[MOVED] Economic Quantity Order Question

[help123]

Assume that a retailer purchases a product which costs £5.00. A supplier quotes the following discounts of the product price:

Order size	Discount
0 to 999	0%
1000 to 2499	3%
2500 and over	5%

Suppose that data and cost analysis show an annual holding cost rate of 20%, an ordering cost of £49 per order regardless to the size of orders and annual demand of 5000 products.

The 5% discount for the 2500-products minimum order quantity looks tempting. However, realising that higher order quantities result in higher inventory holding cost, the retailer has to carry out a thorough cost analysis before making a final ordering decision.

Determine the quantity of products the retailer should order each time they place and order, in such a way as to minimise the total cost incurred.

I don't understand how to make the discounts a price? is it 5x3% etc????

 

[help123]

[MOVED, SPLIT] Economic Quantity Order Question

Hi i do not understand where to start with this, any help appreciated!

Assume that a retailer purchases a product which costs £5.00. A supplier quotes the following discounts of the product price:

Order size	Discount
0 to 999	0%
1000 to 2499	3%
2500 and over	5%

Suppose that data and cost analysis show an annual holding cost rate of 20%, an ordering cost of £49 per order regardless to the size of orders and annual demand of 5000 products.

The 5% discount for the 2500-products minimum order quantity looks tempting. However, realising that higher order quantities result in higher inventory holding cost, the retailer has to carry out a thorough cost analysis before making a final ordering decision.

Determine the quantity of products the retailer should order each time they place and order, in such a way as to minimise the total cost incurred.

 

[stapel]

It's never a good sign when the poster doesn't bother finding an appropriate category, instead tossing the question into the first open slot, and then shows how work whatsoever. Please show me I'm wrong: write back with your thoughts and efforts so far, explaining clearly where you are getting stuck. Thank you!

 

[Ishuda]

Got curious but they (whoever they are) say that a little knowledge is dangerous so be warned. Having read a little about this, this is the way I would approach it. There will be several things we need to know not addressed in the problem:
(1) Lead Time. Orders arrive instantly so we don't have to worry about overlap on amount of stock or other problems involved with cycle of order/wait for arrival of order.
(2) Demand function (rate). That is. will we need much more on Valentines day (maybe it's flowers) or maybe Christmas season or ...? We will assume a constant demand for this problem so that inventory steadily decrease to zero when the next order comes in. That means that, on average, we will have Q/2 items in stock where Q is the order amount.
(3) We will use only one discount rate when ordering, that is a fixed order size. We won't order 999 units one time and 2500 the next.

Let N be the number of orders in the year, C be the cost associated with the actual product (the £5.00 minus discount), Q be the quantity ordered, F be the fixed cost per order (the £49), H be the holding cost (the 20% of average inventory), and T be the time (in years) between orders. We have these relationships:
N = 1 / T
Q = 5000 T
and the following for total order cost during the year O_y
O_y = N (Q C + F) + 0.2 Q/2

Now re-write the formula in terms of Q and use the discount table to get a cost C to determine the best quantity to order.

EDIT: Note thought that holding is proportional to quantity in the above. If it should be proportional to value then it certainly changes the best order quantity.