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practical management science

Practical Management Science 5th Edition Wayne L. Winston, Christian Albright - Solutions

The Gilette Company buys a product using the price schedule given in the file P12_32.xlsx. The company estimates the unit holding cost at 10% of the purchase price and the ordering cost at $100 per order. Gilette’s annual demand is 1500 units.a. Determine how often the company should order.b.
Each year, Shopalot Stores sells 10,000 cases of soda. The company is trying to determine how many cases to order each time it orders. It costs $150 to process each order, and the cost of carrying a case of soda in inventory for one year is 20% of the purchase price. The soda supplier offers
The manager of a hardware store decides to use the EOQ with shortages model to determine the ordering policy for tape measures. Using economic considerations, the manager determines that she should use an order quantity of Q = 30 and have a maximum shortage of b = 3. The lead time for her supplier
A car 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 is willing to backlog some demand but estimates that if he is short one car for one year, he will lose $20,000
Chicago Mercy Hospital needs to order drugs that are used to treat heart attack victims. Annually, 500 units of drug 1 and 800 units of drug 2 are used. The unit purchasing cost for drug 1 is $150 per unit, and the unit cost of purchasing drug 2 is $300. It costs $20 to store a unit of each drug
Software EG, a retail company, orders two kinds of software from Tele-Hard Software. Annually, Software EG sells 800 units of product 1 and 400 units of product 2. The unit purchasing cost is $30 per unit of product 1 and $25 per unit of product 2. It costs $5 to store a unit of either product for
Customers at Joe’s Office Supply Store demand an average of 6000 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 25% of the $200 cost of a desk. One week elapses between the placement of an order and the arrival of
In the previous problem, assume that it costs $300 to place an order. The holding cost per DVD player held in inventory per year is $15. The cost each time a customer orders a DVD player that is not in stock is estimated at $40. (All demand is backlogged.)a. Find the optimal ordering policy for
Suppose the annual demand for Soni DVD players at an appliance store is normally distributed with mean 150 and standard deviation 45. When the store orders these DVD players from its supplier, it takes an amount of time L for the order to arrive, where L is measured as a fraction of a year. In each
A hospital must order the drug Porapill from the manufacturer of the drug. It costs $500 to place an order. Annual demand for the drug is normally distributed with mean 10,000 and standard deviation 3000, and it costs $5 to hold one unit in inventory for one year. (A unit is a standard
How do your answers to part a of the previous problem change if, instead of incurring a $40 penalty cost for each shortage, the store has a service level requirement of meeting 95% of all customer demands on time? In each case (L known with certainty and L random) what penalty cost p is this
Chicago’s Treadway Tires Dealer must order tires from its national warehouse. It costs $10,000 to place an order. Annual tire sales are normally distributed with mean 20,000 and standard deviation 5000. It costs $10 per year to hold a tire in inventory, and the lead time for delivery of an order
A hospital orders its blood from a regional blood bank. Each year, the hospital uses an average of 1040 pints of type O blood. Each order placed with the regional blood bank incurs a cost of $250. The lead time for each order is five days. It costs the hospital $20 to hold one pint of blood in
A firm experiences demand with a mean of 100 units per day. Lead time demand is normally distributed with mean 1000 units and standard deviation 200 units. It costs $6 to hold one unit for one year. If the firm wants to meet 90% of all demand on time, what is the expected annual cost of holding
A department store is trying to decide how many JP Desksquirt II printers to order. Because JP is about to come out with a new model in a few months, the store will order only a limited number of model IIs. The cost per printer is $200, and each printer is sold for $230. If any model IIs are still
Work the previous problem when the demands are positively correlated, as they might be with products such as peanut butter and jelly. Now use r = 0.3, r = 0.5, and r = 0.7 in your simulations.
Based on Ignall and Kolesar (1972). Dominic’s Pizza Parlor receives 30 calls per hour for delivery of pizza. It costs Dominic’s $10 to send out a truck to deliver pizzas. Each minute a customer spends waiting for a pizza costs the pizza parlor an estimated $0.20 in lost future business.a. How
Suppose that instead of ordering the amount Q specified by the EOQ formula, the order quantity 0.8Q is used. Show that the sum of the annual ordering cost and the annual holding cost increases by 2.5%.
A drugstore 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 per bottle. Assume that the store’s cost of capital is 10%, there is no storage cost, and antibiotics spoil and cannot be sold if they spend more than
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-moving or slow-moving item.
