Implementing programmable automation typically requires substantial investment, or capital expenditure, which upper management must deem justified. Most collegiate engineering and technology programs offer engineering economic analysis courses that present numerous methods of justifying capital expenditures, such as developing cash flows over the life of the project and considering the time value of money. However, the decision of whether or not to invest in an automation project is still very difficult for a firm to make because of the large number of variables to be considered. Many larger firms have arcane justification methodologies. A productivity analysis, on the other hand, is a simple, single metric that can clearly show when an automation project should be funded. It compares the performance of the system before and after the automation is applied. In fact, it provides such great scrutiny of a system that it should be used prior to any automation plans. In so doing, the automation strategies, defined in Chapter 1, can be accurately applied. This chapter focuses on how productivity calculations are used to identify, evaluate and justify automation.

2.2 Productivity Calculations

Recall that the productivity of a manufacturing system is determined by the simple ratio,

productivity = output/input,

where, as we will see, the input and output units are number of parts per monetary unit.

For manufacturers of discrete products a system’s output is the number of parts produced over a certain time frame. The system inputs are those resources needed to acquire and convert raw material into a finished product over that same time frame. Typical resource input comprises labor, capital, material, and energy. Even though each of these inputs is vastly different, they can be expressed in monetary terms. Thus, productivity will be expressed in terms of the number of parts produced per dollar of input (# of parts/$ input). This is a simple and effective means of accessing a manufacturing operation, machine, process, system or facility’s performance.

Obviously, the time frame over which a form of input is measured should be the same as the output that results. For products manufactured in high quantities, the time unit is usually hours; however, time units of days, weeks, or years can be used as well.

A partial productivity (P_P) calculation considers only one input (such as labor). It is defined as:

P_P = P_O/P_I,

where

P _O	=	number of parts output from a process in a specified time frame (# of parts/hr); this is often termed the production rate of the process
P _I	=	amount of money input into the process over the same time frame ($/hr).

A combined productivity (P_C) calculation considers two or more inputs. Accordingly, combined productivity is given by the following equation:

P_C = P_O/SP_I

where

SP _I

monetary sum of partial productivity measures input over a given time frame ($/hr).

Thus,

SP_I = P_{I labor} + P_{I cap} + P_{I mat} + P_{I energy}

The following examples demonstrate calculation of partial and combined productivity.

Example 2.1

A manufacturing process can produce 120 parts per hour. The process requires two laborers, each earning $18/hour. What is labor partial productivity of the process?

Solution

The governing equation is:

P_{P labor} = P_O /P_{I labor}

The output in parts per hour is

P_O = 120 parts/hr

Since there are 2 laborers, the labor input is

P_{I labor} = 2 laborers × ($18/hr)/laborer = $36/hr.

Thus,

P_{P labor} = P_O/P_{I labor} = (120 parts/hr)/($36/hr) = 3.33 parts/$.

So here the process can produce 3.33 parts for every dollar of labor input.

Example 2.2

The manufacturing process described in Example 2.1 uses a machine with capital cost of $45/hr. The machine requires 75 kW of power to operate. Cost of electricity is $0.057/kW-hour (kWh). The machine processes 150 lb of material per hour. The material costs $0.45/lb. Using the labor input costs found in Example 2.1, calculate the combined productivity of the process.

Solution

The governing equations are

P_C = P_O/SP_I

SP_I = P_{I labor} + P_{I cap} + P_{I mat} + P_{I energy}.

The output in terms of parts per hour was given as

P_O = 120 parts/hr.

The labor partial productivity input was determined in Example 2.1 to be

P_{I labor} = $36/hr.

The cost of capital to run the machine is given as

P_{I cap} = $45/hr.

The cost of energy input per hour is found by converting power into energy. For 1 hour of operation the energy used will be:

energy = (power)(time) = (75 kW)(1 hr) = 75 kWh.

Thus, the machine will use 75 kWh for every hour of use. Therefore, the cost of the energy input into the process will be

P_I _energy = (energy use/hr)(electricity cost) = (75 kWh/hr)($0.057/kWh) = $4.28/hr.

The material cost input into the process is determined by multiplying the amount of material used per hour by the cost of the material:

P_{I mat} = (material use per hr)(material cost) = (150 lb/hr)($0.45/lb) = $67.50/hr.

Therefore,

SP _I	=	P_{I labor} + P_{I cap} + P_{I mat} + P_{I energy}
	=	$36/hr + $45/hr + $67.50/hr + $4.28/hr = $152.78/hr.

Correspondingly,

P_C = P_O/SP_I = (120 parts/hr)/($152.75/hr) = 0.79 part/$.

When all the inputs to the system are considered, the process produces less than one part (0.79) for every dollar of input.

In the examples listed above, the process output in parts/hr was provided. Typically this information is determined through calculations. The following section provides mathematical concepts to quantify production and thereby provide a method of calculating output in parts/hr. Subsequent sections demonstrate how to develop input capital costs of automated machines.

2.3 Process Outputs and Mathematical Concepts for Quantifying Production

In order to determine if an automation strategy selected will provide the desired productivity improvements we must first quantify the current and proposed manufacturing process. Or, in other words, we must measure and document each process’s performance. This serves as the output for the productivity calculations. The performance of the automation can then be quantified, and productivity calculations as well as direct comparison of the automation to the existing process can be made.

There is one measure, as observed in the last section, which is of prime importance. That measure is called the production rate (P_O) of the process. It is a measure of how many parts are produced over a specific time period, typically expressed in parts per hour. This measures the output of the process. By combining this measure with other factors, several other mathematical quantifying concepts, in addition to productivity, can be examined.

2.3.1 Production Rate

Prior to determining production rate, one must determine the operational cycle time of a process. The operational cycle time includes all time element activities involved in producing one part.

Figure 2-0 Milling process example

Consider the machining process operation in Figure 2-0. This particular operation involves drilling two holes and milling a slot into the part shown. The operational cycle time is the time from the start of processing a part to the point at which the next part is started. The time elements for this operation include loading and unloading the part into the machine, machining the part, and changing tools as needed. Thus, the operational cycle time for this process can be given as

t_c = t_o + t_wh + t_th

where,

t _c	=	operational cycle time, expressed in min/part
t _o	=	time of actual processing, expressed in min/part
t _wh	=	workpiece handling time, expressed in min/part
t _th	=	tool handling time, expressed in min/part.

