m7103 ps2 prakash abhijeet

8/10/2019 M7103 PS2 Prakash Abhijeet

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LOGISTICS SYSTEMS ASSIGNMENT

1)

As the question is asking for p & q value only, by equating the Bass model

equation with an equation with one dependent variable and two independent

variables we will basically get one intercept and two coefficients which can be

written in terms of p,q & m

Thus the regression equation gives us the values of pm, (q-p) & -q/m

Multiplying the first and third value we can eliminate m and thus can calculatethe value of p & q from it.

CD

q 0.259017615

p 0.003436348

The respective values of p & q for the CD Is as mentioned above. As my

adjusted R square value is around .97 for both the regression equations, the fit

of the line is good. That is closer the line of regression is to all the points.

Thus the estimated value of p & q as per regression eqn is better

approximated

Cassette

q 0.278532284

p 0.005993557

The respective value of p&q for the cassette is as above.



5.1

a)

A= $12.8D=2400

V=$0.4

R=0.25$/$/year

EOQ in units = sqrt (2AD/vr)

= sqrt(2*2400*12.8/0.4*0.24)

= 800 units

For EOQ in dollars , the yearly demand in dollars= 2400*0.4= $960

EOQ in dollars = Sqrt( 2AD(dollar value of demand in an year)/r)

= $313.534

EOQ in months’ supply—

Basically my assumption for this answer is that EOQ in month’s supply means

that as per calculation of EOQ data , for how many months that EOQ in units

will meet the supply needs.

AS the demand is constant the supply for every month =2400/12=200

As EOQ is 800, EOQ in month’s supply =800/200

= 4 months’ supply



Thus the change in A is basically changing the EOQ values as A is a

multiplicative component in the equation.

As A is increased 4 times from 3.2 to 12.8 the relative values of A changes by

sqrt(4) times ie 2 times.

b) With change in values of A and r the values of

A=3.2$

R=0.3

EOQ in units = sqrt(2*2400*3.2/0.3*0.4)

= 357.77 units

= 358 units (rounding up the EOQ value)

EOQ in dollars = sqrt(2*2400*3.2*0.4/0.3)

=$143.108

EOQ in months supply =358/200=1.8 months

b) The change in value of r from 0.24 to 0.3 makes sense as the value of EOQ

reduces, as r

5.3)

For discounted films the TRC for the company can be calculated from –

Purchase price of goods+ TRC

As A=$3, D = 10000, V=1.26, r=0.24$/$/year

TRC=sqrt(2*3*10000*1.26*0.24)



=$134.7

TC= $12600+$134.7

=$12734.7

In the second cost when the firm is manufacturing its own items a setup cost of

$20 is attached to every production lot and v changes to $1.23

Thus to find the replenishment and holding cost in this case we can use the

forul Economic production quantity ie

Sqrt(2SD/vr)*sqrt(1/1-D/m)

Where S is the set up cost =$20

m is the per day production capacity of machine for unit time ie an year =500

*365

Thus

EPQ =1196.64 or 1197 units

NOW TRC for this EPQ=

D/Q*S+Q/2 vr(1/1-d/m)

=$334.7

From the standpoint of just just replenishment and holding cost, this cost while

the firm is manufacturing its own products is much higher than the same for

while the firm is procuring the low cost rolls. Thus as the question asks fromthe standpoint of replenishment and ordering cost the company should go for

procuring the discounted films.

Some conditions which might affect the decision are if we take into account

the purchase price of the item. As we can see that the prices of the films differ

when the firm is procuring it from its in house production



Thus inclusion of these two costs may change my decision. In the first case the

TC while buying low cost film is $12734.7 .

While manufacturing its own product the total cost will be $12300+334.6

Which gives 12634.7. Thus the total cost of production comes out to be lessthan cost of procurement and thus inclusion of this factor will make me change

my decision.

Another scenario which may change the scenario is if company can vary its

production capacity or not. IF the firm can only produce in batches of 500 per

day without increasing or decreasing it then we cannot produce as per EOQ as

mentioned above and that too may change the decision I am taking.

