Operation Research Questions

Question 1: The Cost-Less Corp. supplies its four retail outlets from its three plants. The shipping cost per shipment from each plant to each retail outlet is given below. RI R2 R3 R4 PI 30 10 25 20 P2 15 25 30 10 P3 20 30 15 20 Part a) Formulate this problem as an assignment problem and solve it to find the best strategy for assigning production plants to retail outlets. (No need to show your steps, only list all possible assignments and minimum assignment cost) Part b) Each plant can produce up to 150 products per month Retail outlets 1. 2. and 3 need to receive 100. 120, 150. and 100 products per month. The company makes a revenue of 10 in for the manufacture of each unit of product. (Only show the table) Part c) Use the minimum cost rule to construct an initial BF solution and calculate its transportation cost. (Show the final solution) Question 2: Consider the following activities and their durations and requirements for construction project. Activity Duration (days) Activity Predecessors Optimistic Most likely Pessimistic A - 2 7 9 B - 3 6 9 C - 3 5 8 D A 15 19 20 E B.C 6 9 10 F C 2 4 6 G A.E 4 8 13 H G I 2 4 Part a) Draw the project network and determine the critical path in the project network using most likely activity durations. (Show the network, total flow of each activity, and critical path) Part b) How many days activity F could be delayed its early start date without delaying the start date of other activities? (Explanations and calculations) Part c) If company's president wants to have 95% chance of completing the project before July 30, when should the project began? (Explanations and calculations) Question 3: The Makonsel company is fully connected supply chain that produces goods in production centers (Atlanta and Birmingham) and sells them at its markets or retail outlets in Pittsburgh and Detroit. After production, the goods are stored in one of the warehouses in Nashville and Memphis and then they are sent to one of the cities in Cincinnati, Columbus, or Richmond for final delivery. The possible logistic paths and their travel times (hrs) are listed in the table below: Atlanta 4 6 Birmingham 3 3 - - Nashville - - 5 6 9 Memphis 7 9 12 Indianapolis - - - - 6 3 Columbus - - - 3 3 Richmond - 6 9 Part a) Use dynamic programming to find the shortest path for delivering products from Atlanta to Detroit. (Define stages and states, show all tables and final solution) Trucks with limited transportation capacity of 1000 products are used to transport the goods. The transportation cost is 0.01 (S/hour per product) and there is also: fixed charge of $500 for transportations from Atlanta to Nashville. The tables below show other costs and capacities. Plants Production Cost ($) Production Capacity Atlanta 8 3000 Birmingham 6 6000 Product Price Markets Min Demand ($) Detroit 5000 100 Pittsburgh 3000 50 Part b) Formulate the problem as linear programming model to find the best logistic strategy for this supply chain. Part c) Use software to solve the problem (Show the screen shot of the setting window and results) Part d) Investigate the effects of transportation capacity on total profit (Be creative, no specific requirement)