PRODUCTION MANAGEMENT II (NON INSTANTANEOUS MODEL)

Q = Number of Pieces per order

Cc=Carrying Cost

P=Daily Production Rate

D=Daily Demand Rate

T=Length of The Production in days

Co=Order Cost

Please, kindly memorize the above.

Below is the formula for this topic:

Formula 1.           TC = Co  . P + Cc   . Q (1-d)

                                             Q              2      p

TC means Total Cost:  The dot, means multiplication.

Formula2: Q = √2CoD

                       Cc (1-d)

                                  P

Illustration:

Assume the values for the model parameters are as follows:

1.       Ordering cost per order = 0.50k

2.       Carrying cost per unit, inventory per year N100

3.       Annual demand = N4,900

4.       Annual production rate = N9,800 unit

Required:

i.                     Calculate the Optimal quantity order

ii.                   Calculate the total cost

Solution:

First of all, bring out the variables:

Co=0.50k, Cc=N100, D=4,900, P=9,800

Ok, let’s solve it:

Q* = √(2)(0.50)(4,900)

            (100) (1-4,900)

                           9,800

Q* = √4,900

         (100)(0.5)

Please, do yourself the favour of using a calculator.  After, calculating the top, we have 4,900 and below, we are left with (100) (0.5). 

Let’s continue:

Q* = √4,900

              50

(100) multiply by (0.5) will give 50.  That is how we got that 50.

Let’s ride on:

Q* = √98

4,900 by 50 will give you 98.

Then the square root of 98.

You will approximate to 10 unit.  Because this question ask us to find the quantity.

So the answer will be 10 units.

We have solve for no.i., let’s solve for no.ii that says calculate the total cost.

Let’s bring the formula for the total cost:

Formula 1.           TC = Co  . P + Cc   . Q (1-d)

                                             Q              2      p

All you need to do is to substitute the figures:

TC= (0.5) (4,900) + (100) (10) (1-4,900)

                     10                    2        9,800

I have not done anything strange here:  I just substitute the figure based on the formula given.

So, let’s calculate now:

TC= (0.5) (490) + (100) (5) (0.5)

Explanation: 4,900 by 10 will give us 490 and 10 by 2 will give us 5. Then 4,900 by 9,800 and minus 1 that is constant will give you 0.5.  That is how we have all those figures above.

Let’s take it further:

TC= 245 + 250

Explanation: 0.5 x 490 will give you 245 and 100 x 5 x 0.5 will give you 250.

Finally, 245 + 250 will give us 495.

So, TC = 495:

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