Final answer:
The EOQ for a supermarket when stock-outs are not allowed can be computed using the given demand, order cost, and holding cost, leading to an EOQ of approximately 2190 units. The annual holding cost for this EOQ is calculated to be #5475. Adjustments are needed for the EOQ formula to calculate the EOQ and holding costs when stock-outs are allowed.
Step-by-step explanation:
The question revolves around the calculation of the Economic Order Quantity (EOQ) for a supermarket considering stock-out conditions. The EOQ formula is specific in inventory management for optimizing the ordering quantity of inventory and balancing holding costs against order costs.
To calculate the EOQ when stock-out is allowed, adjustments to the basic EOQ formula need to be made, taking into account the cost of shortages. However, the EOQ without considering stock-outs is calculated using the standard formula: EOQ = √[(2DS)/H], where D is the demand, S is the setup or order cost, and H is the holding cost per unit.
For the given question:
The EOQ when stock-outs are not allowed can be calculated as follows:
EOQ = √[(2 × 60000 × 200) / 5]
= √[(2 × 12000000) / 5] = √(24000000 / 5)
= √4800000
≈ 2190 units (rounded to nearest whole unit)
The difference in annual holding costs between the scenarios with and without stock-outs would be the cost per unit per annum multiplied by half of the EOQ (since average inventory level is EOQ/2).
Annual holding cost without stock-outs = (EOQ/2) × H
= (2190/2) × 5
= 1095 × 5
= #5475
If stock-outs are allowed, the formula for EOQ would need to incorporate the cost of shortages, and the calculation for annual holding cost would need to consider this adjusted EOQ value, which would require specific information about the penalty cost and the rate of stock-outs.