CHAPTER 14AGGREGATE PLANNING

Outline

• Aggregate Planning– Issues– Costs

• Two Strategies– Chase Strategy– Level Strategy

• Optimization

Hierarchy of Production Decisions

Aggregate Planning

Master Production Schedule

Material Requirements Planning

Operations Scheduling

Vehicle Routing

Forecast of Demand

Master Production Schedule

200200

Ladder-back chair

Kitchen chair

Desk chair

1 2

April May

790790

3 4 5 6 7 8

200200

150150

120120

200200

150150

200200

120120

Aggregate production plan for chair family

550550

Materials Requirement Planning

Back slats

Leg supports

Seat cushion

Seat-frameboards

Frontlegs

Backlegs

Issues in Aggregate Planning

• Smoothing– Hiring, firing workers

• Bottleneck problems– Sharp change in demand

• Planning horizon– Inaccurate forecasts are associated with too large

horizon and planning may be ineffective with too small horizon

• Nature of Demand– Forecasts are usually wrong!

Aggregate Production Planning• Input

– Demand forecast– Level of resources– Relevant cost information

• Output– Aggregate production quantities

• production, inventory, backorder

– Level of resources needed• Workforce, overtime, machine capacity level,

subcontracting

Costs in Aggregate Planning• Smoothing costs

– Hiring and firing costs

• Inventory holding costs– Cost of capital, storage, insurance, losses

• Shortage costs– Backorder, lost sales

Costs in Aggregate Planning

• Production costs– Straight time costs

• Labor costs, regular time ($/hour)

– Overtime and subcontracting costs• Labor costs, overtime costs ($/hour)

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

Smoothing Costs

Slope = u

nit hirin

g costSlope = unit firing cost

Cos

tNumber of hiresNumber of fires

Inventory Holding

and Shortage

Costs

Slope = u

nit holding cost

Slope = unit backorder cost

Cos

tPositive inventoryBackorder

A Feasible Aggregate Plan

Period

Cum

ulat

ive

Num

ber

of U

nits

A feasible productionschedule

Inventory

CumulativeNetDemand

Constraints

• Limits on overtime

• Limits on layoffs

• Limits on capital available

• Limits on stockouts and backorders

• Chase strategy– Zero inventory, no holding cost, no shortages– Zero inventory is difficult to achieve

Two Simple Strategies

Time

Units

Production

Demand

Two Simple Strategies

• Level strategy– Stable workforce, no hiring/firing, no overtime,– no subcontract

Time

Production

Demand

Units

Optimization

• Linear Programming– Excel Solver

• Difficulty– Integer variables: number of workers

Example

• Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10, 000; winter, 8,000; spring 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring if the overtime is necessary to prevent stock-outs at the end of those quarters. Overtime is not available during fall. (Continued...)

Example

Relevant costs are: hiring, $100 for each temp; layoff, $200 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime $8 per hour. Assume that the productivity is 0.5 units per worker hour, with eight hours per day and 60 days per season.

• Develop a production plan using

(1) all the constraints as stated

(2) chase strategy, no overtime, work hours not flexible

(3) chase strategy, no overtime, flexible hours (self study)

Example

(4) Suppose that a level strategy will be used without any overtime. What is the minimum number of workers required to avoid shortages? Develop a production plan using the minimum number of workers required to avoid shortages.

(5) Assuming that the shortages are allowed and that 6 new workers will be hired in the beginning of the fall term develop a production plan using level strategy and no overtime (self study)

(6) Assuming that the overtime will be used in fall and winter to prevent shortages and that 7 new workers will be hired in the beginning of the fall term, develop a production plan using level strategy with overtime (self study)

Example

Problem 1: The original problem

Forecast Beginning Production Production Production Inventory Required Hours Hours

Required AvailableFall 10000 500Winter 8000Spring 7000Summer 12000

Overtime Workers Workers Actual Ending Hours Hired Fired Production Inventory

FallWinterSpringSummer

Example

Bakorder Overtime Hiring FiringCost Cost Cost Cost

FallWinterSpringSummer

Inventory Straighttime Total CostHolding Cost

CostFallWinterSpringSummer

Total

Problem 1: The original problem

Forecast Beginning Net Production WorkersInventory Production Hours Required

Required RequiredFall 10000 500

Winter 8000Spring 7000

Summer 12000Workers Workers Actual Ending

Hired Fired Production InventoryFall

WinterSpring

Summer

Problem 2: Chase, no overtime, work hours not flexible

Example (Chase)

Example (Chase)

Bakorder Overtime Hiring FiringCost Cost Cost Cost

FallWinterSpringSummer

Inventory Straighttime Total CostHolding Cost

CostFallWinterSpringSummer

Total

Problem 2: Chase, no overtime, work hours not flexible

Example (Chase)Problem 3: Chase, no overtime, flexible hours

Net Production Workers Workers WorkersProduction Hours Required Hired Fired

Requirement RequiredFall 9500 19000 40 10 0Winter 8000 16000 34 0 6Spring 7000 14000 30 0 4Summer 12000 24000 51 21 0

Hiring Firing Straight TotalCost Cost time Cost

CostFall 1000 0 95000 96000Winter 0 1200 80000 81200Spring 0 800 70000 70800Summer 2100 0 120000 122100Total 370100

Example (Level)Problem 4: Constant workforce, no overtime, no shortages

Workers hired Initial hiring costWorkers fired Initial firing costTotal workers Initial recruitment cost

Straighttime cost

Computation of the workforce to avoid shortages

Production Cumulative Cumulative WorkersRequirement Production units Required

Requirement producedper worker

Fall 9500Winter 8000Spring 7000Summer 12000

Forecast Beginning Actual Ending Inventory Production Inventory

Fall 10000 500Winter 8000Spring 7000Summer 12000

Inventory Backorder Total costHolding Cost

CostFallWinterSpringSummer

Total

Problem 4: Constant workforce, no overtime, no shortages

Example (Level)

Problem 5: Constant 36 workers, no overtime, shortages allowed

Example (Level)

Workers hired 6 Initial hiring cost 600Workers fired 0 Initial firing cost 0Total workers 36 Initial recruitment cost 600

Straighttime cost 345600

Problem 5: Constant 36 workers, no overtime, shortages allowed

Example (Level)

Forecast Beginning Actual Ending Inventory Production Inventory

Fall 10000 500 8640 -860Winter 8000 -860 8640 -220Spring 7000 -220 8640 1420Summer 12000 1420 8640 -1940

Inventory Backorder Total Holding Cost Cost

CostFall 0 8600 8600Winter 0 2200 2200Spring 7100 0 7100Summer 0 19400 19400

Total 383500

Problem 6: Constant 37 workers, overtime to prevent shortages

Example (Level)

Workers hired 7 Initial hiring cost 700Workers fired 0 Initial firing cost 0Total workers 37 Initial recruitment cost 700

Straighttime cost 355200

Problem 6: Constant 37 workers, overtime to prevent shortages

Example (Level)

Forecast Beginning Regular Units UnitsInventory Production Available Overtime

Before OTFall 10000 500 8880 -620 620Winter 8000 0 8880 880 0Spring 7000 880 8880 2760 0Summer 12000 2760 8880 -360 360

Ending Inventory Overtime Total Inventory Holding Cost Cost

CostFall 0 0 9920 9920Winter 880 4400 0 4400Spring 2760 13800 0 13800Summer 0 0 5760 5760

Total 389780

Reading and Exercises

• Chapter 14 Pages 558-571

• Problems 4,5