The director of a large public library must schedule employees to reshelf books and periodicals checked out of the library. The number of items checked out will determine the labor requirements. The following data reflect the number of items checked out of the library for the past three years: Year 1 1.804 2.711 2,509 2.432 2,468 2,378 2,175 2.445 1.908 1.922 2,417 2274 Year 2 2.056 2,321 2,442 2.088 2.694 2,122 2,206 1,869 2,489 2.291 2.352 2.189 Year 3 1,976 2,564 2,616 2,150 2,195 2,663 2,011 1,678 1,778 2,065 2,158 2.440 Month January February March April May June July August September October November December The director needs a time-series method for forecasting the number of items to be checked out during the next month. Suppose that the director considers the best forecast to be the one that minimizes the absolute value of mean bias (E). Find the best simple moving average forecast you can using the director's criteria Using the director's criteria, the best forecast for the next month is tems to be checked out (Enter your response as a whole number.)

The director of a large public library must schedule employees to reshelf books and periodicals checked out of the library. The number of items checked out will determine the labor requirements. The following data reflect the number of items checked out of the library for the past three years: Year 1 1.804 2.711 2,509 2.432 2,468 2,378 2,175 2.445 1.908 1.922 2,417 2274 Year 2 2.056 2,321 2,442 2.088 2.694 2,122 2,206 1,869 2,489 2.291 2.352 2.189 Year 3 1,976 2,564 2,616 2,150 2,195 2,663 2,011 1,678 1,778 2,065 2,158 2.440 Month January February March April May June July August September October November December The director needs a time-series method for forecasting the number of items to be checked out during the next month. Suppose that the director considers the best forecast to be the one that minimizes the absolute value of mean bias (E). Find the best simple moving average forecast you can using the director's criteria Using the director's criteria, the best forecast for the next month is tems to be checked out (Enter your response as a whole number.)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section4.8: Data Envelopment Analysis (dea)

Problem 43P

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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.
Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
A machine shop manufactures two types of bolts. The bolts require time on each of the three groups of machines, but the time required on each group differs, as shown in the table below. Type I Type IIMachine 1 0.2 min 0.2 minMachine 2 0.6 min 0.2 minMachine 3 0.04 min. 0.08 min Production schedules are made up one day at a time. In a day, 300, 720, and 100 minutes are available, respectively, on these machines. Type I bolts sell for 15¢ and type II bolts for 20¢. (a) How many of each type of bolt should be manufactured per day to maximize revenue?(b) What is the maximum revenue?(c) Suppose the selling price of type I bolts began to increase. Beyond what amount would this price have to increase before a different number of each type of bolts should be produced to maximize revenue?
At modern woodworks, president and producer of apple crates sold to growers, has been able, with his current equipment, to produce 240 crates per 100 logs. He currently purchases 100 logs per day, and each log requires 3 labor hours to process. He believes that he can hire a profesional buyer who can buy a better quality log at the same cost. if this is the case, he can increase hos production to 260 crates per 100 logs. His labour-hours will increase by 8 hours per day. What will be the impact on productivity (measured in crates per labor-hour) if the buyer is hired?
The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 270 x1 + 230x2 + 240x3+ 220x4 + 190x5 + 270x6 + 230x7 + 220x8 st. x1 + x2 + x5 + x7 ≥ 1 (Building A constraint] x1 + x2 + x3 ≥ 1 (Building B constraint} x6 + x8 ≥ 1 (Building C constraint} x1 + x4 + x7 ≥ 1 (Building D constraint} x2 + x7 ≥ 1 (Building E constraint] x3 + x8 ≥ 1 (Building F constraint) x2 + x5 + x7 ≥ 1 (Building G constraint} X1 + x4 + x6 ≥ 1 (Building H constraint] x1 + x4 + x8 ≥ 1 (Building I constraint} x1 + x2 + x7 ≥ 1 (Building J constraint} xj= {1, if crew j is selected {0, otherwise Set up the problem in Excel and find the optimal solution. a. What…
The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 270x1 + 290x2 + 250x3+ 270x4 + 230x5 + 180x6 + 180x7 + 280x8s.t. x1 + x2 + x5 + x7 ≥ 1 {Building A constraint}x1 + x2 + x3 ≥ 1 {Building B constraint}x6 + x8 ≥ 1 {Building C constraint}x1 + x4 + x7 ≥ 1 {Building D constraint}x2 + x7 ≥ 1 {Building E constraint}x3 + x8 ≥ 1 {Building F constraint}x2 + x5 + x7 ≥ 1 {Building G constraint}x1 + x4 + x6 ≥ 1 {Building H constraint}x1 + x4 + x8 ≥ 1 {Building I constraint}x1 + x2 + x7 ≥ 1 {Building J constraint}xj = {1, if crew j is selected0, otherwisexj = 1, if crew j is selected0, otherwise Set up the problem in Excel and find…
According to the XYZ Apartment Rental Company ER diagram, which of the following is true? Each building must have more than one builder Each building must have multiple apartments Each building must have at least 8 apartments Each building must have more than 2 apartments Answer: ____
A political candidate is planning his media budget for an upcoming election. He has $90,500 to spend. His political consultants have provided him with the following estimates of additional votes as a result of the advertising effort: -for every small sign placed by the roadside, he will garner 20 additional votes. -for every large sign placed by the roadside, he will garner 30 additional votes. -for every thousand bumper stickers placed on cars, he will garner 15 additional votes. -for every hundred personal mailings to voters, he will garner 40 additional votes. -for every radio ad heard, he will garner 485 additional votes. The costs for each of the advertising devices, along with the practical minimum and maximum that should be planned for each, are shown on the following table. How should the candidate plan to spend his campaign money? Advertising Medium Cost Minimum Maximum Bumper stickers (thousands) $30…
Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.
KrazySockzThe KrazySockz Company is known for their colorful yetcomfortable socks. They have forecasted their demand for the nextsix months as follows: Month 1 demand is 30,000, month 2demand is 50,000, month 3 demand is 20,000, month 4 demand is10,000, month 5 demand is 15,000 and month 6 demand is 20,000.At the beginning of month 1 they have 15,000 pairs of socks onhand. KrazySockz currently has 40 production employees. Each productionemployee costs the company the company $4,000 per month ($3,200 salary and $800in other costs) per month. Production employees can work up to 160 hours permonth before they must be paid overtime. Overtime is paid at a rate of $30 per hourand production employees can not work more than 30 hours per month overtime. Ittakes 15 minutes of labor and $0.75 of raw material to produce a pair of socks.KrazySockz can hire or fire employees each month. Hiring a production employeeincurs a cost of $3,500 and firing a production employee costs $4,500. At the end…
You are the district manager for the NCDNR aka the Game Wardens. You staff your law enforcement officers such that they have a 10 hour work day in a single shift. This means that they work 4 days in a row and have 3 consecutive days off. For your district, you need to make sure that you have at least: 10 working on Saturday, 0 on Sunday, 3 on Monday, 3 on Tuesday, 5 on Wednesday, 4 on Thursday, and 8 on Friday. Your current compensation plan approved by the state is: Days off M,T,W T,W,Th W,Th,F Th,F,Sa F,Sa,Su Sa,Su,M Su,M,T Wage 3000 2900 2820 2750 2600 2700 2720 Questions:  What is the objective function value?  How many employees do you have?  How many people show up for work on Sunday, despite this not being necessary according to the scheduling requirements?
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