
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Transcribed Image Text:**Table 18.4: Infinite-Source Values for \( L_q \) and \( P_0 \) Given \( \lambda/\mu \) and \( M \)**
This table provides the infinite-source queueing values for \( L_q \) (average number of customers in line) and \( P_0 \) (probability of zero customers in the system) based on the ratio \( \lambda/\mu \) (arrival rate/service rate) and the number of servers \( M \).
Each row of the table is organized as follows:
- **\( \lambda/\mu \)**: This column lists the ratio of arrival rate to service rate, ranging from 0.15 to 4.3.
- **\( M \)**: Indicates the number of servers in the system, ranging from 1 to 10.
- **\( L_q \)**: Represents the average number of customers in line for the queue.
- **\( P_0 \)**: Shows the probability that there are zero customers in the system.
For each value of \( \lambda/\mu \), data is arranged under different values of \( M \), showing how \( L_q \) and \( P_0 \) vary with changes in these parameters.
The table helps in understanding how queue lengths and idle probabilities fluctuate with different server counts and demand ratios, facilitating decision-making in service systems planning and optimization.

Transcribed Image Text:**Problem 18-7 (Algo)**
The manager of a regional warehouse must decide on the number of loading docks to request for a new facility in order to minimize the sum of dock costs and driver-truck costs. The manager has learned that each driver-truck combination represents a cost of $205 per day and that each dock plus loading crew represents a cost of $1,118 per day. Use Table 18.4.
**a. How many docks should be requested if trucks arrive at the rate of four per day, each dock can handle five trucks per day, and both rates are Poisson?**
- **Answer is complete and correct.**
- Number of dock(s): **1**
**b. An employee has proposed adding new equipment that would speed up the loading rate to 5.71 trucks per day. The equipment would cost an additional $100 per day for each dock. What is the lowest daily total cost that can be achieved with the new equipment? (Round your cost amount to 2 decimal places and all other calculations to 3 decimal places.)**
- **Answer is complete but not entirely correct.**
- The daily total cost with the new equipment is: **$1,441.13**
*Explanations:*
- Part (a) Analysis: The number of docks is calculated based on the arrival rate and handling capacity, ensuring the optimal number of docks to minimize costs.
- Part (b) Analysis: An additional cost is considered with new equipment. The proposed loading rate adjustment and its financial impact on daily costs are evaluated. The given answer may need reassessment for full accuracy.
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