TRUE FALSE Management science is an approach to decision making based on the scientific method. Management science makes extensive use of quantitative analysis. Management Science is also known as operations research and decision science Modern management science research is generally considered to have originated during the World War I period.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 84P

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The eTech Company is a fairly recent entry in the electronic device area. The company competes with Apple. Samsung, and other well-known companies in the manufacturing and sales of personal handheld devices. Although eTech recognizes that it is a niche player and will likely remain so in the foreseeable future, it is trying to increase its current small market share in this huge competitive market. Jim Simons, VP of Production, and Catherine Dolans, VP of Marketing, have been discussing the possible addition of a new product to the companys current (rather limited) product line. The tentative name for this new product is ePlayerX. Jim and Catherine agree that the ePlayerX, which will feature a sleeker design and more memory, is necessary to compete successfully with the big boys, but they are also worried that the ePlayerX could cannibalize sales of their existing productsand that it could even detract from their bottom line. They must eventually decide how much to spend to develop and manufacture the ePlayerX and how aggressively to market it. Depending on these decisions, they must forecast demand for the ePlayerX, as well as sales for their existing products. They also realize that Apple. Samsung, and the other big players are not standing still. These competitors could introduce their own new products, which could have very negative effects on demand for the ePlayerX. The expected timeline for the ePlayerX is that development will take no more than a year to complete and that the product will be introduced in the market a year from now. Jim and Catherine are aware that there are lots of decisions to make and lots of uncertainties involved, but they need to start somewhere. To this end. Jim and Catherine have decided to base their decisions on a planning horizon of four years, including the development year. They realize that the personal handheld device market is very fluid, with updates to existing products occurring almost continuously. However, they believe they can include such considerations into their cost, revenue, and demand estimates, and that a four-year planning horizon makes sense. In addition, they have identified the following problem parameters. (In this first pass, all distinctions are binary: low-end or high-end, small-effect or large-effect, and so on.) In the absence of cannibalization, the sales of existing eTech products are expected to produce year I net revenues of 10 million, and the forecast of the annual increase in net revenues is 2%. The ePIayerX will be developed as either a low-end or a high-end product, with corresponding fixed development costs (1.5 million or 2.5 million), variable manufacturing costs ( 100 or 200). and selling prices (150 or 300). The fixed development cost is incurred now, at the beginning of year I, and the variable cost and selling price are assumed to remain constant throughout the planning horizon. The new product will be marketed either mildly aggressively or very aggressively, with corresponding costs. The costs of a mildly aggressive marketing campaign are 1.5 million in year 1 and 0.5 million annually in years 2 to 4. For a very aggressive campaign, these costs increase to 3.5 million and 1.5 million, respectively. (These marketing costs are not part of the variable cost mentioned in the previous bullet; they are separate.) Depending on whether the ePlayerX is a low-end or high-end produce the level of the ePlayerXs cannibalization rate of existing eTech products will be either low (10%) or high (20%). Each cannibalization rate affects only sales of existing products in years 2 to 4, not year I sales. For example, if the cannibalization rate is 10%, then sales of existing products in each of years 2 to 4 will be 10% below their projected values without cannibalization. A base case forecast of demand for the ePlayerX is that in its first year on the market, year 2, demand will be for 100,000 units, and then demand will increase by 5% annually in years 3 and 4. This base forecast is based on a low-end version of the ePlayerX and mildly aggressive marketing. It will be adjusted for a high-end will product, aggressive marketing, and competitor behavior. The adjustments with no competing product appear in Table 2.3. The adjustments with a competing product appear in Table 2.4. Each adjustment is to demand for the ePlayerX in each of years 2 to 4. For example, if the adjustment is 10%, then demand in each of years 2 to 4 will be 10% lower than it would have been in the base case. Demand and units sold are the samethat is, eTech will produce exactly what its customers demand so that no inventory or backorders will occur. Table 2.3 Demand Adjustments When No Competing Product Is Introduced Table 2.4 Demand Adjustments When a Competing Product Is Introduced Because Jim and Catherine are approaching the day when they will be sharing their plans with other company executives, they have asked you to prepare an Excel spreadsheet model that will answer the many what-if questions they expect to be asked. Specifically, they have asked you to do the following: You should enter all of the given data in an inputs section with clear labeling and appropriate number formatting. If you believe that any explanations are required, you can enter them in text boxes or cell comments. In this section and in the rest of the model, all monetary values (other than the variable cost and the selling price) should be expressed in millions of dollars, and all demands for the ePlayerX should be expressed in thousands of units. You should have a scenario section that contains a 0/1 variable for each of the binary options discussed here. For example, one of these should be 0 if the low-end product is chosen and it should be 1 if the high-end product is chosen. You should have a parameters section that contains the values of the various parameters listed in the case, depending on the values of the 0/1 variables in the previous bullet For example, the fixed development cost will be 1.5 million or 2.5 million depending on whether the 0/1 variable in the previous bullet is 0 or 1, and this can be calculated with a simple IF formula. You can decide how to implement the IF logic for the various parameters. You should have a cash flows section that calculates the annual cash flows for the four-year period. These cash flows include the net revenues from existing products, the marketing costs for ePlayerX, and the net revenues for sales of ePlayerX (To calculate these latter values, it will help to have a row for annual units sold of ePlayerX.) The cash flows should also include depreciation on the fixed development cost, calculated on a straight-line four-year basis (that is. 25% of the cost in each of the four years). Then, these annual revenues/costs should be summed for each year to get net cash flow before taxes, taxes should be calculated using a 32% tax rate, and taxes should be subtracted and depreciation should be added back in to get net cash flows after taxes. (The point is that depreciation is first subtracted, because it is not taxed, but then it is added back in after taxes have been calculated.) You should calculate the company's NPV for the four-year horizon using a discount rate of 10%. You can assume that the fixed development cost is incurred now. so that it is not discounted, and that all other costs and revenues are incurred at the ends of the respective years. You should accompany all of this with a line chart with three series: annual net revenues from existing products; annual marketing costs for ePlayerX; and annual net revenues from sales of ePlayerX. Once all of this is completed. Jim and Catherine will have a powerful tool for presentation purposes. By adjusting the 0/1 scenario variables, their audience will be able to see immediately, both numerically and graphically, the financial consequences of various scenarios.
