Slide 1 LESSON 9: AGGREGATE PLANNINGEXAMPLES

Outline

- Examples
- Chase Strategy
- Level Strategy
- Optimization

Slide 2 Two Simple Strategies

- Chase strategy
- Produce as much as needed
- Zero inventory, no holding cost, no shortages
- Zero inventory is difficult to achieve because work hours may not be flexible
- Low inventory costs, high smoothing costs

- Level strategy
- Produce a constant amount each period
- Stable workforce, no hiring/firing, no overtime,
- no subcontract
- Low smoothing costs, high inventory costs

Slide 7 Optimization

- The chase and level strategies are two extreme strategies. Chase strategy minimizes inventory costs and level strategy minimizes smoothing costs. The goal of optimization is to identify a production plan that minimizes the total inventory and smoothing costs.This can be done using linear programming.
- Lesson 10 discusses the application of linear programming using Excel Solver.

Slide 8 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...)

Slide 9 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)

Slide 10 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)

Slide 11 Example

Problem 1: The original problem

Forecast

Beginning

Production

Production

Production

Inventory

Required

Hours

Hours

Required

Available

Fall

10000

500

Winter

8000

Spring

7000

Summer

12000

Overtime

Workers

Workers

Actual

Ending

Hours

Hired

Fired

Production

Inventory

Fall

Winter

Spring

Summer

Slide 12 Example

- Problem 1 sample computation:
Production required in fall = forecast in fall - beginning inventory in fall = 10,000 - 500 = 9,500

Production hours required in fall = production required in fall / productivity in units per worker = 9,500 / 0.50 = 19,000 hours

Production hours available in fall = 30 workers 60 days per season 8 hours per day = 14,400 hours

Overtime and temporary workers are not available in fall

Actual production in fall = production hours available in fall productivity in units per worker = 14,400 0.50 = 7,200 units

Slide 13 Example

- Problem 1 sample computation (continued):
Ending inventory in fall = actual production in fall - production required in fall = 7,200 - 9,500 = -2,300 units

Beginning inventory in winter = ending inventory in fall = -2,300 units

Overtime hours required in winter = production hours required - production hours available = 20,600 - 14,400 = 6,200 hours

Actual production in winter = (production hours available in winter + overtime hours in winter) productivity in units per worker = (14,400+6,200) 0.50 = 10,300 units

Slide 14 Example

- Problem 1 sample computation (continued):
Workers hired in summer = (production hours required in summer - production hours available in summer) / number of working hours per worker in summer [Note: the result should be rounded up, the number of workers is an integer and enough workers should be hired to avoid shortages]

= (23,600-14,400)/(60 days per season 8 hours per day)

= 19.167 rounded up to 20

Note: Actual production in summer is 11,800 units, as much as required. The assumption is that temporary workers will not work for full 480 hours, but only as much as needed. So, they can be stopped after producing 11,800 units.

Slide 15 Example

Problem 1: The original problem

Backorder

Overtime

Hiring

Firing

Cost

Cost

Cost

Cost

Fall

Winter

Spring

Summer

Inventory

Straighttime

Total

H. Cost

Cost

Cost

Fall

Winter

Spring

Summer

Total cost

Slide 16 Example

- Problem 1 sample computation:
Straighttime cost in summer = actual production hours $5 per hour = 23,600 hour 5 per hour = $118,000

Note: the actual production hour in summer is the same as production hours required in summer because sufficient number of temporary worker are hired and the temporary workers can be stopped after producing the required amount of products.

Slide 17 Example (Chase Strategy)

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

Forecast

Beginning

Net

Production

Workers

Inventory

Production

Hours

Required

Fall

10000

500

Winter

8000

Spring

7000

Summer

12000

Workers

Workers

Actual

Ending

Hired

Fired

Production

Inventory

Fall

Winter

Spring

Summer

Slide 18 Example

- Problem 2 sample computation:
Workers required in fall = production hours required in fall / number of working hours per worker in fall [Note: the result should be rounded up, the number of workers is an integer and enough workers should be hired to avoid shortages]

= 19,000/ (60 days per season 8 hours per day)

= 39.583 rounded up to 40

Number of workers hired in fall = Number of workers required in fall - number of workers available in the beginning of fall = 40 - 30 = 10

Slide 19 Example

- Problem 2 sample computation (continued):
Actual production in fall = Number of workers available in fall 60 days per season 8 hours per day 0.5 units per worker per hour = 40 60 8 0.50 = 9,600 units

Ending inventory in fall = actual production in fall - production required in fall = 9,600--9,500 = 100 units

Beginning inventory in winter = ending inventory in fall = 10 units

Number of workers fired in winter = Number of workers available in the beginning of winter - number of workers required in winter = 40 - 33 = 7.

Slide 20 Example (Chase Strategy)

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

Hiring

Firing

Straight

Inventory

Total

Cost

Cost

time

Holding

Cost

Cost

Cost

Fall

Winter

Spring

Summer

Total

Slide 21 Self Study

Example (Chase Strategy)

Problem 3: Chase, no overtime, flexible hours

Slide 22 Example (Level Strategy)

Problem 4: Constant workforce, no overtime, no shortages

Computation of the workforce required for avoiding shortages

Net

Cumulative

Cumulative

Workers

Production

Net

units

Required

Requirement

Production

produced

Requirement

per worker

Fall

9500

Winter

8000

Spring

7000

Summer

12000

Workers hired

Initial hiring cost

Workers fired

Initial firing cost

Total workers

Straighttime cost

Slide 23 Example (Level Strategy)

- Problem 4 computation of number of workers required:
Step1:

For each period compute the cumulative net production requirement

Step2:

For each period compute the cumulative units produced per worker

Step 3:

For each period compute the number of workers required to meet the cumulative demand upto that period by dividing the cumulative net production by the cumulative units produced and rounding up.

Slide 24 Example (Level Strategy)

- Problem 4 computation of number of workers required:
Number of workers required to meet the cumulative demand upto

Fall

Winter

Spring

Summer

Step 4:

The number of workers required is the maximum of all the numbers obtained in Step 3

Number of workers required = max ( ) =

Slide 25 Example (Level Strategy)

Problem 4: Constant workforce, no overtime, no shortages

Forecast

Beginning

Actual

Ending

Inventory

Production

Inventory

Fall

10000

500

Winter

8000

Spring

7000

Summer

12000

Inventory

Backorder

Total

Cost

Cost

Cost

Fall

Winter

Spring

Summer

Total cost

Slide 26 Self Study

Example (Level Strategy)

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

Slide 27 Self Study

Example (Level Strategy)

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

Slide 28 Self Study

Example (Level Strategy)

Problem 6: Constant 37 workers, overtime to prevent shortages

Slide 29 Self Study

Example (Level Strategy)

Problem 6: Constant 37 workers, overtime to prevent shortages

Slide 30 READING AND EXERCISES

Lesson 9

Reading: Section 3.4, pp. 121-127 (4th Ed.), pp. 117-125 (5th Ed.)

Exercises: 9, 13 and 14, pp. 127-129 (4th Ed.), pp. 123-124 (5th Ed.)

Lesson 10

Reading: Section 3.5-3.6, pp. 129-138 (4th Ed.), pp. 125-135 (5th Ed.)

Exercises: 17, 19 and 20, pp. 138-139 (4th Ed.), pp. 133-134 (5th Ed.)