Question

Question 3(30 marks) The Economic Order Quantity is a model used to manage inventory and to decide how much of any particular item to order when stocks need to be replenished. This model determines the optimal order quantity in terms of minimizing the total inventory costs (a) Explain with the help of a graph, the Economic Order Quantity Model in inventory management? (15 Marks) (b) XYZ company manufactures mobile phones and have a strong global presence in every part of the world. The Operations Manager of XYZ wants to determine the Economic order quantity of batteries to buy for their phone with the minimum cost. The annual consumption of batteries is 50 000 units and every time the Manager places an order with the local supplier, the administrative cost is Rs 1000 and other ordering cost is Rs 150. The supplier sells a battery at a unit price of Rs 200. The store manager at XYZ has estimated that the carrying cost of a battery is 10% of unit cost. Calculate the (1) Economic Order Quantity (4 marks) (2) Number of orders in a year of 365 days (3 marks) (3) The time interval between orders (3 marks) (4) The total annual cost (5 marks)

Answer 1

a) Economic order quantity is considered the most cost-efficient method of ordering material. The objective is to order the quantity that minimizes the total cost. It is an optimal tradeoff between inventory carrying cost and ordering cost. The EOQ is the point where the ordering costs curve intersects the inventory holding cost curve. it is the point where inventory holding cost equals the ordering cost. The graph below illustrates how the annual ordering costs and holding costs change as the reorder quantity increases; the EOQ is marked as the lowest point of the total cost line. Thus it touches the total cost curve at the lowest point. refer graph

Annual Cost Total Cost Holding Costs Ordering Costs EOQ Re-Order Quantity

the holding cost increases as the ordering quantity increases while the ordering cost decrease with increase in order size hence economic order quantity represents the intersection point of both these curve.

b) total ordering cost per order = administrative cost + other ordering cost = 1000 + 150 = 1150

1) EOQ = sqrt[2 * annual demand * total ordering cost per order / (carrying cost as a percentage of unit cost * unit cost)]

= sqrt[2 * 50000 * 1150 / (10% * 200)]

= 2398 units

2) number of orders in a year = total demand / economic order quantity = 50000 / 2398 = 21 orders

3) time interval between orders = number of days in a year / number of orders = 365 / 21 = 17 days

4) total annual cost = material cost + ordering cost + inventory carrying cost

= (annual demand * unit cost) + (number of orders * total ordering cost per order) + (0.5 * economic order quantity * carrying cost as a percentage of unit cost * unit cost)

= (50000 * 200) + (21 * 1150) + (0.5 * 2398 * 10% * 200)

= Rs 10048130