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Statistics
For the following highway network system, determine the maximal flow in vehicles per hour:The highway commission is considering adding highway section 34 to permit a flow of 2000 vehicles
Refer to the Contois Carpets problem, for which the network representation is shown in Figure. Suppose that Contois has a beginning inventory of 50 yards of carpet and requires an inventory of 100
Sanders Fishing Supply of Naples, Florida, manufactures a variety of fishing equipment that it sells throughout the United States. For the next three months, Sanders estimates demand for a particular
Solutions Plus is an industrial chemicals company that produces specialized cleaning fluids and solvents for a wide variety of applications. Solutions Plus just received an invitation to submit a bid
The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in El Paso and gradually built a customer base
In the market share analysis of Section 17.1, suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped
Management of the New Fangled Softdrink Company believes that the probability of a customer purchasing Red Pop or the company’s major competition, Super Cola, is based on the customer’s
One cause of the downtime in Problem 3 was traced to a specific piece of computer hardware. Management believes that switching to a different hardware component will result in the following
A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no
Data collected from selected major metropolitan areas in the eastern United States show that 2% of individuals living within the city limits move to the suburbs during a one-year period while 1% of
Assume that a third grocery store, Quick Stop Groceries, enters the market share and customer loyalty situation described in Section 17.1. Quick Stop Groceries is smaller than either
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities:a. Which brand appears to have the most loyal customers? Explain.b.
Suppose that in Problem 8 a new toothpaste brand enters the market such that the following transition probabilities exist:What are the new long-run market shares? Which brand will suffer most from
Given the following transition matrix with states 1 and 2 as absorbing states, what is the probability that unit in states 3 and 4 end up in each of the absorbingstates?
In the Heidmans Department Store problem of Section 17.2, suppose that the following transition matrix is appropriate:If Heidmans has $4000 in the 030-day category
The KLM Christmas Tree Farm owns a plot of land with 5000 evergreen trees. Each year KLM allows retailers of Christmas trees to select and cut trees for sale to individual customers. KLM protects
A large corporation collected data on the reasons both middle managers and senior managers leave the company. Some managers eventually retire, but others leave the company prior to retirement for
Data for the progression of college students at a particular college are summarized in the following matrix of transition probabilities.a. What states are absorbing states?b. Interpret the transition
The game of blackjack (sometimes called “21”) is a popular casino game. The goal is to have a hand with a value of 21 or as close to 21 as possible without exceeding 21. The player and the dealer
The Mohawk Discount Store is designing a management training program for individuals at its corporate headquarters. The company wants to design the program so that trainees can complete it as quickly
Bridge City Developers is coordinating the construction of an office complex. As part of the planning process, the company generated the following activity list. Draw a project network that can be
Construct a project network for the following project. The project is completed when activities F and G are bothcomplete.
Assume that the project in Problem 3 has the following activity times (in months):a. Find the critical path.b. The project must be completed in 11/2 years. Do you anticipate difficulty in meeting the
Management Decision Systems (MDS) is a consulting company that specializes in the development of decision support systems. MDS obtained a contract to develop a computer system to assist the
Consider the following project network and activity times (in weeks):a. Identify the critical path.b. How much time will be needed to complete this project?c. Can activity D be delayed without
Embassy Club Condominium, located on the west coast of Florida, is undertaking a summer renovation of its main building. The project is scheduled to begin May 1, and a September 1 (17-week)
Colonial State College is considering building a new multipurpose athletic complex on campus. The complex would provide a new gymnasium for intercollegiate basketball games, expanded office space,
Hamilton County Parks is planning to develop a new park and recreational area on a recently purchased 100-acre tract. Project development activities include clearing playground and picnic areas,
The following estimates of activity times (in days) are available for a small project:a. Compute the expected activity completion times and the variance for each activity.b. An analyst determined
Building a backyard swimming pool consists of nine major activities. The activities and their immediate predecessors are shown. Develop the projectnetwork.
Assume that the activity time estimates (in days) for the swimming pool construction project in Problem 11 are as follows:a. What are the critical activities?b. What is the expected time to complete
Suppose that the following estimates of activity times (in weeks) were provided for the network shown in Problem 6:What is the probability that the project will be completed?a. Within 21 weeks?b.
