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Click

toeditM

asters

ubtitle

style

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batchsize

Maxim

umprofit

&Maxim

umrate

ofr

eturn

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Outlinev The production Range

v Effect on production cost

v Maximum profit batch size

v Maximum returnv Maximum rate of return

v Comparison of various criteria

v summary

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The production range

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P =

v Convenient measure of increase incosts above the minimum

v P >1

v QI=Qm[P Sq.root (P2-1)]

v

QII= Qm[P + Sq.root(P2-1)]

Variable cost

MinimumVariable cost

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v In conclusion when managers go for

scheduling a number of products, desirabledegree of flexibility can be ascertained inselecting batch sizes from this productionrange

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Effect on Production Cost

v Effect of P on Y depends upon Ratioof constant cost to variable cost perpiece

v If u >>, slight increase in P does notcause a noticeable change in Totalproduction cost

v Refer Ex. 5

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MaximumP

rofit

Batch

size

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v Minimum Cost batch size is unrelatedto sales price

v Profit for whole batch also dependsupon number of pieces in thatbatch

v Batch size can`t be increased toomuch as production costs will leavevery marginal profit per piece

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Example

v A product is sold at a rate of 500 pieces a day

and is manufactured at a rate of 2500pieces a day. The setup costs of themachines are $1,000 and the storage costsare found to be 1.5*10 -3 dollars per piece

per day. Labour charges are$3.20,materials $2.10 and overhead$4.10per piece. If the interest charges are8%, find the Maximum profit batch size andthe costs of the production run.

Y=$10.5 per piece

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Implicationsv Technical advantages like setup time per piece is

reduced, schedule becomes smooth &

uninterrupted

v Detailed method analysis is possible in long runsand may lead to saving labor , materials &overhead costs thus reduces total productioncost per piece

v If production method is not changed productioncost function is unchanged & if we go for Qphigher cost per piece is incurred

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v The product remains for a longer time in

stock

v This criteria may mislead

Cli k i t dd i t

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Maxim

umRetu

rn

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v Ratio of profit to the cost of production run

v n =

v To attain max return Y should be min,implies that batch is produced atminimum production cost

v nm=

ZQ*

Y

P-11+u/2

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Maximum Rate of returnv Time factor has great importance when turnover

of capital is consideredv High rate of return implies stock to be kept at min

level & replenished at short interval times bysmall batches

v Batch size yielding max ROR is called economicbatch size and it is < Qm

v F.E Raymond & P.T Norton suggested , economicbatches are more profitable because a higher ROR

on capital invested is achieved

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v Rate of return (ROR) can also be found in

terms of sales price (Y), Production cost(Y), and batch size(Q) & then maximize thisexpression

v ROR is the profit realized for every monetaryunit invested/unit time

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Features of economic batchsize

v Points to be remembered byProduction Managers

v Reduction in setup cost will reduceeconomic batch size

v Below Qm cost function is steep &far more sensitive to batch size

v Less capital is tied to a particular

production runv Production time is shorter

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Comparison of various criteriav 25% increase in variable cost causes 7.1%

increase in total production costsv At q=1.4 profit function is max & 20% higher

than profit at Qm

Ratio of profit to cost of production is down by

15%

ROR is 40% lower & half of its max

v At q=0.73 ROR is max

Ratio of profit to cost of production is same

But Cost of production is almost half

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Implication for Managersv For most cases the best production

range should lie between Qe & Qm (ifcosts at Qe are not to high)

v This range is called economic

production rangev It may prove to be too narrow & may

have to be expanded whenscheduling difficulties arise

v Function of ROR is sensitive to batchsize & leaves little room for flexibility

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Summaryv The minimum cost batch should be preferred

in case of keen competition or likelychanges in pricing policies

v Maximum profit batch involves highinvestment & low capital turnover & low

profit and should be chosen if sometechnical advantages are to be gained

v An economic batch size should be preferredunless special benefits are to be gained

from longer production run