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operations research an introduction

Questions and Answers of Operations Research An Introduction

5 Let Xt be the location of your token on the Monopoly board after t dice rolls. Can Xt be modeled as a Markov chain? If not, how can we modify the definition of the state at time t so that X0, X1, .
4 Referring to Problem 1, suppose that tomorrow’s Smalltown weather depends on the last two days of Smalltown weather, as follows: (1) If the last two days have been sunny, then 95% of the time,
3 A company has two machines. During any day, each machine that is working at the beginning of the day has a 1 3chance of breaking down. If a machine breaks down during the day, it is sent to a
2 Consider an inventory system in which the sequence of events during each period is as follows. (1) We observe the inventory level (call it i) at the beginning of the period.(2) If i 1, 4 i
1 In Smalltown, 90% of all sunny days are followed by sunny days, and 80% of all cloudy days are followed by cloudy days. Use this information to model Smalltown’s weather as a Markov chain.
In recent years, students of finance have devoted much effort to answering the question of whether the daily price of a stock share can be described by a Markov chain. Suppose the daily price of a
Choosing Balls Find the transition matrix for Example 2.
Find the transition matrix for Example 1.
Let X0 be the price of a share of CSL Computer stock at the beginning of the current trading day. Also, let Xt be the price of a share of CSL stock at the beginning of the tth trading day in the
An urn contains two unpainted balls at present. We choose a ball at random and flip a coin. If the chosen ball is unpainted and the coin comes up heads, we paint the chosen unpainted ball red; if the
At time 0, I have $2. At times 1, 2, . . . , I play a game in which I bet $1. With probability p, I win the game, and with probability 1 p, I lose the game. My goal is to increase my capital to $4,
7 Use LINGO to determine the values of q and r that minimize expected annual cost for Example 5. How close are your answers to those given in the text?
6 A company currently has two warehouses. Each warehouse services half the company’s demand, and the annual demand serviced by each warehouse is N(10,000, 1,000,000). The lead time for meeting
5 A fur dealer buys fur coats for $100 each and sells them for $200 each. He believes that the demand for coats is N(100, 100). Any coat not sold can be sold to a discount house for $100, but the fur
3 We are given the following information about a product:Cost of placing an order $100 Cost per item $5 Sale price per item $8 Annual holding cost 40% of cost of item Annual demand 5,000
2 An optometrist orders eyeglass frames at a cost of $40 per frame and sells each frame for $70. Annual holding cost is 20% of the optometrist’s cost of purchasing a frame. Each time frames are
3 Consider the exchange surface in Figure 11. The current inventory policy has yielded 3,586 orders per year, an AII of $1,367,000, and 0.89% shortages.a Without changing orders per year and AII, by
2 Explain how to draw an exchange curve where the xcoordinate is AII and the y-coordinate is percentage of all requests for stock that result in shortages.
A company stocks two products. Relevant information is given in Table 17.1 Draw an exchange curve.2 Currently, the company is ordering each product ten times per year. Use the exchange curve to
3 Suppose we have found the optimal (R, S) policy for the back-ordered case and that S 50. Is the following true or false?The optimal S for the lost sales case has S > 50.
2 Chicago’s Treadway Tires Dealer must order tires from its national warehouse. It costs $10,000 to place an order and $400 to review the inventory level. Annual tire sales are N(20,000,
1 A hospital must order the drug Porapill from Daisy Drug Company. It costs $500 to place an order and $30 to review the hospital’s inventory of the drug. Annual demand for the drug is N(10,000,
Lowland Appliance replenishes its stock of color TVs three times a year. Each order takes1/9 year to arrive. Annual demand for color TVs is N(990, 1,600). The cost of holding one color TV in
4 A firm experiences demand with a mean of 100 units per day. Lead time demand is normally distributed, with a mean of 1,000 units and a standard deviation of 200 units. It costs$6 to hold one unit
2 For Problem 2 of Section 16.6, determine the reorder point that yields 80%, 90%, 95%, and 99% values of SLM1.What reorder point would yield an average of two stockouts per year?
1 For Problem 1 of Section 16.6, determine the reorder point that yields 80%, 90%, 95%, and 99% values of SLM1.What reorder point would yield an average of 0.5 stockout per year?
