A company has introduced a process improvement that reduces processing time for each

unit, so that output is increased by $25\%$ with less material, while $1$ additional worker is required.

Under the old process, $5$ workers could produce a total of $60$ units per hour $($for all the $5$ workers

in total$).$ Material input is $$16$ per unit.

For the new process, $1$ additional worker is required, and material cost is now $$10$ per unit.

For both situations: overhead cost is charged at $1\mathrm{.}6$ times of the labour cost; Labour costs are $$12$

per hour per person; And the finished units sell for $$31$ per unit.

Compute the multifactor productivity ratio for old and new processes

What increase in productivity is associated with the process improvement? $($Numerical

comparison between the two processes$).$

SOLUTION

$$Before$$ productivity $=(60*31)/[(5*12)+(60*16)+(1\mathrm{.}6*5*12)]=1\mathrm{.}667$

$$After$$ productivity $=(60*31*1\mathrm{.}25)/[(6*12)+(75*10)+(1\mathrm{.}6*6*12)]=2\mathrm{.}481$

productivity increase $=[(2\mathrm{.}481-1\mathrm{.}667)/1\mathrm{.}667]*100=48\mathrm{.}83\%$