Question

A company will begin stocking remote control devices. Expected monthly demand is 800 units. The controllers can be purchased from either supplier A or supplier B. Their price lists are as follows: SUPPLIER A SUPPLIER B Quantity Unit Price Quantity Unit Price 1–199 $14.00 1–149 $14.10 200–499 13.80 150–349 13.90 500 + 13.60 350 + 13.70 Click here for the Excel Data File Ordering cost is $40 and annual holding cost is 25 percent of unit price per unit. a-1. Which supplier should be used? Supplier A Supplier B a-2. What order quantity is optimal if the intent is to minimize total annual costs? 150 500 200 350 300 1

Answer 1

Answer:

I will take Supplier A and make orders of 500 units as give lower inventory cost

From the proposed units the best option to inimize cost is 500 units.

Explanation:

    Supplier A      Supplier B

    1 –199 $14.00         1–149 $14.10

200–499   13.80    150–349 13.90

     500+    13.60          350 + 13.70

Holding Cost 25% of the unit price.

D = annual demand =

800 monthly x 12 month = 9,600 per year

S= setup cost = ordering cost = 40

H= Holding Cost = $13.60 x 25% = 3.40

Optimal Order Quantity

taking $13.60 (order size must be over 500)

$Q_{opt} = \sqrt{\frac{2DS}{H}}$

$Q_{opt} = \sqrt{\frac{2(9,600)(40)}{3.40}}$

OOQ: 475.2708206

As it is below the 500 to get the $13.60 price is not a cost minimizing option but, it can be better than the alternative

Ordering 9600 / 500 x $40 = $768

Holding: 500/2 x $13.60 x 25% = $850

Total $ 1,618

Using Supplier B of $13.70 (reqirement order size +350)

H= Holding Cost = 13.70 x 25% = 3.43

$Q_{opt} = \sqrt{\frac{2(9,600)(40)}{3.43}}$

OOQ = 473.5330787

This order size will minimize the inventory cost.

Ordering 9600 / 474 x $40 = $810

Holding: 474/2 x $13.70 x 25% = $812

Total $ 1,622

Given cases:

Ordering 9600 / 150 x $40 = $2,560

Holding: 150/2 x $14.00 x 25% = $262.5

Total $ 2,822.5

Ordering 9600 / 500 x $40 = $768

Holding: 500/2 x $13.60 x 25% = $850

Total $ 1,618

Ordering 9600 / 200 x $40 = $1,920

Holding: 200/2 x $13.80 x 25% = $345

Total $ 2,265

Ordering 9600 / 350 x $40 = $1,097

Holding: 350/2 x $13.70 x 25% = $599

Total $ 1,696

Ordering  9600 / 300 x $40 = $1280

Holding 300/2 x $13.80 x 25%  = $517.5

Total $1797.5