1) For an order-up-to model with lead time L periods, which of the following sta
ID: 348014 • Letter: 1
Question
1) For an order-up-to model with lead time L periods, which of the following statement is TRUE
Order will be placed every L + 1 periods
Order will be received every L + 1 periods
Inventory decision is made to balance the supply and demand over L+1 periods
Safety stock increases proportionally in lead time L, i.e., if lead time L increases n times, safety stock also increases n times
2) Demand each period is normally distributed and an order up-to model is used to decide order quantities. Which of the following influences the chosen order up-to level (i.e., a change in which of the following would change the chosen order up-to level)?
I. The mean of demand in one period
II . The standard deviation of demand over L+1 periods
III. The target in-stock probability
a)Only I
b)Only II
c)Only II
d)I and II
e)I and III
f)II and III
g)I, II and III
3) Which of the following statement of risk pooling effect is NOT true
Risk pooling effect improves the business’s profit by attracting more demand
Risk pooling effect reduces the inventory holding cost by reducing safety-stock
Risk pooling effect is more significant when the inventory consolidation scale is larger
Risking pooling effect enables the business to achieve the same critical ratio using less inventory
Explanation / Answer
(1)
An order will be placed in every 'P' period where P is the review period. An order will be received in every 'L' period and not L+1 periods. Safety stock is proportional to the square root of (lead time + review period). So, option (1), (2), and (4) are incorrect.
Option (3) is correct because after having one period spent, we are ordering for the next L periods and hence are able to control the inventory of L+1 period.
(2)
Order-up-to-level (T) = d(P+L) + safety stock
d = mean demand
When Lead time is fixed,
Safety stock = function of (std deviation of demand, L, P, in-stock probability)
When Lead time also has variability,
Safety stock = function of (std deviation of demand, std. deviation of lead time, d, L, P, in-stock probability)
So, in any case, T will depend on d, std deviation of demand, and in-stock probability.
So, the correct answer is g) I, II and III
(3)
The risk pooling is done to aggregate the inventory because variability remains lower at aggregation. A lower inventory level is required when inventories of different places are put together in a single warehouse. We need to keep lower safety stocks and the same critical ratio (or, in-stock probability) is attainable at lower inventory level. Option (2), (3), (4) are all correct.
We cannot think a situation where risk pooling is related to demand. The demand for a product will depend only on customers' preference and willingness to buy that product. So, Option (1) should be selected as the correct answer.
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