5.4

D=4000 units/year

A=$5

V= $4 per 100 units

R=0.25$/$/year

A)

EOQ= sqrt(2*5*4000/0.004/.25)

=2000 units

Thus EOQ for the item is 2000 units

B) Time between two successive orders is 1/(D/Q)

=6 months

C) The production manager insists that A=$5 is just a guess



For three months’ supply the Q=(4000/12)*3 =1000

Now he wants to find values of A for this order as per three months’ supply i.e.

order quantity of 1000 units which will make the EOQ based on A=5 more

preferable in terms of inventory holding cost and carrying cost.Thus TRC (Q*) < TRC(Q 3 months & variable A)

Or, Sqrt( 2*5*4000*.04*.25)< 4000/1000*A + (1000/2)*.04*.25

Or,A>$3.75

Thus for all values of A >$3.75 and order quantity of 1000 the EOQ based on

A=5 will be more preferable to be ordered because the TRC for the EOQ basedon A=5 will always be less than TRC for orders of 1000 quantity and A>$3.75

5.21

First we need to find the EOQ for the whole demand considering no discounts

given.

D=3075 units/yr

A=$50

V=$2

R=0.2$/$/yr

Thus EOQ for this =877 units

The EOQ falls above the first break point of 500 and thus the first batchdiscount can be applied for all the items below & above 500

Now, when the supplier orders for any quantity above 500 he gets a discount

of 10%

Thus new cost for orders above 500 = 1.9$

Thus basically the price for all the items becomes 1.9$

Calculating the new EOQ with v=1.9 will be 900 units



Now there is another break point which is for orders more than 1000, thus we

need to find out whether the TC for 900 units is less than that for 1000 units or

not.

TC for 900 units = 3075*1.9 +sqrt(2*50*3075*1.9*0.2)

= $6184.33

Now there is another break point at 1000 which gives 15% discount

Thus v=$1.70

Thus if we calculate EOQ when the price offered for all the products is 1.70,

EOQ=sqrt(2*3075*50/1.7*0.2), we get 952 units , basically it shows that we

are not entitled for the discount in this case , thus to avail discount we cannot

order as per EOQ for price of $1.7

Thus calculating TC when the order quantity is 1000,

We get

$1000*1.7+ 3075/1000*50+1000/2*0.2*1.7

=$5551.25

Now , this TC for ordering 1000 items in a lot is much lesser than the last order

quantity.

As the total cost curve has an upward trend at 1000 if we order even a singlequantity above it the TC will be higher and at the same time if we go below

1000 we won’t be getting the 15% discount

Thus the order quantity in this case should be 1000 units keeping in mind that

only decision which is affecting my choice is the lowest cost.

Time period between two consecutive orders will be 1/3075/1000 years



Ie 16 weeks approx.. Thus he should be ordering every 16 weeks from

suppliers.

6)

There are 3700 skus being handled by me and every SKU has a constant

demand of 6000 units for the year; plus or minus 10%

Thus no of units for every SKU vary from 5400 to 6600

The unit price of the SKU vary from $ 4 to $ 6

IHC for the item is 18%

One time ordering cost for the item is $50

Thus the total relevant cost will be when the unit price touches the lowest

range as well as no of units in every SKU also touches the lowest range

Thus TRC will vary from

3700 *Sqrt( 2*5400*50*4*.18) to 3700 *Sqrt( 2*6600*50*6*.18)

0r, $ 2307091 to $ 3123816

The web ordering system will reduce the ordering cost to $ 5

Thus the TRC in this case will range from

$729566 to $987837.64

Thus the minimum savings in cost after implementation of two systems will be

the difference minimum of 1st

TRC and minimum of 2nd

TRC as the difference in

cost items of the two orders is same the diff in TRC will give a true picture of

the actual difference between two costs.



Thus I am willing to pay anything below my minimum savings for the

implementation of web ordering system ie $1577525

B)

The conclusion which I have reached here through calculation gives me full

confidence in my estimation as this is the minimum savings which I will gain

from the implementation of the web ordering cost.

In worst case scenario too I will be saving this much amount after this

implementation. Thus any payment for this system which is below this amount

gives me 100% confidence that my estimation is right.

C)

If the ordering cost reduces to .05 $, the total cost will be

$72956 to $98783

Thus I can pay anything below ($2307091-$72956) ie $2234135 for the web

ordering system in this case.

Assumptions in this case- Though SKUS are relatively homogenous, the orders

are being procured from different suppliers and thus we cannot find a common

eoq for all the orders in one batch. As the suppliers are different the common

EOQ using sqrt(2*3700*5400/4*.18) will give a value of 52679 units. Now this

is a combined EOQ if we are procuring from one supplier. If there are many

suppliers we cannot club the unit order for every SKU in one lot to minimize

the total relevant cost. In this case we need to divide the total EOQ acrossdifferent suppliers and then we will incur different ordering/replenishment

cost for different SKU.

Thus assuming that EOQ/TRC formulation Is per sku I have found the TRC value

for each SKU and found the total TRC for 3700 skus.

m7103 ps2 prakash abhijeet

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