Question

on paper please

The manager at a large manufacturer is planning warehousing needs for the coming year. She predicts that warehousing needs has the following distribution as shown in the table. The manager can obtain a full-year lease at S6 per square foot per year. The loss of margin due to the shortage of warehouse space is $14 per square foot per year. Assume an order can only be placed in the increment of 1000, how large the annual contract should the manufacturer sign? Demand Di Probability pi Cumulative Probability of Demand being Di or less 1000 2000 3000 4000 5000 0.1 0.15 0.05 0.15 0.25 0.3 0.45 0.6 0.85 6000 0.25 0.15 7000

Answer 1

If the manager purchases additional sq foot of space and does not use it, then the waste will cause the cost of over estimation. This is also known as overstocking of inventory (Co) and the unit value of this cost is $6.

If the manager purchases less sq foot than the demand and runs short in the course of the operation then there will be opportunity loss. This is also known as the understocking cost of inventory (Cu) and the unit value of this cost is $14.

Using this information we need to determine the critical ratio and place it on the probability distribution table.

The formula for critical ratio = Cu/(Cu+Co)

This makes the critical ratio of this problem to be 14/20 = 0.7

Now looking at the table we see that we either need to choose 5000 or 6000 as Di if we want to be closest to 0.7 of cumulative probability. However these two options give us a probability of 0.6 and 0.85.

If we choose 5000 and have a probability of 0.6 then we will incur opportunity loss cost of $14 per sq feet. The difference may be of 0.1 but the loss will be 0.1*14 = 1.4

If we choose 6000 and have a probability of 0.85 then we will incur wastage cost of $6 per sq feet. The difference may be of 0.15 but the loss will be 0.15*6 = 0.9

Since our probabilistic loss is lesser at 6000 with a cumulative probability of 0.85, that will be our choice.

Answer: the manufacture should sign a contract for 6000 sq feet