Make sure to identify and define the decision variables, and formulate the objective function and constraints for each problem. You may use Excel to solve the mathematical problems. 1. Sunchem, a manufacturer of printing inks, has five manufacturing plants worldwide. Their locations and capacities are shown in Table 1 along with the cost of producing 1 ton of ink at each facility. The major markets for the inks are North America, Europe, Japan, South America, and the rest of Asia. Demand at each market is shown in Table 1. Transportation costs from each plant to each market in U.S. dollars are shown in Table 1. Management must come up with a production plan for the next year. a. If no plant can run below 50 percent capacity, how much should each plant produce and which markets should each plant supply? b. If there are no limits on the minimum amount produced in a plant, how much should each plant produce?
Evaluate how linear programming modeling helps managers in their analysis to make optimal decisions and analyze the problem, the objective function, constraints, and decision variables. Share a real-world application.
Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions…
An investor is considering investing in stocks, real estate, or bonds economic conditions. Suppose that the probabilities for good, stable and poor conditions are 0.2, 0.4 and … (figure it out), respectively. Table 1 shows the payoff returns for the investor’s decision situation. Table 1: Investment returns Economic Conditions Investment Good Stable Poor Stocks R5 000 R7 000 R3 000 Real estate -R2 000 R10 000 R6 000 Bonds R4 000 R4 000 R4 000 Assuming the probabilities of the occurrence of the state of nature are unknown, what will be the best investment alternative; a) If the decision maker is pessimistic about the future state, (3) b) If the decision maker strikes a compromise between the maximin and maximax, assuming the coefficient of pessimism is 0.2. (4) c) If the decision is based on opportunistic loss. (6) d) If we use the equally likelihood criterion
How do you address unrestricted decision variables (can be positive, negative or zero) in linear programming?
“Good Intentions” (GI) company produces two products, which it sells on both a cash and credit basis. Revenues from credit sales will not have been received but are included in determining profit earned during the current six-month period. Sales during the next six months can be made either from units produced during the next six months or from the beginning inventory. Relevant information about products one and two is as follows. During the next six months, at most 150 units of product type 1 can be sold on a cash basis, and at most 100 units of product 1 can be sold on a credit basis. It costs £35 to produce each unit of product type 1, and each sells for £40. A credit sale of a unit of product 1 yields £0.50 less profit than a cash sale (because of delays in receiving payment). Two hours of production time are needed to produce each unit of product 1. At the beginning of the six-month period, 60 units of product 1 are in the inventory. During the next six months, at most 175 units…
A Make-or-Buy DecisionTriple X Company manufactures and sells refrigerators. It makes some of the parts for the refrigerators and purchases others. The engineering department believes it might be possible to cut costs by manufacturing one of the parts currently being purchased for $8.25 each. The firm uses 100,000 of these parts each year. The accounting department compiles the following list of costs based on engineering estimates:Fixed costs will increase by $50,000.Labor costs will increase by $125,000.Factory overhead, currently running $500,000 per year, maybe expected to increase 12 percent.Raw materials used to make the part will cost $600,000.Given the preceding estimates, should Triple X make the part or continue to buy it?
A manufacturer makes two products ,laptops bags and briefcases. Each must be processed through two work areas. Work are #1 has 50 hours of available production time each week. Work area #2 has 60 hours of available production time each week. Manufacturing of a laptop bag requires 3 hours in work area #1 and 2 hours in work area #2. Manufacturing of a briefcase requires 1 hours in work area #1 and 4 hours in work area #2. Profit is $6 per laptop $9 per window.a) Define decision variables that will tell how many units to build (laptops bags and briefcases) per week.b) Develop an objective function that will maximize profits per weekc) Develop production constraints for work area #1 and #2.d). What is the optimal solutions.
what will happen if the right hand side value of a constraint in two variable linear programming problems is changed? a. optimal measure of performance may change b. parallel shift must be made in the graph of that constraint c. optimal valued for one or more of the decision variables may change d. all of the above e. none of the above
Ten different types of brownies are sold. You arethinking of developing a new brownie for sale.Brownies are rated on the basis of five qualities: price,chocolate flavor, chewiness, sweetness, and ease ofpreparation. You want to group the 10 brownies on themarket into three clusters. Each cluster should containbrownies that are relatively similar.a. Why would this be useful to you?b. How would you do it?
3. Using the following table, perform ALL FIVE of the techniques for Decision Making under Uncertainty: Maximax, Maximin, Hurwicz Realism (α = 0.4), LaPlace and Minimax Regret. Show the work on excel file. SIZE OF FIRST STATION GOOD MARKET FAIR MARKET POOR MARKET ($) ($) ($) Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,000