3.	Rancanglah desain Simulasi Sistem antrian : Model 1phase multi Channel dengan kapasitas layanan 170 orang perhari dengan jam layanan pkl. 0x.00-1x.30, Jika waktu istirahat 1 jam, Waktu tempuh dari tempat antri ke tempat layanan 0,5 menit: 
A.	Berapakah jumlah nasabah yang dapat terlayani, pada masing-masing channel (a,b,c) di atas pada pkl15.00-16.00? 
B.	Berapakah waktu yang digunakan jika digunakan antrian system 3 channel yang melayani antrian 372 dan 435 nasabah per hari dengan asumsi seperti tersebut diatas? 
 


To design and analyze the queuing system for a 1-phase multi-channel model with specific service capacity and working hours, we'll break down the problem into several parts. We'll calculate the number of customers that can be served per channel and the total time required to serve given numbers of customers using a 3-channel system.

### Given Information:
1. **Service Capacity**: 170 people per day.
2. **Working Hours**: \(0x.00-1x.30\) with a 1-hour break.
3. **Time to travel from queue to service point**: 0.5 minutes.

### Assumptions for Working Hours:
- Let's assume \(0x = 09\) and \(1x = 18\), representing a working day from 09:00 to 18:30 with a 1-hour break.
- Total working hours per day = 9.5 hours - 1 hour break = 8.5 hours.

### Step-by-Step Solution:

**Step 1: Calculate the total available working minutes per day:**
\[ 8.5 \text{ hours} \times 60 \text{ minutes/hour} = 510 \text{ minutes/day} \]

**Step 2: Calculate the effective service rate per minute:**
\[ \text{Service rate per minute} = \frac{170 \text{ customers}}{510 \text{ minutes}} \approx 0.333 \text{ customers/minute} \]

**Step 3: Calculate the service capacity per channel per hour:**
Assuming there are 3 channels (a, b, c), each channel serves:
\[ \text{Service capacity per channel per hour} = 0.333 \text{ customers/minute} \times 60 \text{ minutes/hour} \approx 20 \text{ customers/hour} \]

### Part A: Number of Customers Served from 15:00 to 16:00
Each channel can serve approximately 20 customers per hour. Hence, from 15:00 to 16:00, the number of customers served by each channel is:
\[ \text{Number of customers per channel} = 20 \]

So, channels a, b, and c can each serve 20 customers in this time period.

### Part B: Time Required to Serve 372 and 435 Customers with a 3-Channel System

**Case 1: Serving 372 Customers**
1. **Total service rate for 3 channels:** 
\[ \text{Total service rate} = 3 \times 20 \text{ customers/hour} = 60 \text{ customers/hour} \]

2. **Total time required to serve 372 customers:**
\[ \text{Total time (hours)} = \frac{372 \text{ customers}}{60 \text{ customers/hour}} = 6.2 \text{ hours} \]

3. **Including travel time from queue to service (0.5 minutes/customer):**
\[ \text{Total travel time (minutes)} = 372 \times 0.5 \approx 186 \text{ minutes} \]
\[ \text{Total travel time (hours)} = \frac{186}{60} \approx 3.1 \text{ hours} \]

4. **Total time including travel:**
\[ 6.2 \text{ hours} + 3.1 \text{ hours} \approx 9.3 \text{ hours} \]

**Case 2: Serving 435 Customers**
1. **Total time required to serve 435 customers:**
\[ \text{Total time (hours)} = \frac{435 \text{ customers}}{60 \text{ customers/hour}} = 7.25 \text{ hours} \]

2. **Including travel time from queue to service (0.5 minutes/customer):**
\[ \text{Total travel time (minutes)} = 435 \times 0.5 = 217.5 \text{ minutes} \]
\[ \text{Total travel time (hours)} = \frac{217.5}{60} \approx 3.625 \text{ hours} \]

3. **Total time including travel:**
\[ 7.25 \text{ hours} + 3.625 \text{ hours} \approx 10.875 \text{ hours} \]

### Summary:
**A. Number of customers served per channel from 15:00 to 16:00:** 20 customers per channel (a, b, c).

**B. Time required using a 3-channel system:**
- For 372 customers: **9.3 hours**.
- For 435 customers: **10.875 hours**.

Would you like more details or have any questions?

Here are some related questions you might find useful:
1. How to calculate the average waiting time in a queuing system?
2. What is the utilization factor for each channel in the given scenario?
3. How to optimize service capacity for multiple channels?
4. What is the effect of increasing the number of service channels on customer wait time?
5. How to simulate different queuing scenarios using probability distributions?

**Tip:** Always consider both the service rate and travel time when designing and analyzing queuing systems to get a comprehensive understanding of the system's efficiency.

Explore the design and analysis of a multi-channel queuing system with a daily service capacity of 170 customers. Calculate service rates, travel times, and total service time for different customer scenarios. Learn the principles of queuing theory and application in service system design.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation