STOR 572 Simulation for Analytics
Assignment #2 - due Friday, February 7, 2025
Model the problems below in Arena. When you’ve finished, upload your final Arena models (.doe files) to the Homework 2 Assignment on Canvas, and submit written answers to Gradescope.
1. Parts arriving at a machine shop undergo two stages of processing: first, some basic cutting, shaping, and fitting done by a single human operator, followed by more precise milling and finishing tasks carried out by a single automated machine. Furthermore, the shop processes two distinct types of parts: Type 1 and Type 2.
Times between arrivals of Type 1 parts follow a log-normal distribution with a log mean of 11.5 hours and log standard deviation of 2.0 hours, and arriving parts wait in a queue designated only for Type 1 parts until the human operator is available to process them. The times needed for the human operator to process Type 1 parts have a triangular distribution with minimum 5, mode 6, and maximum 8 hours.
Inter-arrival times for Type 2 parts follow an exponential distribution with mean 15 hours. These parts wait in a second queue designated only for Type 2 parts until the same human op- erator is available to process them, and their processing times follow a triangular distribution with parameters 3, 7, and 8 hours.
Once human processing is complete, parts are sent to a single first-come-first-served queue for the automated machine, where processing times for both part types follow a triangular distribution with parameters 4, 6, and 8 hours. Completed parts then exit the system.
Simulate a period of 5,000 hours in this machine shop to estimate the average total time in system for all parts (lumped together regardless of type), the average numbers of parts in the two designated queues for arriving parts, and average utilization of the human operator.
2. A production system consisting of a series of four consecutive automatic workstations is de- signed to operate in remarkably consistent fashion: a new part arrives at the first station for processing every 9.8 minutes, transfer times between stations are negligible, and processing times at all stations are constant. The catch - workstations will occasionally fail. In particu- lar, there are two types of failures: major failures and jams. System data are provided in the table below, with all times in minutes.
Use exponential distributions for the uptimes and uniform distributions for repair times (e.g., a jam at Workstation 3 takes U(2.8, 4.2) minutes to repair). Run your simulation for 10,000 minutes and report on the proportion of time each workstation spends in the failed state.