• 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

Two Simple Strategies

Chase Strategy

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Production

Chase Strategy

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CumulativeDemand

CumulativeProduction

Level Strategy

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Level Strategy

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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.

• 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

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

Example

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

• Problem 1 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

Example

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

Example

• Problem 1 (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.

Example

Problem 1: The original problem

Example

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

• 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.

Example

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

Example (Chase Strategy)

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

• 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

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.

Example

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

Example (Chase Strategy)

Hiring Firing Straight Inventory Total

Cost Cost time Holding Cost

Cost Cost

Fall

Winter

Spring

Summer

Total

Problem 3: Chase, no overtime, flexible hours

Net Production Workers Workers Workers

Production Hours Required Hired Fired

Requirement Required

Fall 9500 19000 40 10 0

Winter 8000 16000 34 0 6

Spring 7000 14000 30 0 4

Summer 12000 24000 51 21 0

Hiring Firing Straight Total

Cost Cost time Cost

Cost

Fall 1000 0 95000 96000

Winter 0 1200 80000 81200

Spring 0 800 70000 70800

Summer 2100 0 120000 122100

Total 370100

Example (Chase Strategy)Self Study

Problem 4: Constant workforce, no overtime, no shortages

Example (Level Strategy)

Workers hired Initial hiring cost

Workers fired Initial firing cost

Total workers Straighttime cost

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

• 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.

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 ( ) =

Example (Level Strategy)

40583.39240/9500 ===

Problem 4: Constant workforce, no overtime, no shortages

Example (Level Strategy)

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

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

Workers hired 6 Initial hiring cost 600

Workers fired 0 Initial firing cost 0

Total workers 36 Initial recruitment cost 600

Straighttime cost 345600

Example (Level Strategy)Self Study

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

Forecast Beginning Actual Ending

Inventory Production Inventory

Fall 10000 500 8640 -860

Winter 8000 -860 8640 -220

Spring 7000 -220 8640 1420

Summer 12000 1420 8640 -1940

Inventory Backorder Total

Holding Cost Cost

Cost

Fall 0 8600 8600

Winter 0 2200 2200

Spring 7100 0 7100

Summer 0 19400 19400

Total 383500

Example (Level Strategy)Self Study

Problem 6: Constant 37 workers, overtime to prevent shortages

Workers hired 7 Initial hiring cost 700

Workers fired 0 Initial firing cost 0

Total workers 37 Initial recruitment cost 700

Straighttime cost 355200

Example (Level Strategy)Self Study

Problem 6: Constant 37 workers, overtime to prevent shortages

Forecast Beginning Regular Units Units

Inventory Production Available Overtime

Before OT

Fall 10000 500 8880 -620 620

Winter 8000 0 8880 880 0

Spring 7000 880 8880 2760 0

Summer 12000 2760 8880 -360 360

Ending Inventory Overtime Total

Inventory Holding Cost Cost

Cost

Fall 0 0 9920 9920

Winter 880 4400 0 4400

Spring 2760 13800 0 13800

Summer 0 0 5760 5760

Total 389780

Example (Level Strategy)Self Study