Bads, Inc., sells an average of 1,000 food processors each year. Each order for food processors placed by Bads costs $50. The lead time is one month. It costs $10 to hold a food processor in
Suppose that for a given inventory situation, average annual demand is 1,000 and the EOQ is 100. Demand during a lead time is random and is described by the probability distribution in Table 12. For
9 Suppose annual demand for a product is normally distributed, with a mean of 600 and a variance of 300.Suppose that the lead time for an order is always one month.Show (without using Equation (8))
8 Explain the following statement: Faster-moving items require larger safety stocks than slower-moving items. (Hint:Does E(D)/q large imply that an item is fast-moving or slowmoving?)
7 Suppose that a cost of S dollars (independent of the size of the stockout) is incurred whenever a stockout occurs during a cycle. Under the assumption of backlogged demand, use marginal analysis to
5 In Figure 3, assume that demand occurs at a constant rate during each cycle. Approximate the average level of onhand inventory between t 0 and t 7. Also approximate the average number of
3 We are given the following information for a product:Order cost $50 Annual demand N(960, 3,072.49)Annual holding cost $6/item/year Shortage cost $80 per unit Lead time one month Sales
2 Furnco sells secretarial chairs. Annual demand is normally distributed, with mean of 1,040 chairs and standard deviation of 50.99 chairs. Furnco orders its chairs from its flagship store. It costs
1 A hospital orders its blood from a regional blood bank.Each year, the hospital uses an average of 1,040 pints of Type O blood. Each order placed with the regional blood bank incurs a cost of $20.
Each year, a computer store sells an average of 1,000 boxes of disks. Annual demand for boxes of disks is normally distributed with a standard deviation of 40.8 boxes. The store orders disks from a
2 Assume that the Federal Reserve Board can control the growth rate of the U.S. money supply. Also assume that during a year in which the money supply grows by x%, the Gross Domestic Product (GDP)
Condo Construction Company is bidding on an important construction job. The job will cost $2 million to complete. One other company is bidding for the job. Condo believes that the opponent’s bid is
6 I. L. Pea is a well-known mail-order company. During the Christmas rush (from November 1 to December 15), the number of orders that I. L. Pea must fill each day (five days per week) is normally
5 Motorama TV estimates the annual demand for its TVs is (and will be in the future) normally distributed, with a mean of 6,000 and standard deviation of 2,000. Motorama must determine how much
4 A hot dog vendor at Wrigley Field sells hot dogs for$1.50 each. He buys them for $1.20 each. All the hot dogs he fails to sell at Wrigley Field during the afternoon can be sold that evening at
3 Joe is selling Christmas trees to pay his college tuition.He purchases trees for $10 each and sells them for $25 each. The number of trees he can sell is normally distributed with a mean of 100 and
2 Condo Construction Company is going to First National Bank for a loan. At the present time, the bank is willing to lend Condo up to $1 million, with interest costs of 10%. Condo believes that the
1 a In Example 3, why is it unrealistic to assume that the distribution of the number of no-shows is independent of q?b If the number of no-shows were normally distributed with a mean of .05q and a
The ticket price for a New York–Indianapolis flight is $200. Each plane can hold up to 100 passengers. Usually, some of the passengers who have purchased tickets for a flight fail to show up
The American Bar Association (ABA) is holding its annual convention in Las Vegas. Six months before the convention begins, the ABA must decide how many rooms should be reserved in the convention
9 Some universities allow an employee to put an amount q into an account at the beginning of each year, to be used for child-care expenses. The amount q is not subject to federal income tax. Assume
4 If co is fixed, will an increase in cu increase or decrease the optimal order quantity?
3 If cu is fixed, will an increase in co increase or decrease the optimal order quantity?
In August, Walton Bookstore must decide how many of next year’s nature calendars should be ordered. Each calendar costs the bookstore $2 and is sold for $4.50. After January 1, any unsold calendars
1 Pizza King and Noble Greek are two competing restaurants. Each must determine simultaneously whether to undertake small, medium, or large advertising campaigns.Pizza King believes that it is
c Explain why marginal analysis fails to find the value of q that minimizes E(q). 1 Suppose E(q) is E(0) = 8, E(1) = 6, E(2) = 5, E(3) = 7, E(4) =6, E(5) = 5.5, E(6) = 4.5, and E(7) = 5.