The actual processing time (t_o) and workpiece handling time (t_wh) occur for each part processed. The tool handling time (t_th), however, may not occur for each part. Perhaps a tool can process 100 parts before it needs to be changed. Thus, the time it takes to change the tool must be divided or averaged over those 100 parts.

The above equation is valid not only for machining type processes but also for assembly, molding, or almost any type of discrete manufacturing process. Consider the following examples.

Example 2.3

The following table lists the steps for a machining process. The times listed are those needed to load, unload, and process one part. Calculate the operational cycle time (t_c).

Solution

The governing equation is

t_c = t_o + t_wh + t_th.

From the table above, combine steps 2 and 4 to determine the total processing time per part (t_o). Thus,

t_o = 2 min/part + 3 min/part = 5 min/part.

The work handling time (t_wh) is a summation of results in steps 1, 3, and 5:

t_wh = 0.75 min/part + 0.5 min/part + 0.25 min/part = 1.5 min/part.

To determine the tool handling time (t_th), find the average time it takes to change tools over the 20 parts:

t_th = 5 min/20 parts = 0.25 min/part.

Thus the operational cycle time becomes

t_c = 5 min/part + 1.5 min/part + 0.25 min/part = 6.75 min/part.

Example 2.4

An injection molding machine processes an 8-cavity mold in 2.6 min per cycle. The parts are automatically ejected from the mold and travel by conveyor to the next process. Every 200 cycles the mold is cleaned and sprayed with mold release. This takes 15 min to complete. Calculate the operational cycle time (t_c).

Solution

The governing equation is

t_c = t_o + t_wh + t_th.

First, calculate the actual processing time per part (t_o). Recognize that the process produces 8 parts each cycle and that each cycle takes 2.6 min. Thus,

t_o = (2.6 min/cycle)(cycle/8 parts) = 0.325 min/part.

Since the parts are automatically ejected from the mold, the workpiece handling time is zero:

t_wh = 0.

Mold cleaning and reapplication of mold release is equivalent to changing a tool in a machining process. Thus, the time it takes to accomplish these tasks needs to be averaged over each part produced in those 200 cycles:

t_th = 15 min/[(200 cycles)(8 parts/cycle)] = 0.0094 min/part.

Therefore, the operational cycle time becomes

t_c = 0.325 min/part + 0 + 0.0094 min/part = 0.334 min/part.

Consider a process manufacturing system. In this system parts are produced in batches or lots. Each time a part is to be produced the machines that produce the part must be set up to process that particular part. This setup time needs to be captured in the production rate calculations. Therefore, for process manufacturing systems the time to process a batch of parts is calculated and then converted into average production time. The equation to calculate the batch processing time is

t_b = t_su + Qt_c,

where

t _b	=	batch processing time (min)
t _su	=	time to set up machine to produce batch (min)
t _c	=	operational cycle time per part (min/part)
Q	=	number of parts in batch (parts).

The average production time then becomes

t_p = t_b /Q,

where

t_p = average production time (min/part)

Q = number of parts in batch (parts).

Once the cycle time of the process is known, the production rate can be calculated. Note that the production rate depends on the manufacturing system employed. Hence, the variable R is used to represent the average production rate for the various processes discussed. The average production rate for a process can be determined by taking the reciprocal of the average production time:

R_p = 1/t_p,

where

R_p = average production rate (parts/min)

t_p = average production time (min/part).

Note that it is often more desirable to express the average production rate (R_p) in units of parts/hr.

Example 2.5

Calculate the production rate (R_p) of the process listed in Example 2.3 in units of parts/hr, assuming the part is produced in batches of 3000 parts and it takes 4 hr to set up the machine to produce the batch.

Solution

First, determine the batch production time (t_b) and then the average production time (t_p). From the average production time, calculate production rate (R_p) in parts/hr. The governing equations are

t_b = t_su + Qt_c

t_p = t_b/Q

R_p = 1/t_p,

where the values are

t _c	=	6.75 min/part (calculated in Example 2.3)
t _su	=	4 hr
Q	=	3000 parts.

It is important to keep consistent units: convert operational cycle time to units of hr/ part. Thus,

t_c = (6.75 min/part)(1 hr/60 min) = 0.1125 hr/part.

The batch production time is then

t_b = 4 hr + (3000 parts)(0.1125 hr/part) = 4 hr + 337.5 hr = 341.5 hr.

The average production time is

t_p = 341.5 hr/3000 parts = 0.1138 hr/part.

Therefore the production rate is

R_p = 1/t_p = 1/0.1138 hr/part = 8.78 parts/hr.

The last example highlights how to determine production rate of any type of manufacturing process in which parts are run in batches and setup time is a significant portion of batch production time. As setup time decreases and quantities processed increases, operational cycle time approaches the same value as average production time. This is the case in quantity type manufacturing systems. Thus, the production rate can be determined directly from the operational cycle time:

t_p = t_b/Q = (t_su + Qt_c)/Q.

Since setup time becomes small relative to the product of quantity and operational cycle time t_c, then clearly

t_p ~ t_c.

Then

R_pq = 1/t_c,

where

R_pq = average production rate for a quantity manufacturing systems (parts/min)

t_c = operational cycle time (min/part).

Example 2.6

Calculate the average production rate (R_pq) of the injection molding process in Example 2.4, in units of parts/hr.

Solution

The injection molding process is a quantity type manufacturing process. Therefore, the governing equation is

R_pq = 1/t_c.

Taking the operational cycle time from Example 2.3 and converting the units to hr/ part yields

t_c = (0.334 min/part)(1 hr/60 min) = 0.00567 hr/part.

Therefore

R_pq = 1/(0.00567 hr/part) = 179.64 parts/hr.

