chapter 3 aggregate planning handout

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CHAPTER 3: AGGREGATE PLANNING

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Outline

IntroductionAggregate planning strategiesAggregate planning through linear programmingUpdating the aggregate planDiscussion of model assumptions

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1. Introduction: Now that we have a forecast…

It is time to plan for the future… It would be useful to have rough-cut plans for the following: Production level

• Regular, overtime, subcontracting

Inventory to be held

Backlogs

Machine capacity

• Increase/decrease

Workforce

• Hire/Lay off

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1. Introduction: A definition of aggregate planning

Given the demand forecast for each period in the planning horizon, determine the production level, inventory level, and capacity level (internal and outsourced) for each period that maximizes the firm’s profit over the planning horizon.

AggregatePlanning

• Demand forecast: for an aggregate output

• Choice of planning horizon: anywhere from 3 months to 18 months

• Production level: overtime / regular time

• Inventory level: on-hand inventory / backlog

• Capacity level: in-house / subcontracted

• Workforce level: hiring / layoff decisions

INPUTS OUTPUTS

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1. Introduction: Information needed for aggregate planning

Demand forecast

Production cost• Labor cost: regular and overtime ($/hour)

• Cost of subcontracting production ($/unit or $/hour)

• Cost of changing capacity

Labor/machine hours required per unit of demand

Inventory holding cost ($/unit/period)

Stock-out or backlog cost ($/unit/period)

Constraints• Limits on overtime

• Limits on layoffs

• Limits on capital available

• Limits on backlog

• …

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1. Introduction: examples of aggregate planning decisions

“Layoff” in this context can mean actions other than simply firing an employee. For example, “job banks” were a form of lay-off that persisted in the auto industry for more than 20 years.

Source: http://www.npr.org/templates/story/story.php?storyId=5185887

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Hiring and layoff may also refer to adjusting the level of temporary / seasonal workers as opposed to permanent hiring or firing.

Source: http://www.govexec.com/dailyfed/0810/080910mag1.htm

Source:http://detnews.com/article/20090124/AUTO01/901240355/Toyota-looks-into-layoffs

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Companies frequently adjust output in response to changes in demand forecast. This would translate into changes in production and inventory levels.

Source: http://economictimes.indiatimes.com/articleshow/3994494.cms

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Companies frequently adjust output in response to changes in demand forecast. This would translate into changes in production and inventory levels.

Source: http://www.nytimes.com/2010/06/18/business/businessspecial4/18toyota.html

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2. Aggregate planning strategies – Chase

Chase Strategy

Time

Demand

Every period, adjust capacity so that it is equal to demand and produce an amount equal to capacity.

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2. Aggregate planning strategies – Flexible utilization

Flexible Utilization Strategy

Time

Demand

Invest in the highest capacity that will be ever needed and, in every period, produce an amount equal to demand.

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2. Aggregate planning strategies – Level

Level Strategy

Time

Demand

Invest in moderate capacity level at the beginning, and keep production level at capacity.

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2. Aggregate planning strategies – comparison

Capacity Investment

Cost

Capacity Change

Cost

Inventory /Backlog

Cost

Production Cost

Chase

Flexible Utilization

Level

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3. Aggregate planning through linear programming Example 1

Red Tomato Tools: Create a plan for the next six months.

Actions Available (combinations can be used):

• Add workers during peak period,

• Layoff workers during slow months,

• Subcontract some work,

• Build up inventory during slow months,

• Build up backlog during the fast months.

Status Quo:

• At the beginning of January, there are 1000 tools in inventory.

• At the beginning of January, Red Tomato employs 80 workers.

• Management requires 500 tools to be in inventory at the end of June.

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Additional Information:

• Each employee works 8 hours per day and 20 days per month.

• Unmet demand backlogged and met from the subsequent months’ production.

• All demand must be met eventually.

• Inventory costs are charged monthly on the basis of inventory at the end of a month.

• An employee cannot work more than 10 hours of overtime per month.

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Material cost $10/unit

Inventory holding cost $2/unit/month

Backlog cost $5/unit/month

Hiring and training cost $300/worker

Layoff cost $500/worker

Labor hours required 4/unit

Regular time cost $4/hour

Overtime cost $6/cost

Subcontracting cost $30/unit

Selling price $40/unit

Profit Revenue Cost= -

= Unit Price × Total Demand

What is an appropriate objective?

Month Demand Forecast

January 1600

February 3000

March 3200

April 3800

May 2200

June 2200

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Decision Variables / Notation:

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

Ht = # employees hired at the beginning of month t, t=1, …, 6

Lt = # employees laid off at the beginning of month t, t=1, …, 6

Pt = # units produced in month t, t=1, …, 6

It = inventory at the end of month t, t=1, …, 6

St = # units backlogged at the end of month t, t=1, …, 6

Ct = # units subcontracted for month t, t=1, …, 6

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

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Objective function:

Regular time labor cost:

Overtime labor cost:

Cost of hiring & layoff:

Cost of inventory and backlog:

Cost of material and subcontracting:+

Total cost over six months=

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Constraints:

Workforce balance constraints:

Capacity constraints:

Inventory balance constraints:

Overtime limit constraints:

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We will write the constraints in a slightly different form in preparation for the spreadsheet model we will utilize:

Workforce balance constraints:

Capacity constraints:

Inventory balance constraints:

Overtime limit constraints:

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Use Excel Solver to find the optimal solution. Our work is in “Chapter 3 Example 1.xls.” See below for what we enter in the Excel Solver dialog box.

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Here is the optimal solution we find using Excel Solver:

Period t

# Hired Ht

# Laid off Lt

Workforce Size Wt

OvertimeOt

Inventory It

BacklogSt

SubcontractCt

Total Prod’n

Pt

0 0 0 80 0 1000 0 0 2583

1 0 15 65 0 1983 0 0 2583

2 0 0 65 0 1567 0 0 2583

3 0 0 65 0 950 0 0 2583

4 0 0 65 0 0 267 0 2583

5 0 0 65 0 117 0 0 2583

6 0 0 65 0 500 0 0 2583

Total cost over six months = $422,275

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Suppose now the demand forecast is modified as follows.

Month Old Demand Forecast

New Demand Forecast

January 1600 1000

February 3000 3000

March 3200 3800

April 3800 4800

May 2200 2000

June 2200 1400

How is the new forecast different from the previous one?

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We again use Excel Solver to find the optimal solution. See Chapter 3 Example 2.xls.

Total cost over six months = $432,858

The cost increased. Why?

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4. Updating the aggregate plan

How do we update the aggregate plan over time?

Jan Feb Mar Apr May Jun Jul

Jan Feb Mar Apr May Jun Jul

Create an aggregate plan for these six months with the demand forecast that exists at the beginning of January.

At the end of January, update the demand forecast for Feb thru Jun and generate a new forecast for Jul. Create an aggregate plan for Feb thru Jul.

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5. Discussion: model assumptions

What are some assumptions that you would like to modify? How would you modify them?

chapter 3 aggregate planning handout

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