Answer to Question #121203 in Financial Math for William

Question

1)The basic Economic Order Quantity model with constant demand serves as the foundation of inventory studies.
(i)State six assumptions of the basic Economic Order Quantity (EOQ) Model. Hence derive the optimal order quantity, explaining all the parameters used and show all steps used in arriving at your model.

(ii)Draw the costs in your model as a function of the replenishment quantity.

(iii)Show that the optimal total cost function is of the form where the terms have the usual meanings.

(iv)The all-units discount model was applied to the following quantity discount situation in which the demand rate is 500 units per year, ordering cost is GHS 40, and the annual holding cost rate is 20% of the unit cost. What order quantity do you recommend?

Discount Category Order Size Discount (%) Unit Cost (GHS)
1 0 to 99 0 10.0
2 100 or more 3 9.70

Answer 1

Assumptions in an EOQ model.

Odering cost is constant.

Annual demand is knon and is constant.

There is no delay in replenishment of stock.

The optimal plan is calculated for only one product.

There is no cash discount settlement and purchase cost is constant.

Cost in the replenishment quantity.

Odering cost -its all the costs incurred till the order reaches the buyers premises.

Carrying cost -all the cost of maintaining and storage of the product till its sold.

Holding cost - cost incurred by financing storage cost /opportunity cost of holding inventory instead of investment elsewhere.

$$EOQ=\sqrt{2×S×D\over H}$$

Optimal total cost

Total cost =Annual ordering cost +holding cost

Annual cost is ${D\over Q}+S$

Where D is annual demand

S is oder cost

Qis economic oder quantity

Holding cost ${Q\over2}×H$

Where H is holding cost per oder

Total cost is $\therefore {D\over Q}+S+{Q\over 2}×H$

Iv.

$$Q=\sqrt{2×500×100\over 40}$$

$$Q=50$$