Aggregate Planning
Aggregate Planning
Aggregate Planning
Learning Objectives: Understand the concepts and methods of aggregate planning Formulate and solve capacity planning problem
Demand Management
Demand management is the interface between manufacturing planning and control and the marketplace. Activities include: Forecasting. Order Processing. Making delivery promises.
Long-range planning
Intermediate-range planning
Short-range planning
Operations managers
Figure 13.1
Process Planning
Long Range
Services
Weekly Workforce & Customer Scheduling Daily Workforce & Customer Scheduling
Short Range
Forecasts needed
Annual demand by item and by region
Plant manager
Shop superintendent
Aggregate Planning
Marketplace and demand Product decisions Research and technology
Process planning and capacity decisions Workforce Aggregate plan for production Raw materials available Inventory on hand
Figure 13.2
Business or annual plan Production or staffing Plan (Aggregate Plan) MPS or workforce schedule
Figure 14.1
8
Aggregate Planning
Aggregate Plan
Aggregate Plan: A statement of a companys production rates, workforce levels, and inventory holding based on estimates of customer requirements and capacity limitations
Service Industry
Manufacturing Industry
Aggregate Planning: Attempts to match the supply of and demand for a product or service by determining the appropriate quantities and timing of inputs, transformation, and outputs. Decisions made on production, staffing, inventory and backorder levels. Characteristics of aggregate planning: Considers a "planning horizon" from about 3 to 18 months, with periodic updating Looks at aggregate product demand, stated in common terms Looks at aggregate resource quantities, stated in common terms Possible to influence both supply and demand by adjusting production rates, workforce levels, inventory levels, etc., but facilities cannot be expanded.
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Determines resource capacity to meet demand For intermediate time horizon, 6-12 months Not feasible to build new facility May be feasible to hire/lay off workers, overtime, or subcontract Adjusting capacity OR managing demand
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Aggregate plan
Competitive Pricing
Inventory Levels
14
15
Aggregate Planning Determine the quantity and timing of production for the immediate future
Objective is to minimize cost over the planning period by adjusting
Production rates Labor levels Inventory levels Overtime work Subcontracting Other controllable variables
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Aggregate Planning
Required for aggregate planning
A logical overall unit for measuring sales and output A forecast of demand for intermediate planning period in these aggregate units
Aggregate Planning
Combines appropriate resources into general terms
ABC Company
ABC Co produces nearly 40% of the industrial paints consumed in the India
Matches fluctuating demand by brand to plant, labor, and inventory capacity to achieve high facility utilization High facility utilization requires
Meticulous cleaning between batches
Effective maintenance Efficient employees Efficient facility scheduling
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Aggregate Planning
Quarter 1 Feb 120,000
Jan 150,000
Apr 100,000
Jul 180,000
Sep 140,000
20
21
22
26
27
29
Table 13.1
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Subcontracting
Table 13.1
31
Influencing demand
Table 13.1
32
Table 13.1
33
35
Some combination of capacity options, a mixed strategy, might be the best solution
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Graphical and Charting Methods Popular techniques Easy to understand and use
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Planning Example 1
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Total expected demand Average requirement = Number of production days 6,200 = = 50 units per day 124
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Planning Example 1
Production rate per working day Forecast demand
70 60 50 40 30
Jan
Feb
Mar
Apr
May
June
= Month
= Number of working days
40
22
Figure 13.3
18
21
21
22
20
Planning Example 1
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
Table 13.3
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Planning Example 1
Cost Information Production at Month 50 Units per Day Inventory carry cost Jan 1,100 Subcontracting cost per unit
Average pay rate Overtime pay rate