Davison Construction Company is building a luxury lakefront home in the Finger Lakes region of New York. Coordination of the architect and subcontractors will require a major effort to meet the
Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company. Doug listed the following activity information for this project:a. Draw a
The Daugherty Porta-Vac project discussed in Section 13.2 has an expected project completion time of 17 weeks. The probability that the project could be completed in 20 weeks or less is 0.9656. The
The Porsche Shop, founded in 1985 by Dale Jensen, specializes in the restoration of vintage Porsche automobiles. One of Jensen’s regular customers asked him to prepare an estimate for the
The manager of the Oak Hills Swimming Club is planning the club’s swimming team program. The first team practice is scheduled for May 1. The activities, their immediate predecessors, and the
The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources,
Norton Industries is installing a new computer system. The activities, the activity times, and the project network are as follows:The critical path calculation shows B-D-E-F-H is the critical path,
Consider the following project network and activity times (in days):The crashing data for this project are as follows:a. Find the critical path and the expected project completion time.b. What is the
Refer to Problem 21. Assume that management desires a 12-day project completion time.a. Formulate a linear programming model that can be used to assist with the crashing decisions.b. What activities
Consider the following project network. Note that the normal or expected activity times are denoted Ïi, I = A, B, . . . , I. Let xi = the earliest finish time for activity i. Formulate a
Office Automation, Inc., developed a proposal for introducing a new computerized office system that will improve word processing and interoffice communications for a particular company. Contained in
Because Landon Corporation is being pressured to complete the product development project at the earliest possible date, the project leader requested that the possibility of crashing the project be
R. C. Coleman distributes a variety of food products that are sold through grocery store and supermarket outlets. The company receives orders directly from the individual outlets, with a typical
Suppose that the R&B Beverage Company has a soft drink product that shows a constant annual demand rate of 3600 cases. A case of the soft drink costs R&B $3. Ordering costs are $20 per order and
A general property of the EOQ inventory model is that total inventory holding and total ordering costs are equal at the optimal solution. Use the data in Problem 1 to show that this result is true.
The reorder point is defined as the lead-time demand for an item. In cases of long lead times, the lead-time demand and thus the reorder point may exceed the economic order quantity Q*. In such
Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside’s generator production operation, which is operated at a constant rate,
The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $250 per order to cover the expenses of
Tele-Reco is a new specialty store that sells television sets, videotape recorders, video games, and other television-related products. A new Japanese-manufactured videotape recorder costs Tele-Reco
A large distributor of oil-well drilling equipment operated over the past two years with EOQ policies based on an annual holding cost rate of 22%. Under the EOQ policy, a particular product has been
Nation-Wide Bus Lines is proud of its six-week bus driver–training program that it conducts for all new Nation-Wide drivers. As long as the class size remains less than or equal to 35, a six-week
Cress Electronic Products manufactures components used in the automotive industry. Cress purchases parts for use in its manufacturing operation from a variety of different suppliers. One particular
All-Star Bat Manufacturing, Inc., supplies baseball bats to major and minor league baseball teams. After an initial order in January, demand over the six-month baseball season is approximately
Assume that a production line operates such that the production lot size model of Section 14.2 is applicable. Given D = 6400 units per year, Co = $100 and Ch = $2 per unit per year, compute the
EL Computer produces its multimedia notebook computer on a production line that has an annual capacity of 16,000 units. EL Computer estimates the annual demand for this model at 6000 units. The cost
Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7200 copies. The cost of one copy of the book is $14.50.
A well-known manufacturer of several brands of toothpaste uses the production lot size model to determine production quantities for its various products. The product known as Extra White is currently
Suppose that Westside Auto of Problem 4, with D = 12,000 units per year, Ch = (2.50)(0.20) = $0.50, and Co = $25, decided to operate with a backorder inventory policy. Backorder costs are estimated
Assuming 250 days of operation per year and a lead time of five days, what is the reorder point for Westside Auto in Problem 15? Show the general formula for the reorder point for the EOQ model with
A manager of an inventory system believes that inventory models are important decision-making aids. Even though often using an EOQ policy, the manager never considered a backorder model because of
If the lead time for new orders is 20 days for the inventory system discussed in Problem 17, find the reorder point for both the EOQ and the backorder models.
The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 40 cars per month. The cars cost $60 each, and ordering costs are
Assume that the following quantity discount schedule is appropriate. If annual demand is 120 units, ordering costs are $20 per order, and the annual holding cost rate is 25%, what order quantity
Apply the EOQ model to the following quantity discount situation in which D = 500 units per year, Co = $40, and the annual holding cost rate is 20%. What order quantity do yourecommend?