Consider the flow-line type manufacturing system shown in Figure 2.1. In it the product is traveling to each workstation via a conveyor belt. At each workstation the product is processed accordingly. Upon completion of the processing, the product is moved to the next station. The transporting of the part is coordinated with the time it takes to complete the processing at each workstation. Some workstations finish processing sooner than others. However, the conveyor cannot move the parts until the slowest process (i.e., the process that takes the most time) is completed. This workstation is called the bottleneck station.

Figure 2-1 Flow-line manufacturing system

When all the stations have processed the product, it exits the conveyor belt. Thus, at specific time intervals a finished product is produced. The time interval may be expressed in minutes, hours, days, weeks, months, or even years. The production rate has been defined as the number of parts produced per hour, which corresponds to number of parts that drop off the conveyor line in an hour in this example. Therefore, to calculate the production rate it is necessary one determine how often a part falls from the conveyor. This operational cycle time of the flow line (t_c) is the sum of the time to move the product between the workstations and the actual processing time at the bottleneck station. In equation form:

t_cf = t_r + max t_o

where

t_cf = operational cycle time of flow line system (min/part)

t_r = time to transfer parts between stations (min/part)

max t_o = actual processing time of bottleneck workstation (parts/min).

The production rate or cycle rate of the flow line then becomes

R_c = 1/t_cf,

where R_c = cycle rate of a flow-line manufacturing system (parts/min).

Example 2.7

Calculate the cycle rate (R_c) of the flow-line manufacturing system shown in Figure 2-1; assume the transfer rate is 3 sec per part and the processing time for each work station is as shown in the table.

Workstation	Processing time (m in/pc)
1	1. 5
2	0. 7 5
3	1. 2 5
4	1. 5
5	0. 5

Solution

The governing equations are

t_cf = t_r + max t_o

R_c = 1/t_cf.

The transfer rate was given as

t_r = 3 sec/part or 0.05 min/part.

The actual process time for each workstation is given in the table. Workstation 4 has the maximum process time of 1.5 min/part. Thus,

max t_o = 1.5 min/part.

The operational cycle time of the flow-line is then

t_cf = 0.05 min/part + 1.5 min/part = 1.55 min/part.

The cycle rate is then:

R_c = 1/1.55 min/part = 0.645 part/min or 38.7 parts/hr.

2.3.2 Other Mathematical Quantifying Concepts

Although productivity is of primary importance in justifying automation, other quantifying concepts come into play as well. These include production capacity, utilization, availability, and manufacturing lead-time.

Production capacity is the maximum rate of output of a particular product for a manufacturing system over a specified time period. The time can be expressed in days, weeks, months, or years. The system under consideration could be the whole plant, a production line, or a manufacturing cell. The calculation takes the production rate of the system under consideration and multiplies it by the number of hours worked during the specified time interval and the number of subsystems producing at that production rate. The general form of the equation is:

P_c = Rn_mhrs_w,

where

R	=	production rate of system (R_p, R_pq, or R_c) in parts/hr
n _m	=	number of machines or work centers producing at that rate
hrs _w	=	hours worked during the specified time interval.

Example 2.8

Calculate the monthly production capacity (P_c) of a product produced by the injection molding process described in Example 2.4. Assume the plant uses 3 injection molding machines and molds to produce the part. Also, assume the plant operates in three 8-hour shifts per day, 5 days per week. Suggest a plan by which the plant may increase production capacity in the short term. How could it do so in the long term?

Solution

The governing equation is

P_c = Rn_mhrs_w,

where

R _pq	=	179.64 parts/hr (calculated in Example 2.6)
n _m	=	3
hrs _w	=	(3 shifts)(8 hr/shift)(5 days/week)(4 weeks/month) = 480 hr/month.

Thus,

P _c

(179.64 parts/hr)(3)(480 hr/month) = 258,681 parts/month.

To increase production in the short term the plant could run the injection presses on weekends. Doing so would increase hours worked (hrs_w). Long term solutions might include building more molds to run on more injection molding machines (increase n_m) and/or increase the production rate (R). This could be accomplished by building molds with more cavities or decreasing the process’s operational cycle time (t_c).

Production capacity is a theoretical value. In practice, actual production may be significantly less due to lack of orders, lack of supplies, processing problems, or labor issues. Thus, management will often evaluate the utilization of a manufacturing system. Utilization U is defined as the ratio of the actual number of products divided by production capacity. Thus,

U = 100Q /P_c,

where

Q	=	actual production over specified time frame
P _c	=	production capacity over specified time frame.

Note that U is expressed as a percentage.

Example 2.9

Calculate the utilization of the injection molding process described in Example 2.8 if actual production in the previous month was 175,000 parts.

Solution

The governing equation is

U = 100Q/P_c,

where

Q	=	175,000 parts
P _c	=	258,681 parts/month.

Thus,

U = (100)(175,000 parts)/258,681 parts = 67.7%.

Additionally, a manufacturing system under repair may not be fully used. Thus, the availability of a system, expressed as a percentage, can be calculated. It is determined by the equation

A = 100(t_mtbf − t_mtbr)/t_mtbf

where

A	=	availability
t _mtbf	=	mean time between failures (hr)
t _mtbr	=	mean time to repair (hr).

These two measures provide solid insight into a manufacturing system and can also help in identifying automation opportunities. Additionally, if utilization and availability information is known within a facility, realistic actual production values can be calculated. Consider the following example.

Example 2.10

A manufacturing system has a theoretical production capacity of 100,000 parts/ month. Typical utilization of the system is 80% and availability is 93%. What is the anticipated actual monthly production of the system?

Solution

Rearranging the equation for utilization and factoring in the availability of the system yields the following equation:

Q = UP_cA.

Thus,

Q = (80%)(100,000 parts/month)(93%) = 74,400 parts/month.

