Page 256 - DMGT501_OPERATIONS_MANAGEMENT

Operations Management

Notes 2. Minimum average yearly cost is given by:
T EOQ = (D × A) / Q EOQ + (Q EOQ × r) / 2
= (600 × 80) /400 + (400 × 0.60) / 2
= 240.
3. The optimum number of orders per year is:
N EOQ = D/Q EOQ = 600/ 400 = 3/2

4. The optimum period of supply per optimum order is
T EOQ = 1 / N EOQ = 1 / (3 / 2)
= 2 / 3
5. Ordering 20% higher than EOQ:

Ordering quantity = (120 × 400) / 100 = 480 units
With
Q EOQ = 400 and Q = 480,
The ratio k = Q / Q EOQ = 480/400 = 1.2
We have

T /T EOQ = [(1 / k + k) /2]
Q
= (1 / 1.2 + 1.2)/2
= 61 / 60
Thus the cost would increase by 1/60th

Or 240 × 1/60 = 4

‘Shortages are undesirable, but some organizations create shortages
intentionally’. How is this justified from an economic point of view? Derive

an expression for total cost in the inventory model for intentional
shortages.

10.2 More Complex Models

For simple inventory models, we assumed that future demand is known with certainty. Generally,
however, this is not the case for companies like BPCL. The demand varies from day to day as
well from period to period. Making things, even more complex is the fact that BPCL provides
a principle product that is not distinguishable from similar products provided by other ‘oil’
companies. In such cases Stochastic Inventory Models need to be used. But before that we will
look into stochastic models where the selling price of an item varies with the order size, and how
this is handled in inventory management.

10.2.1 Quantity Discounts or Price-break Models

Each of us has purchased goods in larger quantities than we immediately need so that we could
pay a lower unit price. When demand is certain, delivery is instantaneous (no stock outs), and

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