b If marginal analysis is used to determine the value of q that minimizes E(q), what is the answer? 1 Suppose E(q) is E(0) = 8, E(1) = 6, E(2) = 5, E(3) = 7, E(4) =6, E(5) = 5.5, E(6) = 4.5,
Patty is trying to determine which of two courses to take. If she takes the operations research course, she believes that she has a 10% chance of receiving an A, a 40% chance for a B, and a 50%
1 Suppose E(q) is E(0) = 8, E(1) = 6, E(2) = 5, E(3) = 7, E(4) =6, E(5) = 5.5, E(6) = 4.5, and E(7) = 5.a What value of q minimizes E(q)?
15 Although the Von Neumann–Morgenstern axioms seem plausible, there are many reasonable situations in which people appear to violate these axioms. For example, supposea recent college graduate
5 A company produces three types of items. A single machine is used to produce the three items on a cyclical basis. The company has the policy that every item is produced once during each cycle, and
2 Suppose Joe’s is considering manufacturing desks. It costs $250 to set up a production run, and Joe’s has the capacity to manufacture up to 10,000 desks per year. What is the optimal production
1 Customers at Joe’s Office Supply Store demand an average of 6,000 desks per year. Each time an order is placed, an ordering cost of $300 is incurred. The annual holding cost for a single desk is
4 The Nitro Fertilizer Company is developing a new fertilizer. If Nitro markets the product and it is successful, the company will earn a $50,000 profit; if it is unsuccessful, the company will lose
2 In Problem 1, suppose that Square City manufactures the washing machines. The company can manufacture washing machines at a rate of 30,000 per year. What manufacturing policy will minimize the
1 Observed demand for air conditioners during the last four quarters was as follows: fall, 100; winter, 50; spring, 150; summer, 300. Is it reasonable to use an EOQ model in this situation?
4 For the model developed in this section, determine a the average length of time it takes to meet demand for a unit.b the fraction of all demanded units that are backordered.
3 Suppose that instead of measuring shortage in terms of cost per shortage year, a cost of S dollars is incurred for each unit the firm is short. This cost does not depend on the length of time
2 A Mercedes dealer must pay $20,000 for each car purchased. The annual holding cost is estimated to be 25%of the dollar value of inventory. The dealer sells an average of 500 cars per year. He
1 Show that the optimal order quantity for the backlogged demand model is always at least as large as the EOQ but that the maximum inventory level for the backlogged demand model cannot exceed the
Each year, the Smalltown Optometry Clinic sells 10,000 frames for eyeglasses. The clinic orders frames from a regional supplier, which charges $15 per frame. Each order incurs an ordering cost of
4 A company has the option of purchasing a good or manufacturing the item. If the item is purchased, the company will be charged $25 per unit plus a cost of $4 per order. If the company manufactures
3 The production process at Father Dominic’s Pizza can produce 400 pizza pies per day; the firm operates 250 days per year. Father Dominic’s has a cost of $180 per production run and a holding
2 A company can produce 100 home computers per day.The setup cost for a production run is $1,000. The cost of holding a computer in inventory for one year is $300.Customers demand 2,000 home
1 Show that the optimal run size always exceeds the EOQ.Give an intuitive explanation for this result.
Macho Auto Company needs to produce 10,000 car chassis per year. Each is valued at$2,000. The plant has the capacity to produce 25,000 chassis per year. It costs $200 to set up a production run, and
5 In Problem 4, suppose the cost per order is $1 and the monthly demand is 50 thermometers. What is the optimal order quantity? How small a discount could the supplier offer and still have the
Each time an order is placed for disks, how many boxes of disks should be ordered? How many orders will be placed annually? What is the total annual cost of meeting the accounting firm’s disk needs?
