Operations Research

1. Multi-Echelon Distribution
   Consider the following multi-echelon distribution problem. Products must be distributed from a pair of factories to three warehouses. The products are then shipped to five distribution centers. A private trucking fleet is used for all shipping. Prices per unit shipped are shown on each of the arcs. The capacity of some shipping lanes is limited by the number of trucks available for each delivery segment.
   
   Question: How many units should be shipped along each shipping lane to satisfy demand while minimizing the delivery cost?
2. Pipeline Flow Problem
   An company has the following pipeline network, where each pipeline is labeled with its maximum flow rate (in thousands of gallons per hour).
   
   Question: What is the network’s maximum possible flow rate from the start to the end?
3. Northwest Travel Problem

The travel times (hours) along various routes in the Pacific Northwest is shown below.

Question 1: What is the quickest route from Seattle to Denver?

Question 2: What is the quickest route from Portland to Cheyenne?

Question 3: What is the quickest route from Seattle to Denver, if you are required to pass through both Butte and Salt Lake City along the way?

Question 4 : A snow storm has closed down I-90. With I-90 closed, what is the quickest alternate route from Seattle to Denver?

You are designing a telecommunications system and need to connect a series of offices (shown as nodes) with fiber optic cable. You have information about which offices need to be connected (following diagram) and the cost for several possible network links.

Question 1 : For the nodes shown below, please develop a minimum spanning tree using the greedy algorithm to find the optimal set of links. Specify which links are to be used and the resulting total cost to develop the network.

Question 2 : Due to damage from an earthquake, the office at node J has lost power and can no longer be part of the network due to reliability concerns. You’ve been instructed to keep the C-J link but not to link node J directly to any other locations. Redevelop the network as modified by these instructions. Specify what links are to be used and the resulting total cost.

6 ) Consultant by Day, Instructor by Night

Each class night, Mike drives from his office to the University Center. He has multiple routes he could take, each of which varies in distance, speeds, and traffic. The following map shows the various routes available, with the stars representing the start and end points.

Some road segments are connected with curves and others with nodes. Travel times for each road segment are shown and represent a best guess about delays from traffic and unsignalized intersections. The first and last segments (Office—Alley/H and 40 ^th /Old Seward—University) are assumed to have no time associated with them.

Question 1 : Using only those travel segments that have a time associated with them, find the shortest path from Mike’s office to the University Center.

Question 2: Once you have found your solution, comment on how confident you are with your answer. Are the travel times reasonable? Are the other routes that may be better? If you have changes to suggest, implement them and present your new findings as well.

7 ) Conference Planning Project

As the operations research expert on a conference planning team, you’ve been asked to look at the likelihood of completing the preparation work in time for the conference’s start date. Since the start date for the conference is known, you’re under a lot of pressure to make sure the team can complete the work in time. The activities to be performed, their times (in days), and the precedence constraints are as follows:

Question 1: Draw the network for this project. You can use either AOA or AON.

Question 2 : Build a project network in Excel to represent all of the paths. Show the time for each path through the network. Identify the critical path(s). Specify the completion date (days from the start).

Question 3 : Comment on the mean times and variance of the paths. Are any paths close in duration or highly variable? In other words, are there are non-critical paths that you think could become critical?

Question 4 : What completion date are you 80% confident of achieving? 40% confident?

8) Commuter Bus Scheduling

You’ve been tasked with scheduling the routes on a commuter bus system to ensure adequate service is been provided to each of the transit locations, while minimizing the operating cost. Your company currently owns three buses that it uses to provide this service. Route information, including the operating cost and the transit locations served, is shown in the following table.

Question: Develop an Excel model to select the three routes to be served by your company’s buses in order to minimize the total operating cost while including a stop at each of the transit locations.

Price: $49.99

Solution: The downloadable solution consists of 35 pages, 1966 words and 6 charts.
Deliverable: Word Document