# don-t-know-the-formula

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Besides the single-order inventory scenario, there are many other situations where a “newsboy” type of analysis is relevant. Some capacity planning situations, for example, are essentially newsboy problems. In general, we face newsboy-type characteristics when we have

- One opportunity to decide how much capacity to put in place,
- At the time the decision needs to be made, there is uncertainty as to how much capacity is required,
- There is cost associated with putting capacity in place, and implicitly or explicitly a cost of having too much (more than needed) capacity,
- There is a cost associated with having too little (less than needed) capacity.

As an example, consider the following scenario: I have to decide how many employees to schedule to work the afternoon shift next Saturday. Any employees scheduled will work the entire shift whether I need them or not, and they earn $12.00 per hour over the 8-hour shift.

If it turns out the number of employees scheduled to work is insufficient to meet customer demand, I can call in some extra employees. These people will earn $18.00 per hour over the 8 hour shift.

At the time I am deciding how many employees to schedule, here is what I know about the number of employees (X) required to meet customer demand during the shift in question:

x = | 2 | 3 | 4 | 5 | 6 | Sum |
---|---|---|---|---|---|---|

P(X = x) | 0.15 | 0.20 | 0.30 | 0.20 | 0.15 | 1.00 |

Use the decision table approach to determine the number of employees to schedule for the Saturday afternoon shift, in order to minimize the expected cost of covering the unknown requirements.

**HINTS:**

Using the decision table approach, your options are to schedule 2, 3, 4, 5, or 6 employees to come in and earn $12.00 per hour. Your decision table should have a row for each of these alternatives. This is equivalent to having a row for each different inventory order quantity.

Your decision table should have a column for each number of employees that will actually be required. Again, this could be 2, 3, 4, 5, or 6 employees.

For each cell of the table, compute the total cost of covering the Saturday afternoon requirements. This includes the cost of paying $12.00 per hour for each person scheduled to work, plus the cost of paying people $18.00 per hour if they were not scheduled but instead get called in. For example, if you scheduled 3 people to work, but the number of people actually required is 5 (so you had to call in 2 extra people), your total hourly cost if 3*12 + 2*18 = $72.00. This would be a total of 72*8 = $576 for the 8 hour shift.

Notice the basic issue at hand: The people earning $12.00 per hour cost less, but I am paying for them whether I need them or not. The people earning $18.00 per hour cost more, but I only pay for them if I actually need them. This is a very common scenario, where one type of resource is more flexible but also more costly. The decision boils down to how much of the “cheaper” resource to put in place now, vs. how much of the more “expensive” resource to have to use (or not) later. The optimal solution usually involves some combination of the two, and essentially involves determining what portion of the requirements probability distribution should be “covered” with the cheaper but less flexible resource. Notice, in this case we have one chance to decide how many employees to schedule at the regular wage of $12.00 per hour. Any shortfall in the number scheduled vs. the number actually needed is made up with people earning $18.00 per hour.

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