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Problem 16

# The order size associated with the economic-order-quantity (E00) model will necessarily decline if a. Ordering costs rise b. Storage costs rise c. Insurance costs for materials in storage fall d. Stockout costs rise

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In conclusion, using the EOQ model, the order size will necessarily decline if ordering costs (scenario a) or storage costs (scenario b) rise, as a higher ordering or carrying cost would prompt businesses to order fewer but larger batches of inventory to minimize costs. The order size will increase if insurance costs for materials in storage fall (scenario c). The effect of rising stockout costs (scenario d) cannot be observed directly using the EOQ model.
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## Step 1: Scenario (a): Ordering costs rise

If the ordering cost (S) increases, then the EOQ will most likely decrease according to the EOQ formula. The reason for this is that a higher ordering cost would prompt the business to order fewer but larger batches of inventory to reduce the costs associated with frequent orders. Thus, the order size will decrease.

## Step 2: Scenario (b): Storage costs rise

If storage costs increase, it implies that the holding (carrying) cost per unit (H) goes up. This would lead to an increase in the EOQ, as businesses will want to reduce the amount of inventory they hold to minimize carrying costs. So, the order size will decrease.

## Step 3: Scenario (c): Insurance costs for materials in storage fall

A decrease in insurance costs means that the holding (carrying) cost per unit (H) would go down. According to the EOQ formula, when holding costs decrease, the EOQ increases. Therefore, the opposite effect is observed in comparison to scenario (b). In this case, the order size will increase.

## Step 4: Scenario (d): Stockout costs rise

A higher stockout cost would encourage businesses to maintain a higher level of safety stock, as running out of stock becomes more expensive. Thus, it would indirectly affect the EOQ model as the overall carrying costs may increase. However, the EOQ formula does not take into account stockout costs. Therefore, we must note that the EOQ formula would not be able to show the effect of stockout costs on order size. In conclusion, based on the EOQ model, the order size will decrease in scenarios (a) and (b), while it will increase in scenario (c). For scenario (d), we cannot observe the effect directly using the EOQ model.

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