Monthly Inventory Ending Change Inventory $ 5 per unit per month +200 $10 per unit +250 200 650 100 0 1,850 +200 400 $ 5 per hour ($40 per day )
$ 7 per hour (above 8 hours per day ) -150 500 1.6 hours per unit
Feb
900 1,050
Mar
Apr
1,050
1,200
1,500
-400 -100
Cost of increasing daily production rate (hiring June 1,000 1,100 and training) Cost of decreasing daily production rate (layoffs)
Total units of inventory carried over from one month to the next = 1,850 units Table 13.3 Workforce required to produce 50 units per day = 10 workers
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Planning Example 1
Costs Cost Information Production at Month carrying 50 Units per Day Inventory carry cost Inventory Jan 1,100 Subcontracting cost per unit Feb Regular-time labor 900 Average pay rate Mar 1,050
Overtime pay rate
Monthly Calculations Demand Inventory Ending Forecast Change Inventory 5 per unit per month $9,250 (= $ 1,850 units carried x $5 per ) per 900 unit +200 $10 unit 200 700 (= $ +200 400 49,600 10 x $40 per day x 5 workers per hour ($40 per day ) ) 800 124 days +250 650
$ 7 per hour (above 8 hours per day ) -150 500 1.6 hours per unit
Aprcosts (overtime, 1,050 1,200 Other hiring, layoffs, Labor-hours to produce a unit May 1,100 1,500 subcontracting) 0 Cost of increasing daily production rate (hiring June 1,000 1,100 Total cost $58,850
and training) Cost of decreasing daily production rate (layoffs)
-400 -100
100 0
1,850
Total units of inventory carried over from one month to the next = 1,850 units Table 13.3 Workforce required to produce 50 units per day = 10 workers
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Planning Example 1
7,000
6,000 Cumulative demand units 5,000 4,000 3,000 Reduction of inventory Cumulative level production using average monthly forecast requirements
2,000
1,000 Jan Feb Mar
Excess inventory
Apr May June
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Figure 13.4
Planning Example 2
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Planning Example 2
Production rate per working day Forecast demand
70 60 50 40 30
Level production using lowest monthly forecast demand
Jan
Feb
Mar
Apr
May
June
= Month
= Number of working days
46
22
18
21
21
22
20
Planning Example 2
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
Table 13.3
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Planning Example 2
Cost Information
Inventory carry cost
In-house production = 38 units $10 per unit per day x$ 124 days 5 per hour ($40 per day) Average pay rate $ 7 per hour = 4,712 units Overtime pay rate
Subcontracting cost per unit (above 8 hours per day) 1.6 hours per unit Subcontract units = 6,200 - 4,712 Cost of increasing daily production rate (hiring $300 per unit = 1,488 units and training) Labor-hours to produce a unit Cost of decreasing daily production rate (layoffs) $600 per unit
Table 13.3
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Planning Example 2
Cost Information
Inventory carry cost
In-house production = 38 units $10 per unit per day x$ 124 days 5 per hour ($40 per day) Average pay rate $ 7 per hour = 4,712 units Overtime pay rate
Subcontracting cost per unit (above 8 hours per day) 1.6 hours per unit Subcontract units = Calculations 6,200 - 4,712 Cost of increasing daily production rate (hiring (= $300 per unit x $40 per day Regular-time labor $37,696 7.6 workers = 1,488 units and training) x 124 days) Labor-hours to produce a unit Costs Cost of decreasing daily production rate (layoffs) $600 per unit
Subcontracting
14,880
$52,576
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Planning Example 3
Month Jan Expected Demand 900 Production Days 22 Demand Per Day (computed) 41
Feb
Mar
700
800
18
21
39
38
Apr
May
1,200
1,500
21
22
57
68
June
1,100
6,200
20
124
55
Table 13.2
Planning Example 3
Production rate per working day
70 60 50 40 30
Jan
Feb
Mar
Apr
May
June
= Month
= Number of working days
51
22
18
21
21
22
20
Planning Example 3
Cost Information
Inventory carrying cost Subcontracting cost per unit Average pay rate Overtime pay rate Labor-hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate (layoffs)
Table 13.3
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Planning Example 3
Cost Information
Month Jan Forecast (units) 900 700
Extra Cost of Decreasing Production (layoff ) month Total Cost per unitcost per $ 7,200
6,800 (= 2 x($40 $600) per day) $ 5 per hour $600 $ 7 per hour 7,000 (= 1 x $600) (above 8 hours per day)
$1,200
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6,400
9,600
15,300
