Question

The current policy is to order 100,000 units when the inventory level falls to 35,000 units. However, forecast demand to meet market requirements for next year is 625,000 units. The cost of placing and processing an order is R250, while the annual cost of holding a unit in stores is 5% of the unit purchase price. Both costs are expected to be constant during the next year. Shop n Pay sells a unit of the product for R15.00 at cost plus 50%. Orders are received two weeks after being placed with the supplier. You should assume a 350-day year and that demand is constant throughout the year.

Question

1. Calculate the total cost of the current ordering policy

Question

Answer 1

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Economic Order Quantity

Economic Order Quantity (EOQ) is the level of inventory that minimizes the total cost of holding and ordering inventory over a period of time. Usually the time period is one year.

The total cost of inventory is the sum of the purchase, ordering and holding costs. As a formula:

TC = PC + OC + HC, where TC is the Total Cost; PC is Purchase Cost; OC is Ordering Cost; and HC is Holding Cost.

Assumptions

To determine the Economic Order Quantity, these costs must be analyzed further. Some assumptions are required:

a) Purchase Cost is a straight-forward "unit cost X number of units" calculation. In other words, volume discounts do not apply. As well, the unit cost remains constant over the year.

b) Order Cost is a fixed overhead cost, and remains constant over the year. It represents, for example, the time value for employees to write up an order, mail it, follow up, inspect the received goods, and make the payment.

c) Holding Cost is fixed over the year. It represents warehouse space, with services such as refrigeration or insurance or security. It also includes the interest cost, which should be set to the "risk-free opportunity-cost" rate.

d) The rate of demand is constant over the year.

e) The total quantity ordered is delivered in one batch.

f) The lead time (between placing an order and receiving it) is constant and does not depend on the order quantity.

g) The quantities are large enough that calculus may be used to determine a minimum point. Calculus requires smooth functions on the real number system. Order quantities assume integral units.

Variables

We will use the following variables:

Q = Quantity being ordered = 100000 units

Q* = the optimal order Quantity: the result being sought

D = annual Demand for the item, over the year = 625,000 units

P = unit Purchase cost   = R10 ( computed below)

O = cost of one Order, regardless of the number of units in the order = R250

H = annual cost to Hold one unit = 5% of the unit purchase price = 5% * 10 = R0.50

Selling price = R15 ( which is cost + 50% ) (50% on cost = 33.33333% on S.P.)

Therefore , Cost = 15 – ( 15*33.3333%) = 15 – 5 = R10

Using the variables, here are the components of the first equation (TC = PC + OC + HC):

1) PC = P x D :                       Purchase Cost = unit Purchase cost times the annual Demand

      = R10 *625,000 units = R 6250000

2) OC = (D x O) / Q :             Order Cost = annual Demand times cost per Order, divided by the order Quantity (number of units)

= ( 625000 * R250 ) / 100000 = R 1750   ( since orders cannot be in fraction we are taking it as 7 instead of 6.25 )

3) HC = (H x Q) / 2:               Holding Cost = annual unit Holding cost times order Quantity (number of units), divided by 2 (because throughout the year, on average the warehouse is half full).

= ( 0.50 * 100000 ) / 2 = R25000

So TC = PC + OC + HC = R 6250000 + R 1750   + R25000 = R 6276750