MSIM3101 Management Science
Individual Assignment 2
Due: 26 April 2024 (Friday: 6:00pm – Online Submission)
Question 1
The Fly-High Airplane Company builds small jet airplanes to sell to corporations for use by their executives. To meet the needs of these executives, the company's customers sometimes order a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is incurred to initiate the production of these airplanes.
Fly-High has recently received purchase requests from three customers with short deadlines. However, because the company's production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers.
The relevant data are given in the table below. The first row gives the start-up cost required to initiate the production of the airplanes for each customer. Once production is under way, the marginal net revenue from each airplane produced is shown in the second row. The marginal net revenue is the purchase price minus the marginal production cost. The third row gives the percentage of the available production capacity that would be used for each plane produced. The maximum total capacity in the whole company is 100%. The last row indicates the maximum number of airplanes requested by each customer (but less will be accepted).
Fly-High now wants to determine how many airplanes to produce for each customer (if any) to maximize the company's total profit (i.e total profit = total net revenue minus start-up costs). Formulate the mixed integer programming model and solve it using Excel solver for this problem.
Question 2
Considering the network below, node 1 is origin and node 7 is destination node. Determine the minimum distance and shortest-route path from node 2 to node 7.
Question 3
Super Construction Company Limited is considering five projects including theme park, outlet shopping mall, distribution centre, museum and office building. The financial success of these project depends on the interest rate movement in the next 10 years. It is foreseeable that the future interest rate may increase, remain stable or decline. The table below shows their 10-year financial return (in million) under each state of nature.
(a) Determine the best investment using Maximin strategy.
(b) Construct an opportunity loss table and determine the best investment using Minimax Regret strategy.
(c) Suppose the probabilities of increase, remain stable and decline of interest rate are 34%, 29% and 37% respectively, suggest which project would you choose by using expected value (EV) as the decision criterion? Show your calculation steps.
(d) Following (c), the manager stated that “It is worth to pay $1.5millions for the perfect information as the company can earn more by making this decision”. Comment on the statement and justify if you agree with the decision of the manager.
Question 4
The Makonsel Company is a fully integrated company that both produces goods and sells them at its retail outlets. After production, the good are stored in the company’s two warehouses until needed by the retail outlets. Trucks are used to transport the goods from the two plants to the warehouses, and then from the warehouses to the three retail outlets.
Using units of full truckloads, Table 1 shows each plant’s monthly output, its shipping cost per truckload sent to each warehouse, and the maximum amount that it can ship per month to each warehouse.
For each retail outlet (RO), Table 2 below shows its monthly demand, its shipping cost per truckload from each warehouse, and the maximum amount that it can be shipped per month from each warehouse.
Management now wants to determine a distribution plan (number of truckloads shipped per month from each plant to each warehouse and from each warehouse to each retail out let that will minimize the total shipping cost.
Table 1
(a) Draw a network that depicts the company’s distribution network. Identify the supply nodes in this network.
(b) Formulate a linear programming model for this problem.
(c) Solve the problem using solver.