Keith Shoe Stores carries a basic black dress shoe for men that sells at an approximate constant rate of 500 pairs of shoes every three months. Keith’s current buying policy is to order 500 pairs
In the EOQ model with quantity discounts, we stated that if the Q* for a price category is larger than necessary to qualify for the category price, the category cannot be optimal. Use the two
The J&B Card Shop sells calendars depicting a different Colonial scene each month. The once-a-year order for each year’s calendar arrives in September. From past experience, the September-to-July
The Gilbert Air-Conditioning Company is considering the purchase of a special shipment of portable air conditioners manufactured in Japan. Each unit will cost Gilbert $80, and it will be sold for
The Bridgeport city manager and the chief of police agreed on the size of the police force necessary for normal daily operations. However, they need assistance in determining the number of additional
A perishable dairy product is ordered daily at a particular supermarket. The product, which costs $1.19 per unit, sells for $1.65 per unit. If units are unsold at the end of the day, the supplier
A retail outlet sells a seasonal product for $10 per unit. The cost of the product is $8 per unit. All units not sold during the regular season are sold for half the retail price in an end-of-season
Floyd Distributors, Inc., provides a variety of auto parts to small local garages. Floyd purchases parts from manufacturers according to the EOQ model and then ships the parts from a regional
For Floyd Distributors in Problem 29, we were given Q*= 25, D = 200, Ch = $5, and a normal lead-time demand distribution with µ = 12 and σ = 2.5.a. What is Floyd’s reorder point if the firm is
A product with an annual demand of 1000 units has Co = $25.50 and Ch = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 25
The B&S Novelty and Craft Shop in Bennington, Vermont, sells a variety of quality handmade items to tourists. B&S will sell 300 hand-carved miniature replicas of a Colonial soldier each year,
A firm uses a one-week periodic review inventory system. A two-day lead time is needed for any order, and the firm is willing to tolerate an average of one stock-out per year.a. Using the firm’s
Foster Drugs, Inc., handles a variety of health and beauty aid products. A particular hair conditioner product costs Foster Drugs $2.95 per unit. The annual holding cost rate is 20%. An
Statewide Auto Parts uses a four-week periodic review system to reorder parts for its inventory stock. A one-week lead time is required to fill the order. Demand for one particular part during the
Rose Office Supplies, Inc., which is open six days a week, uses a two-week periodic review for its store inventory. On alternating Monday mornings, the store manager fills out an order sheet
Managers at Wagner Fabricating Company are reviewing the economic feasibility of manufacturing a part that it currently purchases from a supplier. Forecasted annual demand for the part is 3200 units.
The River City Fire Department (RCFD) fights fires and provides a variety of rescue operations in the River City metropolitan area. The RCFD staffs 13 ladder companies, 26 pumper companies, and
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up
In the Willow Brook National Bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per
Use the single-channel drive-up bank teller operation referred to in Problems 1 and 2 to determine the following operating characteristics for the system:a. The probability that no customers are in
Use the single-channel drive-up bank teller operation referred to in Problems 1–3 to determine the probabilities of 0, 1, 2, and 3 customers in the system. What is the probability that more than
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the
Movies Tonight is a typical video and DVD movie rental outlet for home-viewing customers. During the weeknight evenings, customers arrive at Movies Tonight with an arrival rate of 1.25 customers per
Speedy Oil provides a single-channel automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals
For the Burger Dome single-channel waiting line in Section 15.2, assume that the arrival rate is increased to 1 customer per minute and that the service rate is increased to 1.25 customers per
Marty’s Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 5 per hour. Use the Poisson arrivals and exponential
Trosper Tire Company decided to hire a new mechanic to handle all tire changes for customers ordering a new set of tires. Two mechanics applied for the job. One mechanic has limited experience, can
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer
Pete’s Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate
After reviewing the waiting line analysis of Problem 12, the manager of Pete’s Market wants to consider one of the following alternatives for improving service. What alternative would you
Ocala Software Systems operates a technical support center for its software customers. If customers have installation or use problems with Ocala software products, they may telephone the technical
To improve customer service, Ocala Software Systems wants to investigate the effect of using a second consultant at its technical support center. What effect would the additional consultant have on
The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and
The manager of the Fore and Aft Marina in Problem 16 wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Assume
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