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Time, Rate, and Productivity

Management of OperationsBrad C. Meyer

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Introduction Time, Production Rate, and Productivity are basic measures critical to managing operations. Operations can be considered a transformation process.“Throughput” items are transformed by “processors” in activity that takes time.

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TimeExpressed in duration units:

minuteshoursdaysmonths

Activity time is expressed as number of duration units per throughput item.

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Why determine activity time? To pay fair wagesTo know how much to rightfully expect from an employeeTo promise completion dates to customersTo schedule processors and material purchases, to do capacity planning

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Example times5 minutes per customer10 seconds per part7 weeks per installation

time duration per throughput unit

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Ratethe reciprocal of timenumber of throughput units per unit of time durationcan be a measure of capacity or of actual output generated

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Example rates12 customers per hour6 parts per minute7 installations per year

number of throughput units -------------------------------------------------------------------------------------------------------------

unit of time duration

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Question…Suppose a barber can cut a head of hair in 15 minutes. How many customers does he serve per 8 hour day?

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And the answer is….We don’t know. All we know is that his capacity is 4 per hour or 32 per day. How many he serves depends on how many come to the shop looking for service.Be careful to distinguish between capacity and actual performance.

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Example 1one customer every 6 minutes – time or rate?

This is expressed like a rate: throughput per time, but the number “6” is a time: 6 minutes per customer. Rates should be expressed with a simple unit denominator, like “per minute”, not “per 6 minutes”

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One customer every six minutes:

Time = 6 minutes per customerRate = .16667 customers per minute

or change time units to get: Rate = 10 customers per hour

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Example 2A crew can clean 10 apartments in a four-hour morning.

Time?

Rate?

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Example 2A crew can clean 10 apartments in a four-hour morning.

Time? 4 hours / 10 apartments = .40 hours per apartment (or 24 minutes per apartment)

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Example 2A crew can clean 10 apartments in a four-hour morning.

Rate? 10 apartments / 4 hours = 2.5 apartments per hour.

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Example 2 - extendedA crew can clean 10 apartments in a four-hour morning. The crew has 3 people. What is the time and rate per person?

Time: 3 people working 4 hours is 12 hours total.

12 hours/ 10 apartments = 1.2 hrs per person per apartment

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Example 2 - extendedA crew can clean 10 apartments in a four-hour morning. The crew has 3 people. What is the time and rate per person?

Rate: 10 apartments per 12 total hours =

10/12 = .833 apartments per person per hour.

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Productivitya measure of ability to turn inputs to outputs.

outputproductivity = ------------ input

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Productivity examplesrestaurant: customers per labor hourretail: sales per square footutility plant: kilowatts per ton of coalbank: new loan $ per employee month

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Three kinds of productivitylabor productivityvalue-added labor productivitymultifactor productivity

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labor productivityamount a worker accomplishes

units/ hr or $ / hr

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Example128 garments produced in 360 hours

120 without defects, sell @$200 each 8 with defects, sell @ $90 each Material cost = $70 per dresslabor prod. = 128 garments/360 hrs =.355 garments/hr orlabor prod. = (120*200 + 8*90)/360 hrs = $68.67/hr

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Note: this ignores the $70 material cost of the garments.

To adjust for this, there is another kind of productivity: value-added productivity…

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Value added labor productivity=(ending value – starting value)/hrs

such as:

(selling price – cost of materials)*units made / hrs

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For garment problem:

va prod. = [(200-70)*120 + (90-70)*8]/360

= $43.77 / hr

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Other assumptions:For value added labor productivity,

some subtract overhead (from sales revenue) and some don’t. For purposes of this class, I will specify in the problem which costs to subtract and which to ignore.

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Multifactor productivityMultifactor productivity = value of outputs/cost of inputs (a ratio, hopefully > 1)

value of outputs = price*number of units

cost of inputs = labor+material+overhead

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ExampleMaking CD players, sell for $300Quantity made was 2000.Labor = $30 per unitMaterial = $70 per unitOverhead = $50 per unit

Multifactor productivity = (300*2000)/((30+70+50)*2000) = 2.0

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Example continuedwhat percentage increase in productivity would occur with a 25% savings in material cost?.25*70 = $17.5 reduced material cost70 – 17.5 = 52.5Mf prod = 300*2000 / (30+52.5+50)*2000

= 2.264% change = 100*(new – old)/old = 100*(2.264-2)/2 =13.2%

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Throughput timeThe term “throughput time” is commonly used to describe how long a customer or part stays in a system. It includes both processing time and waiting time. It could include transportation and handling time as well.

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ExampleAt a dental office, a customer spends 8 minutes on average in the waiting room, 25 minutes in the dentist’s chair, and 5 minutes with the receptionist, checking in before the appointment and paying after the appointment. What is the throughput time for a customer at the dental office?

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Total time = 8 + 25 + 5 = 38 minutes.

Note, in a situation like this, the dentist’s processing rate would be based on the 25 minutes she spends per customer, not the 38 minutes in total that the customer spends at the office.