Cost of increasing daily production rate (hiring $3,300 $300 per unit May 1,500 68 12,000 (= 11 x $300) and training) Cost daily rate (layoffs) June of decreasing 1,100 55 production 8,800
$49,600 $9,000
15,300
(= 13 x $600)
16,600 $68,200
Table 13.3
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Plan 2 $ 0 $
Plan 3 0
37,696 0
0 0 0 $52,576
49,600 0
9,000 9,600 0 $68,200
Table 13.5 54
Mathematical Approaches
Other Models
Linear Decision Rule Simulation
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Transportation Method
Sales Period Mar Apr May 800 1,000 750 700 50 150 100 per tire per tire per tire per tire 700 50 150 tires 700 50 130
Demand Capacity: Regular Overtime Subcontracting Beginning inventory Costs Regular time Overtime Subcontracting Carrying $40 $50 $70 $2
Table 13.6
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Transportation Example
Important points
1. Carrying costs are $2/tire/month. If goods are made in one period and held over to the next, holding costs are incurred 2. Supply must equal demand, so a dummy column called unused capacity is added 3. Because back ordering is not viable in this example, cells that might be used to satisfy earlier demand are not available
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Transportation Example
Important points
4. Quantities in each column designate the levels of inventory needed to meet demand requirements
5. In general, production should be allocated to the lowest cost cell available without exceeding unused capacity in the row or demand in the column
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Transportation Example
Table 13.7
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Builds a model based on managers experience and performance A regression model is constructed to define the relationships between decision variables
Other Models
Linear Decision Rule
Minimizes costs using quadratic cost curves Operates over a particular time period
Simulation
Uses a search procedure to try different combinations of variables Develops feasible but not necessarily optimal solutions
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Optimization
Heuristic
Table 13.8
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Table 13.9
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Yield Management
Demand Curve Potential customers exist who are willing to pay more than the $15 variable cost of the room
Passed-up contribution
50
Some customers who paid $150 were actually willing to pay more for the room
$ margin = (Price) x (50 rooms) = ($150 - $15) x (50) = $6,750 $15 Variable cost of room
Money left on the table $150 Price charged for room Price
Figure 13.5 65
Demand Curve
Total $ margin = (1st price) x 30 rooms + (2nd price) x 30 rooms = ($100 - $15) x 30 + ($200 - $15) x 30 = $2,550 + $5,550 = $8,100
60
30
Price
Figure 13.6 66
Duration of use
Unpredictable
Figure 13.7
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Making Yield Management Work 1. 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
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Executive Line
Units
Demand
Time
1.
2. 3.
4.
5. 6. 7.
Increase or decrease working hours (overtime and undertime) Subcontracting work to other firms Using part-time workers Providing the service or product at a later time period (backordering)
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Planning Strategies
Chase Strategies
PURE STRATEGIES
Match demand during the planning horizon by either Vary workforce or vary output rate
Level Strategies
Maintain a constant workforce level or constant output rate during the planning horizon Constant workforce or constant output rate
Mixed Strategies
Pure Strategy
Level Production
Demand
Chase Demand
Demand Production Units
Production
Units
Time
Time
TABLE 14.1
PLANNING STRATEGIES FOR AGGREGATE PLANS Possible Alternatives during Slack Season
Layoffs Layoffs, undertime, vacations No layoffs, building anticipation inventory, undertime, vacations Layoffs, building anticipation inventory, undertime, vacations
Strategy
1. Chase #1: vary workforce level to match demand 2. Chase #2: vary output rate to match demand 3. Level #1: constant workforce level
Regular-Time Costs Overtime Costs Hiring and Layoff Costs Inventory Holding Costs Backorder and Stockout Costs
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Aggregate Planning Methods: Intuitive Methods Intuitive methods use management intuition, experience, and rules-of-thumb, frequently accompanied by graphical and/or spreadsheet analysis.
