Analyzing Capacity and Waiting Time in a Burrito Production System

This assignment analyzes the capacity and waiting times within a burrito production process. It begins by calculating the initial capacity of the system, considering the time taken at each stage of the process and the overall utilization rate. The assignment then assesses the current performance, determining the number of customers potentially left unserved due to capacity limitations. Further analysis focuses on optimizing the production process by identifying and addressing bottlenecks, recalculating capacity, and assessing the impact on customer waiting times. The assignment employs formulas to determine average waiting times in the queue, both under the initial conditions and after optimization, providing insights into the effectiveness of process improvements. The calculations cover key metrics like processing time, arrival rate, service rate, and the impact of these factors on customer wait times and overall system efficiency.

Capacity Questions:
1. Capacity per hour (Pancho Burinto) = Time available / Processing time (Pancho Burinto)
= 3600 secs / 129 sec
= Approx. 30 Burinto/ hour
Working note:
 Time available; capacity is to be calculated for 1 hour which is 3600 seconds
 Processing time: Time taken at first stage + second stage + third stage + fourth
stage + fifth stage = 36sec + 21sec+ 34sec + 28sec + 10sec = 129sec
2. Each workers capacity utilization:
Utilization % (Pancho Burinto) = Current production (burritos per hour) × 100
Capacity (Burritos per hour)
= 92 burritos per hour × 100
30 burritos per hour
= Approx 306%
Interpretation: Assuming per customer ordering 1 burinto; 62 customers are leaving
without any order in peak time.
3. Work load balancing:
After analyzing the whole process it was found that minimum time taken by each five
workers in five steps is as follows: 28sec + 11 sec + 23sec + 21sec + 5sec = 88sec
Capacity per hour (Pancho Burinto) = Time available / Processing time (Pancho Burinto)
= 3600 secs / 88 sec
= Approx. 41 Burinto/ hour (Maximum capacity)
4. Each workers capacity utilization at maximum production:

Utilization % (Pancho Burinto) = Current production (burritos per hour) × 100
Capacity (Burritos per hour)
= 92 burritos per hour × 100
41 burritos per hour
= Approx 224%
Interpretation: Assuming per customer ordering 1 burinto; 51 customers are leaving
without any order in peak time.
Waiting Questions:
1. Total average minutes customers waiting in a queue before served at station 1:
Time in queue = Processing Time (p) × (utilization ) × ( CVa 2 + CVp 2 )
(1 – utilization) ( 2 )
= 129 sec × ( .30 ) × ( 12 + 1.52 )
(1 - .30) ( 2 )
= 129 sec × 0.43 × 1.625
= 90.13 secs or 1.50 minutes per cusotmer
Working note; Utilization = arrival rate / service rate = 39.13sec/ 129sec = 0.30sec
Arrival rate = Total time available / total customers arrive = 3600sec/92
= 39.13sec
2. Total average minutes customers waiting in a queue before served at station 1 at
optimized capacity:
Time in queue = Processing Time (p) × (utilization ) × ( CVa 2 + CVp 2 )
(1 – utilization) ( 2 )
= 88 sec × ( .30 ) × ( 12 + 1.52 )
(1 - .30) ( 2 )
= 88 sec × 0.43 × 1.625

= 61.49 secs or 1.02 minutes per customer