Another important quantifying measure of production is manufacturing lead-time. Manufacturing lead-time is the total time it takes to convert raw material into a finished product. Thus, it is the summation of the time of each individual manufacturing process that the product passes through. Note, however, that a product is not processed continually. There is also non-operation time associated with each operation. Examples of non-operation times include those for moving and queuing of parts between operations, waiting for materials, waiting for tools, and so on. These must be accounted for in the calculation of manufacturing lead-time. Additionally, the time to set up the process, where appropriate, must also be considered. Accordingly, the equation for the manufacturing lead-time of a process manufacturing system consisting of operations (indexed by i) is

t_mlt = sum_i(t_su + Qt_c + t_nop)_i,

where

t _mlt	=	manufacturing lead-time for batch
t _su	=	setup time for a process
Q	=	number of parts in batch
t _c	=	operational cycle time of a process
t _nop	=	non-operation time of a process

Note that this equation can be used for other types of manufacturing systems as well. However, some of the terms may be insignificant. Consider a quantity manufacturing system. The setup time and non-operation time may become very small compared to the batch size. Additionally, in the flow-line system the setup and non-operation time are essentially nonexistent.

Example 2.11

A part is routed through 4 machines in lot sizes of 500 parts/batch. Average non-operation time is 6 hr. Setup and operational cycle times are shown in the table below. Calculate the manufacturing lead-time for the part.

Solution

The governing equation is

t_mlt = sum_i(t_su + Qt_c + t_nop)_i.

Calculate the manufacturing lead-time for each operation:

t _mlt1	=	1 hr/batch + (500 parts/batch)(3 min/part)(1 hr/60 min) + 6 hr/batch = 32 hr/batch
t _mlt2	=	6 hr/batch + (500 parts/batch)(8 min/part)(1 hr/60 min + 6 hr/batch = 78.67 hr/batch
t _mlt3	=	1.5 hr/batch + (500 parts)(4 min/part)(1 hr/60 min + 6 hr/batch = 40.83 hr/batch
t _mlt4	=	(4 hr/batch + 500 parts)(3 min/part)(1 hr/60 min) + 6 hr/batch = 35 hr/batch

Summing operation lead-times gives

t_mlt = t_mlt1 + t_mlt2 + t_mlt3 + t_mlt4 = 32 + 78.67 + 40.83 + 35 = 186.5 hr/batch.

It is relatively easy to visualize how improvements in productivity result in corresponding improvements in these measures. Therefore, such measures can also be used in making the case for automation.

2.4 Process Inputs and Manufacturing Costs

The previous section demonstrated how one would quantify the output of a process with a measure (production rate) that can be used in productivity calculations. In this section, methods of quantifying the input to the process are developed. As shown in Section 2.2, input into the productivity calculation (P_I) is amount of money required for the process step under consideration, which is input into the process over the same time frame as that of the output measurement. Both measurements are in units of $/hr.

Inputs to a process are typically broken down into categories consisting of capital, energy, labor, and material. These categories are termed partial productivity measures. Consideration of a breakdown of the costs to manufacture a product is shown in Figure 2-2.

Figure 2-2 Manufacturing process expenses

Figure 2-2 is a pie chart showing the relative percentage of expenses that make up the final selling price of a representative product. Note that the manufacturing cost is only 40%. Figure 2-3 is a pie chart of the relative percentage of expenses that make up total manufacturing cost for this product. Notice how the categories in Figure 2-3 relate to the partial productivity measures. Direct labor coincides with labor, capital equipment costs with capital; indirect labor is often absorbed into the capital equipment or direct labor costs; materials and supplies category would represent both material and energy. When an automation project is undertaken, its goal is to decrease one or more of the expenses shown in the figure. Thus, these expenses need to be accurately reflected in the productivity calculations. One accomplishes this by expressing the partial productivity measures in $/hr.

Figure 2-3 Manufacturing cost percentages

When one evaluates an existing process, labor rate, energy cost, and raw material costs are typically readily available from the manufacturing firm’s accounting office. Additionally, the capital costs of the existing equipment would be available as well. These rates will include allocated overhead costs. However, capital costs of an alternative—new automated equipment—process must be estimated.

Estimation of capital costs of a proposed automation can be done through simple calculations that take into account the time value of money in conjunction with allocated factory overhead. When a manufacturing firm invests in a capital expenditure, it expects the investment will yield a return. Most firms have a standard rate of return. This figure, expressed as a percentage, should be readily available from a firm’s upper management. With the rate in hand, the automation engineer can begin to make estimated capital cost calculations.

The goal of the capital cost calculations is to represent the cost of the proposed automation in terms that can be used in the productivity calculations. Thus, cost needs to be expressed in terms of $/hr. The calculation breaks the initial cost of the equipment into an annual cost, then spreads that annual cost over the hours the machine is estimated to run in a year; finally, it adds in factory overhead expenses. The estimated hourly capital cost of the automation can be calculated with the following equation:

C_c = C_a(1 + r_foh),

where

C_c = estimated hourly capital cost of the automation ($/hr)

C_a = estimated hourly cost of automation ($/hr)

r_foh = factory overhead rate.

The hourly estimated cost of the automation can be determined from the equation

C_a = (C_If_cr)/h_a,

where

C _I	=	initial cost of the automation ($)
f _cr	=	capital recovery factor
ha	=	time that machine is in operation annually (hr).

The initial cost of the automation (C_I) will be known and hours of machine operation annually (h_a) can be readily determined. The capital recovery factor (f_cr) is determined by the equation

f_cr = r(1 + r)ⁿ / [(1 + r)ⁿ − 1],

where

r = desired rate of return (%)

n = number of years of the service life of the machine.

Figure 2-4 Typical factory overhead costs

Factory overhead rate (r_foh) is the ratio of factory overhead costs to those of the machine under consideration. This is found by distributing the overhead over some variable such as direct labor costs. Typical factory overhead costs are given in Figure 2-4. For any given factory this can be accomplished by taking all of the overhead costs of the firm for one year and dividing it by the total cost spent on direct labor. The formula for this calculation is:

r_foh = C_foh/C_dl,

where

C _foh	=	annual cost of factory overhead ($/yr)
C _dl	=	annual direct labor costs ($/yr).

The following example demonstrates the use of these formulas.

Example 2.12

An automated work cell is being considered to replace an existing process. The cell will cost $150,000 to purchase and is anticipated to have a 4-year service life. The machine will operate for 2080 hours per year. The company spent $2,300,000 on factory overhead and $6,500,000 on direct labor costs last year. Estimate the hourly capital cost to operate the new automated work cell if the manufacturing firm desires a 15% return on its investment.

Solution

The governing equations are

C _c	=	C_a(1 + r_foh )
C _a	=	(C_If_cr)/h_a
f _cr	=	r(1 + r)ⁿ /[(1 + r)ⁿ − 1]
r _foh	=	C_foh/C_dl.

The values are given as

r _foh	=	35%
C _I	=	$150,000
h _a	=	2080 hr
r	=	15%
n	=	4 yr
C _foh	=	$2,300,000/yr
C _dl	=	$6,500,000/yr.

First, calculate capital recovery factor:

f _cr	=	r(1 + r)n/[(1 + r)n − 1]
	=	0.15(1 + 0.15)⁴/[(1 + 0.15)⁴ − 1)
	=	(0.15)(1.749)/(1.749 − 1) = 0.26235/0.749 = 0.3503.

Next, calculate the estimated hourly rate of the work cell (C_a):

C_a = C_If_cr/h_a = ($150,000)(0.3503)/2080 hr = $25.26/hr.

Calculate factory overhead rate:

r_foh = ($2,300,000/yr)/($6,500,000/yr) = 35.4%.

Finally, calculate the hourly capital cost:

C_c = C_a(1 + r_foh ) = ($25.26/hr)(1 + 0.354) = $34.20/hr.

Thus, the estimated capital cost for operating the new automated work cell is $34.20/hr.

2.5 Comparing Alternatives with Productivity Calculations

Section 2.2 demonstrated the basic procedure for calculating the productivity of a process. Sections 2.3 and 2.4 demonstrated how to quantify the output and inputs of a process for use in the productivity calculations. This section is devoted to developing a methodology of performing the actual comparison of the alternatives. This essentially involves organizing the data in a logical, comprehensive manner in which the alternatives can be directly compared. The author has found that this is easily accomplished by organizing the data in a spreadsheet as shown in Figure 2-5.

Figure 2-5 Combined productivity comparison spreadsheet

The spreadsheet, aptly titled “Combined Productivity Comparison,” organizes the productivity data in rows and columns. The column headings are shown at the top in boldface print. The first column lists the description of the measure, the second is the variable used for the measure, and the third column displays the units. The next two columns, “Current Method” and “Proposed Method,” hold the data and calculation results for each method. The close proximity of these two columns enables swift comparison of the two options. The sixth column is reserved for formulas or comments (where certain cells hold formulas for performing the calculations). In the first row is entered the production rate for each method. This rate is determined through calculations dependent on the type of manufacturing system, as was discussed in Section 2.3.1. The next 12 rows are separated into groups corresponding to the partial productivity measures discussed in Section 2.2. The organization of the rows culminates with several combined productivity measures, the group at the bottom of the spreadsheet.

Note that each of the five productivity measure groups contains a new measure, not previously discussed: productivity index. The productivity index is a clear and concise method for comparing partial and combined productivity measures of the two options. Observe that for the so-called current method, each productivity index row contains a value of 1.0. This is because current method is used as a baseline against which the proposed method will be compared. The productivity index for the new method is determined by dividing the proposed method’s productivity (partial or combined) by the current method’s productivity. For example, the formula for the combined productivity index (I_c) is given by the equation

I_c = (P_C) proposed/(P_C) current

where

I_c = combined productivity index

(P_C) proposed = combined productivity of the proposed method (parts/$)

(P_C) current = combined productivity of the current method (parts/$).

Thus, if the proposed method has a productivity index greater than 1, it can be said that it is more productive than the current method. Conversely, a productivity measure of less than 1 indicates the proposed method is less productive than the current measure. Recall that for showing productivity improvement a combined productivity index greater than 1.0 is the key to justifying an investment in automation.

One should always look at combined productivity when comparing two methods. Consideration of only a partial productivity measure can often result in misleading results. However, if partial productivity measures are the same for the two methods being compared, they can be omitted from the calculations. But, odds are that there will always be more than one partial productivity measure to consider.

The following examples demonstrate the use of the spreadsheet.

Example 2.13

A manufacturing firm uses a manual machine for production. Production rate is 100 parts/hr. This current method utilizes two operators at a labor wage rate of $18/hr. The manual machine’s capital cost (including cost of electricity) of operation is $25/hr. This firm is considering replacing the manual machine with a programmable automation work cell. The new cell requires only one operator, but has a capital cost (including cost of electricity) of $65/hr. The production rate of the machine is 125 parts/hour. Perform a combined productivity analysis to determine if the firm should purchase the automated work cell.

Solution

The governing equations are listed in the spreadsheet shown in Figure 2-5. Entering production rate and calculating the labor partial productivity yields:

Eliminating the operator and increasing the production rate results in the proposed method that is 250% as productive as the current method from a labor perspective. Considering this measure alone, the proposed method looks very attractive. However, as mentioned, we must evaluate all of the partial productivities and then calculate the combined productivity prior to passing final judgment. No information on raw material was given, thus it will be omitted from the calculations. Additionally, the cost of energy was given in the capital cost per hour. Thus, the only remaining partial productivity to evaluate is capital.

The increased capital hourly cost of the proposed method in conjunction with only a marginal increase in production rate makes the proposed method is only 48% as productive as the current method, from a capital perspective. Calculating the combined productivity yields:

Thus, the proposed method is 92% as productive as the current method. Thus, the proposed method is not justified and the firm should not purchase the automated work cell. The completed spreadsheet is shown in Figure 2-6.

Figure 2.6 Example 2.13, combined productivity calculation

This is the solution.

The last example demonstrates how to use the combined productivity comparison spreadsheet and highlights the importance of calculating the combined productivity before passing judgment on the proposed method. Another interesting benefit of the combined productivity comparison spreadsheet is that it can be a starting point or roadmap for identifying the type and quantity of improvements necessary to justify automation.

For example, one might ask, “If the proposed method is not justified (viz. Figure 2-6), what improvements would make it justifiable?” Obviously, if the work cell’s production rate would be increased substantially and/or capital cost decreased, the purchase of the work cell might be justified. Thus, by tweaking the values in the spreadsheet, target values for production rate and capital costs can be identified. These targets can then be presented to the suppliers of the work cell as required performance specifications. Consider the following example.

Example 2.14

Based on the results of Example 2.13, determine the following:

a)	Minimum production rate of the proposed method to yield a 20% productivity improvement. Assume all other values are as before.
b)	Maximum capital cost per hour of the proposed method to yield a 20% productivity improvement. Assume all other values are as before.

Solution

Both of these can be determined by two methods. The first is to solve directly by using algebra and rearranging the governing equations accordingly. The other method is a trial and error method that uses the spreadsheet to manually increment the variable in question until the desired result is achieved. For part (a) the result will be solved directly. Trial and error will be used to solve part (b).

Part (a)

The governing equations are

I_c = P_C proposed/P_C current

P_C = P_O/SP_I

SP_I = P_{I labor} + P_{I cap} + P_{I mat} + P_{I energy}.

Note that none of the values in the spreadsheet for the current method changes. Also, all the partial productivity inputs for the proposed method stay the same. Therefore, the following values are given:

I_c = 1.20

P_C current = 1.64 parts/$

SP_I = $83/hr.

Setting up the equations:

1.20 = P_C proposed/1.64 parts/$.

Rearranging yields

P_C proposed = (1.20)(1.64 parts/$) = 1.968 parts/$.

But P_C proposed is determined from the equation

P_C proposed = (P_O/SP_I) proposed.

Dropping “proposed” and entering the correct values gives

1.968 parts/$ = P_O/$83/hr.

Thus, the minimum production rate is

P_O = (1.968 parts/$)($83/hr) = 163.34 parts/hr.

The result is confirmed in the spreadsheet shown in Figure 2-7.

Figure 2-7 Example 2.14, part (a) solution

Part (b)

For this solution, trial and error will be used with the spreadsheet. Start by decrementing capital cost/hr in $10/hr increments. As productivity approaches desired value, decrease the increment until the final number is arrived at, which is approximately $45.50/hr. The result is shown in Figure 2-8.

Figure 2-8 Example 2-14, part (b) solution

This is the solution.

The previous example demonstrates how the spreadsheet variables can be tweaked to identify how the proposed method could be enhanced to make it a more attractive option from a productivity standpoint. Other variables could also be adjusted including reducing or eliminating the operator altogether and looking for material savings with the proposed method. Thus, the spreadsheet can be used as a roadmap to identifying other improvements the proposed method may have to offer.

When a combined productivity analysis indicates that the proposed method is justified, there is still one measure we should consider. That measure is production volume. Its impact on choosing alternatives is discussed in the next section.

2.6 The Impact of Production Volume on Alternatives

Thus far we have assumed that product volume—both current and future—of the process under consideration for automation is sufficient to support an automation investment. In general, when product volumes are low, manual methods are more cost effective. A manufacturing firm does not want to invest significant funds in the manufacture of a product that will no longer be produced in 6 months to year, or for which the annual volume is not great enough. Although predicting future volume, called forecasting, is a risky venture, it is an essential part of doing business. Product forecasts are typically available from marketing or upper management. The risky nature of production volume forecasting is one reason a manufacturing firm needs to see a quick payback of the automation investment. Thus, one must ascertain whether there is sufficient production volume to justify the investment in the automation. This can be accomplished by considering current and proposed methods’ fixed and variable manufacturing costs and performing a production volume breakeven point analysis.

A product’s manufacturing cost can be broken into two categories, fixed costs and variable costs. Fixed costs are costs that are independent of the quantity of product; i.e., they are incurred whether one part or one million parts are produced. These typically include building rent or mortgage costs, property taxes, equipment costs, and equipment maintenance, to name a few. Fixed costs are most conveniently expressed on an annual basis.

Variable costs, on the other hand, are dependent on the quantity of product. The higher the production, the more the cost incurred. Variable costs include direct labor, raw material costs, and energy costs to operate the equipment. Utilizing these concepts the total annual cost of a product can be represented by the following equation:

C_T = C_F + QC_V,

where

C _T	=	total cost incurred on an annual basis ($/yr)
C _F	=	fixed cost of product on an annual basis ($/yr)
Q	=	quantity of parts produced per year (parts/yr)
C _V	=	variable cost per part ($/part).

This formula’s use is demonstrated in the following example.

Example 2.15

Referring to the manual manufacturing method and information in Example 2.13, and given that the annual cost of maintenance for the machine is $8000 and the raw material cost is $1.25 per part, calculate total annual cost of producing 100,000 parts per year

Solution

The given information from the problem statement and taken from Example 2.13 is as follows:

P_O = 100 parts/hr (production rate)

P_{I labor} = $36/hr (2 operators at $18/hr)

P_{I capital} = $25/hr

Q = 100,000 parts/yr

C_{F maint} = $8000

raw material cost = $1.25/part.

The first step is to identify the variable costs, which include the labor wage rate, the machine’s capital cost, and the raw material cost. The labor and machine capital costs must be converted to units of $/part. This is accomplished by dividing the hourly cost by the production rate as follows:

C_{V labor} = P_{I labor}/P_O = ($36/hr)/(100 parts/hr) = $0.36/part

C_{V capital} = P_{I capital}/P_O = ($25/hr)/(100 parts/hr) = $0.25/part.

Next determine the total variable costs by summing each of the individual variable costs:

C_V = C_{V labor} + C_{V capital} + C_{V material}

= $0.36/part + $0.25/part + $1.25/part = $1.86/part.

The fixed cost is simply the annual maintenance costs:

C_F = $8000/yr.

Solving for the total annual cost to make the product yields

C_T = C_F + QC_V = $8000/yr + (100,000)($1.86/part) = $194,000/yr.

Performing a quantity breakeven analysis of two alternatives involves determining the number of parts that have to be produced that would realize the benefits of the alternative. This is significant because manual methods typically have a lower fixed cost and higher variable costs. Thus, when product volumes are low, manual methods are more cost effective. As production volumes increase the advantage goes to automated methods, which typically have a lower variable cost and higher fixed cost. This is illustrated in Figure 2-9.

Figure 2-9 Quantity breakeven point

Figure 2-9 is a plot showing the total annual cost of an automated method versus a manual method for the same theoretical task. The manual method has a lower fixed cost but higher variable costs. The lower fixed cost is evident in the graph by the lower starting point (zero parts produced). The steeper incline indicates higher variable costs. At around 15,000 parts the two lines cross, indicating the two methods have the same total annual cost. This is termed the quantity breakeven point. As the quantity produced is increased from this point, the automated method has a lower total annual cost. If the annual production is 25,000 parts, the cost savings that the automated method provides is the y-axis value difference between the two lines.

Thus, to determine the quantity breakeven point of two methods, the total annual cost equations are set equal to one another (i.e., equate the costs) and solved for the quantity (Q). This is the quantity at which the proposed and the current methods have the same production cost. Anything above this quantity favors the automated method over the manual method for cost efficiency. This is demonstrated in the following example.

Example 2.16

A new automated method is being developed to replace the manual method described in Example 2.15. The new method has a production rate of 165 parts/hr, requires only one operator, and has a capital cost of $45.50/hr. Additionally, the new method decreases material waste, thus reducing raw material costs to $1.00/part. Because of machine sophistication, yearly maintenance costs will increase to $16,000 per year. Perform a productivity analysis to compare the two alternatives for annual production of 100,000 parts/yr. Is the proposed method more productive? Calculate the quantity breakeven point. What is the total annual cost savings if the proposed method were to be used?

Solution

First, perform the productivity analysis (i.e., compare the current method’s hours and maintenance costs with the proposed). Most of the information can be substituted directly into a productivity calculation spreadsheet, with the exception of the capital input. The capital or machine rates for both alternatives are given. However, neither includes maintenance cost. Thus, the maintenance cost, spread over the 100,000 parts, will be added to the hourly machine rate. To proceed, calculate the number of hours it would take to produce 100,000 parts for each method, then divide the maintenance cost by this number.

For the current method,

hrs_curr = (100,000 parts/yr)/(100 parts/hr) = 1000 hr

(P_I _maint)_curr = $8000/1000 hr = $8/hr.

For the proposed method,

hrs_prop = (100,000 parts/yr)/(165 parts/hr) = 606.1 hr

(P_{I maint})_prop = $16,000/606.1 hr = $26.40/hr.

Add these values to the capital hourly rates for both current and proposed methods:

(P_I _capital)_curr = $25/hr + $8/hr = $33.00/hr

(P_I _capital)_prop = $45.50/hr + $26.40/hr = $71.90/hr.

Substituting these values into a productivity analysis spreadsheet yields the following:

Thus, the proposed method is 126% as productive as the current method. The quantity breakeven point indicates the production quantity after which the proposed method becomes more productive. These calculations are shown in the following spreadsheet:

The quantity breakeven point occurs at 16,837 parts. The annual cost savings of the new method will be $39,515 (from $194,000 − $154,485).

2.7 Productivity and the USA Principle

The benefits of productivity analysis in justifying automation of manufacturing processes have been extensively highlighted throughout this chapter. Additionally, we hint at how productivity analysis can be used to identify other enhancements or improvements to the proposed automation. In this section, we discuss using the USA automation strategy in conjunction with a productivity analysis as the starting point for productivity improvements through automation. Thus, instead of performing the productivity analysis after an automated method has been proposed, the analysis will be used during the development of the automated method.

Groover outlined the basic tenets of the USA principle in Automation, Production Systems and Computer-Integrated Manufacturing. It is a simple, common sense approach to developing an automation strategy. “USA” is an acronym for the method’s steps:

Understand the process. This is the crucial first step. There is no better way to understand an existing process than to calculate its productivity. It compels the determination of cycle times, production rates, material costs, and so on. These data can be assembled through time studies, video analysis, and through other data collection techniques. Once all the data are assembled, a preliminary productivity analysis is performed, one that uses the spreadsheet presented in Section 2.6. Data collection and productivity analysis give one a thorough grasp and deep understanding of the existing process.

Simplify the process. It is likely that a process under consideration has never been as extensively evaluated as it will be with these methods. Thus, simple improvements or modifications identified in step 1 may greatly enhance the performance of the existing process. Wasted movements, actions, or procedures can be eliminated and the process reevaluated, the idea being that the new process should be as streamlined as possible and have every opportunity to succeed. Once the new process has stabilized, another productivity analysis using the new data is performed.

Automate the process. Armed with extensive, in-depth knowledge of the simplified existing process, one begins identifying ways to improve productivity through automation, using the automation strategies identified in Section 1.6 as a starting point. Once a general strategy has been selected, a productivity analysis is done, one that compares the existing process and the proposed automated one. The productivity analysis spreadsheet is used and the automated method’s performance adjusted until the desired productivity improvement is achieved.

After the USA principle is applied, data from the productivity analysis in step 3 are the specifications for the new, automated process; these data are used for cost quoting purposes. Once quotations are received, the productivity analysis can be reevaluated. Thus, when it comes time to submit a proposal to upper management for the automation project, justification will have already been completed. Using the USA principle in conjunction with productivity analysis greatly enhances the probability of a successful automation project.

2.8 Summary

Productivity calculations provide a very effective means for identifying, evaluating, and justifying the use of automation in a manufacturing facility. Productivity of a manufacturing system is determined by the ratio of the process outputs divided to the process inputs. If only one input (such as labor) is considered in the calculation, then the calculation is called a partial productivity (P_P) calculation. When two or more inputs are included, the calculation is called a combined productivity (P_C) calculation.

Process measures are used to quantify manufacturing processes. These measures then fill the role of outputs in productivity calculations. The most important process measure in terms of productivity calculations is production rate—the measure of how many parts are produced over a specific time frame, typically expressed in parts per hour. Production rate is calculated from the operational cycle time that includes all time element activities involved in producing one part.

Other important mathematical quantifying concepts include production capacity (the maximum rate of output of a particular product for a manufacturing system over a specified time period), utilization (the ratio of the actual number of products divided by production capacity, expressed in percent), and availability (how often a machine is actually available to perform processing). Manufacturing lead-time is the total time it takes to convert the raw material into the finished product.