Advantage:
Disadvantage:
easy to use and explain many solutions are possible, most of which are not optimal
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Ex 1 Candy Company
Given the following costs and quarterly sales forecasts of a candy company, compare the two strategies: Strategy 1: Level production with constant workforce level Strategy 2: Chase production by varying workforce level
Quarter
Spring Summer Fall Winter
$100 per worker $500 per worker $0.50 per pound per quarter 1000 pounds per quarter 100 workers
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Transportation Method
Alternatives
Quarter
Quarter 1
0
2
h
3
2h
4
3h
I0
r r+h r+2h r+3h u
R1
c c+h c+2h c+3h 0
A method of LP Gather all cost info into one matrix Try to obtain the lowest cost alternative
O1 S1
u
R2
c+b c c+h c+2h 0
O2
s+b s s+h s+2h 0
S2
r+2b r+b r r+h u
R3
c+2b c+b c c+h 0
O3
s+2b r+3b s+b r+2b s r+b s+h r 0
S3
u
R4
c+3b c+2b c+b c 0
O4
s+3b s+2b s+b s 0
Subcontract
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S4
Requirements
D1
D2
D3
D4 + I4
Notations
It = inventory at the end of period t (I0 = beginning inventory) h = holding cost per unit per period, r = regular production cost per unit, o = overtime cost per unit, u = undertime cost per unit s = subcontracting cost per unit, b = backordering cost per unit per period Rt = regular-time capacity in period t Ot = overtime capacity in period t St = subcontracting capacity in period t Dt = forecasted demand for period t U = total unused capacities
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Tableau Method
Step 1: Put all capacities from the total capacity column into the unused capacity column. Next, put unit costs in each of the small boxes Step 2: In column 1 (period 1), allocate as much production as you can to the cell with the lowest cost but do not exceed the unused capacity in that row or the demand in that column. Step 3: Subtract your allocation from the unused capacity for the row. This quantity must never be negative.
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Tableau Method
(Contd)
Step 4: If there is still some demand left, repeat step 2, allocating as much production as possible to the cell with the next-to-lowest cost. Repeat until the demand is satisfied. Step 5: Repeat steps 2 through 4 for periods 2 and beyond. Take each column separately before proceeding to the next. Be sure to check all cells with unused capacity for the cell with the lowest cost in a column.
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Ex 2: Transportation Method
Given the following costs and quarterly sales forecasts, use the transportation method to design a production plan. What is the total cost of the plan?
Quarter 1 2 3 4
Inventory carrying cost = $3 per unit per quarter Production/worker = 1000 units/quarter Regular workforce = 50 workers Overtime capacity = 50,000 units Subcontracting capacity = 40,000 units Regular production cost = $50/unit Overtime production cost = $75/unit Subcontracting cost = $85/unit
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Pure/Mixed Strategy: not guarantee optimal solution LP: can get optimal solution LP: Excel, LINGO, CPLEX, LP Formulation**
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Production Plan (manufacturing aggregate plan): A managerial statement of the period-by-period (timephased) production rates, work-force levels, and inventory investment, given customer requirements and capacity limitations. Staffing Plan (service aggregate plan): A managerial statement of the period-by-period staff sizes and labour-related capacities, given customer requirements and capacity limitations.
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Objectives of Aggregate Planning Objective of aggregate planning frequently is to minimize total cost over the planning horizon. Other objectives should be considered: maximize customer service minimize inventory investment minimize changes in workforce levels minimize changes in production rates maximize utilization of plant and equipment
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Aggregate Planning Strategies Active strategy: Attempts to handle fluctuations in demand by focusing on demand management Use pricing strategies and/or advertising and promotion Develop counter-cyclical products Request customers to backorder or advance-order Do not meet demand
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Passive strategy (reactive strategy): Attempts to handle fluctuations in demand by focusing on supply and capacity management Vary size work force size by hiring or layoffs Vary utilization of labour and equipment through overtime or idle time Build or draw from inventory Subcontract production Negotiate cooperative arrangements with other firms Allow backlogs, back orders, and/or stockouts Mixed strategy: Combines elements of both an active strategy and a passive (reactive) strategy Firms will usually use some combination of the two
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Basic Approaches
Chase approach
capacities (workforce levels, production schedules, output rates, etc.) are adjusted to match demand requirements over the planning horizon. Advantages: anticipation inventory is not required, and investment in inventory is low labour utilization is kept high Disadvantages: expense of adjusting output rates and/or workforce levels alienation of workforce Capacities (workforce levels, production schedules, output rates, etc.) are kept constant over the planning horizon. Advantages: stable output rates and workforce levels Disadvantages: greater inventory investment is required increased overtime and idle time resource utilizations vary over time
Level Approach
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