16 The borough of Staten Island has two “sanitation districts.” In district 1, street litter piles up at an average rate of 2,000 tons per week, and in district 2 at an average rate of 1,000 tons
15 Show that the reorder point in the EOQ model equals the remainder when LD is divided by the EOQ.
14 Consider a firm that knows that the price of the product it is ordering is going to increase permanently by $X. How much of the product should be ordered before the price increase goes into
13 A newspaper has 500,000 subscribers who pay $4 per month for the paper. It costs the company $200,000 to bill all its customers. Assume that the company can earn interest at a rate of 20% per year
12 During each year, CSL Computer Company needs to train 27 service representatives. No matter how many students are trained, it costs $12,000 to run a training program. Since service reps earn a
11 A drug store sells 30 bottles of antibiotics per week.Each time it orders antibiotics, there is a fixed ordering cost of $10 and a cost of $10/bottle. Assume that the annual holding cost is 20% of
10 In terms of K, D, and h, what is the average length of time that an item spends in inventory before being used to meet demand? Explain how this result can be used to characterize a fast- or
9 Suppose that instead of ordering the EOQ q*, we use the order quantity 0.8q*. Use Equation (3) to show that HC(q) OC(q) will have increased by 2.50%.
8 Show that for q q*, an order size of q q* will have a lower cost than an order size of q q*. What is the managerial significance of this result?
7 Suppose we are ordering computer chips. Suppose that in each order, exactly 10% of all chips are defective. As soon as the order arrives, we find out which chips are defective and return them for a
6 Suppose we order three types of clothing for Ceiling Mart. The optimal reorder intervals are 92 days, 21 days, and 60 days. What would be the optimal power-of-two ordering policy?
5 Suppose we order three types of appliances for the appliance store Ohm City. The optimal reorder intervals are 9.2 days, 21.2 days, and 38.1 days. What would be the optimal power-of-two ordering
4 The efficiency of an inventory system is often measured by the turnover ratio. The turnover ratio (TR) is defined by TR a Does a high turnover ratio indicate an efficient inventory system?b If the
3 Father Dominic’s Pizza Parlor receives 30 calls per hour for delivery of pizza. It costs Father Dominic’s $10 to send out a truck to deliver pizzas. It is estimated that each minute a customer
2 Money in my savings account earns interest at 10%annual rate. Each time I go to the bank, I waste 15 minutes in line. My time is worth $10 per hour. During each year, I need to withdraw $10,000 to
1 Each month, a gas station sells 4,000 gallons of gasoline.Each time the parent company refills the station’s tanks, it charges the station $50 plus 70¢, per gallon. The annual cost of holding a
Each hour, D students want to ride a bus from the student union to Fraternity Row. The administration places a value of h dollars on each hour that a student is forced to wait for a bus. It costs the
A department store sells 10,000 cameras per year. The store orders cameras from a regional warehouse. Each time an order is placed, an ordering cost of $5 is incurred. The store pays $100 for each
Braneast Airlines uses 500 taillights per year. Each time an order for taillights is placed, an ordering cost of $5 is incurred. Each light costs 40¢, and the holding cost is 8¢/light/year.Assume
12 Edwina, a commodities broker, has acquired an option to buy 1,000 oz of gold at $50/oz. If she takes the option and if Congress relaxes import quotas, she can sell the gold for$80/oz. If she takes
15 a Suppose you are given a choice between the following options:A1: Win $30 for sure A2: 80% chance of winning $45 and 20% chance of A2: winning nothingB1: 25% chance of winning $30 B2: 20% chance
1 National Express Carriers is interested in two attributes:Attribute 1 The average cost of delivering a letter (known to be between $1 and $5)Attribute 2 Percentage of all letters reaching their
2 Keeney and Raiffa (1976) discuss the assessment of a blood bank’s multiattribute utility function. For simplicity, we assume that the blood bank must determine at the beginning of each week how
4 Gotham City is trying to determine how many ambulances it should have and how to staff them. Each ambulance may be staffed with paramedics or emergency medical technicians. Paramedics are
5 Public service Indiana (PSI) is considering two sites for a nuclear power plant. The following two attributes will influence its determination about where to build the plant:Attribute 1 Cost of the
6 Consider the four points A, B, C, and D in Figure 16.Assume that more of each attribute is desirable and that a decision maker’s utility function exhibits mui. Consider the following two

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