Input of the productivity calculation (P_I) is the amount of money into the process over the same time frame used in the output measurement. Inputs to the process are typically broken down into categories consisting of capital, energy, labor, and material. All of these inputs need to be expressed in terms of dollars per hour. For energy, labor, and material the calculations are straightforward. Capital costs of automation are determined by breaking initial cost of equipment into annual cost spread over annual hours the machine is estimated to run, the result added to factory overhead expenses.

Productivity calculations are a very effective method of comparing automation alternatives. Productivity index is then calculated, giving a clear and concise method for comparing partial and combined productivity measures of the two options being evaluated. One of the options, typically the current method, is assigned a baseline productivity index of 1. If a proposed option has a combined productivity index greater than 1, it can be said that it is more productive than the current method. A combined productivity comparison can serve as a starting point or roadmap for identifying the type and quantity of improvements necessary to justify automation.

To ascertain whether there is sufficient production volume to justify an automation investment, it is important to consider the current and proposed methods’ fixed and variable manufacturing costs. Fixed costs are independent of production quantity; variable costs, on the other hand, are dependent on the quantity. A production volume breakeven point analysis calculates the volume that justifies automation. The quantity breakeven point of two methods is found by setting the total annual cost equations equal and solving for quantity (Q), at which the manual and automated methods cost the same. In general, when product volumes are low, manual methods are more cost effective. As production volumes increase the advantage goes to automated methods.

The USA automation strategy directs us to understand an existing process, to simplify it, and if it is called for, to automate it. Using USA in conjunction with productivity analysis greatly enhances the probability of a successful automation project.

2.9 Key Words

actual processing time

availability

average production time

batch processing time

bottleneck station

capital expenditure

combined productivity

fixed costs

manufacturing lead-time

operational cycle time

partial productivity

production capacity

production rate

productivity

productivity index

quantify

quantity breakeven point

tool handling time

USA principle

utilization

variable costs

workpiece handling time

2.10 Review Questions

1. How can productivity calculations aid in identifying, evaluating, and justifying automation?

2. Explain the difference between partial and combined productivity.

3. A manufacturing process can produce 640 parts/hr. The process requires three laborers each earning $26/hr. What is the labor partial productivity of the process?

4. The manufacturing process described in review question 3 uses a machine that has a capital cost of $95/hr. The machine operates on 150 kW of power. Cost of electricity energy is $0.057/kWh. The machine processes 215 lb material/hr. The material costs $0.85/lb. Using the labor input costs determined in Example 2.1, calculate the combined productivity of the process.

5. The following table lists the steps for a machining process. The listed times are required to load, unload, and process one part. Calculate the operational cycle time (t_c) and production rate (R_p).

6) An injection molding machine processes a 24-cavity mold in 1.3 min/cycle. The parts are automatically ejected from the mold and travel by conveyor to the next process. After every 500 cycles the mold is cleaned and sprayed with mold release. This takes 8 min to complete. Calculate the operational cycle time (t_c) and production rate (R_pq).

7) Calculate the cycle rate (R_c) of the flow-line manufacturing system shown in Figure 2-11, assuming the transfer rate is 5 sec/part and the processing time for each work station is as shown in table below.

Figure 2-11 Flow-line manufacturing system

8) Calculate the monthly production capacity (P_c) of a product made by the injection molding process described in review question 6. Assume the plant uses 8 injection molding machines and molds to produce the part. Also, assume the plant operates in three 8-hour shifts per day, 5 days per week. How could the plant increase production capacity in the short term? In the long term?

9) A manufacturing system has a theoretical production capacity of 500,000 parts/ month. Typical use of the system is 97% and availability is 99%. What is the anticipated actual monthly production of the system?

10) A part is routed through 6 machines in lot sizes of 300 parts/batch. Average non-operation time is 5 hr. Setup and operational cycle times are shown in the table below. Calculate the manufacturing lead-time for the part.

11) An automated work cell is being considered to replace an existing process. The cell will cost $350,000 to purchase and is anticipated to have a 7-year service life. The machine will operate for 2080 hr/yr. Also, consider that the company spent $4,600,000 on factory overhead and $8,250,000 on direct labor costs the preceding year. If the manufacturing firm desires a 10% return on its investment, estimate the hourly capital cost to operate the new automated work cell.

12) A manufacturing firm utilizes a manual machine to make a product. The production rate is 125 parts/hr. This current method uses three operators at a labor wage rate of $18/hr. The manual machine’s capital operation cost (including cost of electricity) is $34/hr. The firm is considering replacing the manual machine with a programmable automation work cell. The new cell only requires one operator, but it has a capital cost (including cost of electricity) of $95/hr. The production rate of the machine is 225 parts/hr. Perform a combined productivity analysis to determine if the firm should purchase the automated work cell.

13) Referring to the manual manufacturing method information given in review question 12, calculate the total annual cost to produce 100,000 parts per year. Note that the annual cost of maintenance for the machine is $16,000. Additionally, the raw material cost is $2.50 per part.

14) A new automated method is being developed to replace the manual method described in review questions 12 and 13. The new method has a production rate of 245 parts/hr, requires only one operator, and has a capital cost of $65.50/hour. Additionally, the new method decreases material waste, thereby reducing raw material costs to $1.00/ part. Because of machine sophistication, yearly maintenance costs will increase to $26,000 per year. Perform a productivity analysis to compare the two alternatives if annual production is 100,000 parts/yr. Is the proposed method more productive? Calculate the quantity breakeven point. What is total annual cost savings if the proposed method is used?

2.11 Bibliography

1. Groover, M.P. (2001). Automation, Production Systems and Computer-Integrated Manufacturing, 2^nd ed. Prentice Hall, Upper Saddle River, New Jersey.

2. Sumanth, David J. (1994). Productivity Engineering and Management. McGraw-Hill.

3. Kandray, Daniel E. (2004). Comparison of fixed automation and flexible automation from a productivity standpoint. Society of Manufacturing Engineers Technical Paper TP04PUB206.

4. Machinery’s Handbook, 25^th ed. (1996). Industrial Press, Inc., New York, New York.

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