronize production with

demand.

Low levels of inventory, but lower average utilization

than the chase strategy.

Should be used when inventory holding cost is high, and

overtime cost is relatively low.


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3. Level Strategy

lever : inventory

Production is not synchronized with demand.

Large inventory, possible backlogs.

Should be used when inventory holding cost and backlog

cost are relatively low.


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Linear Programming

Month Demand ForecastJanuary 1,600

February 3,000

March 3,200April 3,800

May 2,200

June 2,200

Red Tomato Tools


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Linear Programming (continued)

Problem Statement

- Selling price of each tool to retailer for $40.

- A starting inventory of 1,000 tools in January.

- A starting workforce of 80 employees.

- 20 working days in each month.- Work 8 hours / day.

- No more than 10 hours of overtime / month.

- All stockouts are backlogged. (All demand is to be met.)

- An ending inventory of 500 tools at the end of June.


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Item Cost

Materials $10/unit

Inventory holding cost $2/unit/month

Marginal cost of a stockout $5/unit/month

Hiring and training costs $300/worker

Layoff cost $500/worker

Labor hours required 4/unit

Regular time cost $4/hour

Over time cost $6/hour

Cost of subcontracting $30/unit

Costs



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Decision Variables

Wt = Workforce size for month t, t= 1, ..., 6

Ht = # of employees hiredat the beginning of month t, t= 1,..., 6

Lt = # of employees laid offat the beginning of month t, t= 1,..., 6

Pt =Production in month t, t= 1, ..., 6

It =Inventory at the end of month t, t= 1, ..., 6

St = # of units stocked outat the end of month t, t= 1, ..., 6

Ct = # of units subcontractedfor month t, t= 1, ..., 6

Ot = # of overtime hours worked in month t, t= 1, ..., 6



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==

6

1t tW640costlabortimeRegular


Regular time labor cost

- Monthly wage for each worker = $640

(i.e., $4/hour 8hours/day 20days/month)

- Wt = # workers in period t


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=

=6

1t

tO6costlaborOvertime


Overtime labor cost

- Overtime labor cost is $6/hour

- Ot = # of overtime hours worked in period t


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==

+=6

1tt

6

1tt

LH500300

layoff&hiringofCost


Cost of hiring and layoffs

- Cost of hiring a worker is $300.

- Cost of laying off a worker is $500.

- Ht = # hired in period t

- Lt = # laid off in period t


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==

+=6

1t t

6

1t t SI52

stockout&inventoryofCost


Cost of inventory and stockout

- Cost of carrying inventory is $2/unit/month.

- Cost of stocking out is $5/unit/month.

- It = units in inventory in period t

- St = units stocked out in period t


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==

+=6

1t

t

6

1t

t CP 3010

tingsubcontrac&materialsofCost


Cost of materials and subcontracting

- Material cost is $10/unit.

- Subcontracting cost is $30/unit.

- Pt = quantity produced in period t

- Ct = quantity subcontracted in period t


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=====

===

+++++

++6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

CPSIO

LHW

3010526

500300640Min


Objective Function


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Constraints

- Workforce, hiring, and layoff constraints

- Capacity constraints

- Inventory balance constraints

- Overtime limit constraints



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Workforce size for each month is based on hiringand layoffs

.80where,6,...,1tfor W

LHWW0

tt1tt

==+=



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Production for each month cannot exceed capacity

.6,...,1tfor440 OWP ttt =

+



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Inventory balance for each month

.500and,0

,000,1where,6,...,1tfor

IS I

SISDCPI

60

0

tt1tttt1t

=

==++=++



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Overtime for each month

.6,...,1tfor

10

WOtt

=



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negativityNon.0and,500

,0,000,1,80where

,6,...,1tfor010

,0

,04/40

,0

SI

SIWWO

SISDCPIPOW

LHWW

66

000

tt

tt1tttt1t

ttt

tt1tt

=

===

=

=+++

+

=+

=====

===

+++++

++

6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

6

1tt

CPSIO

LHW

3010526

500300640Min

Excel File


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Average Inventory

Average Flow Time

- Littles law (ave flow time = ave inventory/throughput)

T/I2/)II(

1T

1t

tT0

++

=

++ =

=

T

1t

t

1T

1t

tT0 T/D/T/I2/)II(


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RESULTS

Total cost over planning horizon = $422,275

Revenue over planning horizon = $640,000

Average seasonal inventory = 895

Average flow time = 0.34 months


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Month Demand Forecast

January 1,000(1,600)

February 3,000(3,000)

March 3,800(3,200)

April 4,800(3,800)

May 2,000(2,200)

June 1,400(2,200)

Increased demand fluctuation

Scenarios I


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RESULTS

Total cost = $432,858 ($422,275)

Revenue over planning horizon = $640,000 (same)

Average seasonal inventory = 1,075 (895)

Average flow time = 0.40 (0.34) months

Scenarios I (continued)


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Increase in holding cost (from $2 to $6)

Scenarios II

RESULTS

Total cost = $441,200 ($422,275)


Average seasonal inventory = 558 (895)

(Subcontracted amount increased.)



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Increase in holding cost (from $2 to $6)

Aggregate Planning in Practice

RESULTS

Total cost = $441,200 ($422,275)


Average seasonal inventory = 558 (895)

(Subcontracted amount increased.)



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Aggregate Planning in Practice

Think beyond the enterprise to the entire chain

Make plans flexible because forecasts are always

wrong

Build safety stock or safety capacity to deal with

the forecast error

Return the aggregate plan as new data emerges


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1. Identify the types of decisions that are best solvedby aggregate planning.

2. Describe the kind of information needed to produce

an aggregate plan.

3. Explain the basic trade-offs a manager makes to

produce an aggregate plan.4. Formulate and solve aggregate planning problems

using Linear Programming.

Summary

Documents

Planning Lecture 1