A Waiting-Line Problem That Cannot Be Modeled by Standard Distributions

question 53

Essay

A waiting-line problem that cannot be modeled by standard distributions has been simulated. The table below shows the result of a Monte Carlo simulation. (Assume that the simulation began at 8:00 a.m. and there is only one server.
$$\begin{array} { | c | c | c | c | } \hline \text { Customer Number } & \text { Arrival Time } & \text { Service Time } & \text { Service Ends } \\\hline 1 & 8 : 06 & 2 & 8 : 08 \\\hline 2 & 8 : 07 & 10 & 8 : 18 \\\hline 3 & 8 : 12 & 10 & 8 : 28 \\\hline 4 & 8 : 24 & 11 & 8 : 39 \\\hline 5 & 8 : 30 & 5 & 8 : 44 \\\hline\end{array}$$
a. What is the average waiting time in line?
b. What is the average time in the system?

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Definitions:

Conversion Cost

The combined costs of direct labor and manufacturing overheads that are incurred in the process of converting raw materials into finished goods.

Manufacturing Overhead

Indirect factory-related costs that are incurred when a product is manufactured, including costs like rent, utilities, and maintenance of equipment.

Selling and Administrative Expenses

These are indirect costs that are not directly tied to the production of goods or services, including sales personnel salaries, advertising, and office rent.

Period Costs

Costs that are not directly tied to the production process and are expensed in the period they are incurred, such as selling, general, and administrative expenses.