A hospital orders its thermometers from a hospital supply firm. The cost per thermometer depends on the order quantity Q, as shown in the file P12_58.xlsx. The annual holding cost is 25% of the purchasing cost. Let Q80 be the optimal EOQ order quantity if the cost per thermometer is $0.80, and let
In the previous problem, suppose that the cost per order is $1, and the monthly demand is 50 thermometers. What is the optimal order quantity? What is the smallest discount the supplier could offer that would still be accepted by the hospital?Data from Previous Problem:A hospital orders its
Based on Kolesar et al. (1974). Metropolis PD Precinct 88 must determine the minimum number of police cars required to meet its needs for the next 24 hours. An average call for service requires 30 minutes. The number of calls the police department expects to receive during each hour is shown
A computer manufacturer produces computers for 40 different stores. To monitor its inventory policies, the manufacturer needs to estimate the mean and standard deviation of its weekly demand. How might it do this?
Based on Brout (1981). Planner’s Peanuts sells 100 products. The company has been disappointed with the high level of inventory it keeps of each product and its low service level (percentage of demand met on time). Describe how you would help Planner’s improve its performance on both these
Austin (1977) conducted an extensive inventory analysis for the United States Air Force. He found that for over 250,000 items the annual holding cost was assumed to equal 32% of the item’s purchase price. He also found that when an order was placed for most items, a fixed cost of over $200 was
An extremely important concept in queueing models is the difference between rates and times. If λ represents a rate (customers per hour, say), then argue why 1/λ is a time and vice versa.
Use the complete information in the file c13_01.xlsx to answer the following questions:1. Approximately what fraction of the time is Betty idle? Is Ben’s estimate correct?2. Approximately how many calls are lost in an average hour due to a busy signal?3. Use the data to estimate the average
Explain the basic relationship between the exponential distribution and a Poisson process. Also, explain how the exponential distribution and the Poisson distribution are fundamentally different.
Assume that parts arrive at a machining center at a rate of 60 parts per hour. The machining center is capable of processing 75 parts per hour—that is, the mean time to machine a part is 0.8 minute. If you are watching these parts exiting the machine center, what exit rate do you observe, 60 or
Little’s formula applies to an entire queueing system or to a subsystem of a larger system. For example, consider a single-server system composed of two sub-systems. The first subsystem is the waiting line, and the second is the service area, where service actually takes place. Let λ be the rate
Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves immediately (without entering the bank). Suppose that the average number of customers waiting in line in the
Consider a fast-food restaurant where customers enter at a rate of 75 per hour, and three servers are working. Customers wait in a single line and go, in FCFS fashion, to the first of the three servers who is available. Each server can serve one customer every two minutes on average. If you are
The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier
The MM1 Template.xlsx file is now set up so that when you enter any time value in cell H11, the formula in cell I11 gives the probability that the wait in queue will be greater than this amount of time. Suppose that you would like the information to go the other direction. That is, you would like
Expand the MM1 Template.xlsx file so that the steady-state probability distribution of the number in the system is shown in tabular form and graphically. That is, enter values 0, 1, and so on (up to some upper limit you can choose) in the range from cell E11 down and copy the formula in cell F11
Suppose that you observe a sequence of inter-arrival times, such as 1.2, 3.7, 4.2, 0.5, 8.2, 3.1, 1.7, 4.2, 0.7, 0.3, and 2.0. For example, 4.2 is the time between the arrivals of customers 2 and 3. If you average these, what parameter of the M/M/s model are you estimating? Use these numbers to
In the M/M/s model, where µ is the service rate per server, explain why λ < µ is not the appropriate condition for steady state, but λ < sµ is.
Expand the MMs Template.xlsm file so that the steady-state probability distribution of the number in the system is shown in tabular form and graphically. That is, enter values 0, 1, and so on (up to some upper limit you can choose) in the range from cell E12 down and copy the formula in cell F12
A supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18 customers arrive each hour, and the average checkout time for a customer is four minutes. Inter-arrival times and service times are exponentially distributed, and the system can be modeled as an M/M/s
A small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 60 customers per day. On average, 50 customers arrive per day at the bank, and both service times and inter-arrival times are exponentially
In this problem, assume that all inter-arrival and service times are exponentially distributed.a. At present, the finance department and the marketing department each has its own typists. Each typist can type 25 letters per day. Finance requires that an average of 20 letters per day be typed, and
MacBurger’s is attempting to determine how many servers to have available during the breakfast shift. On average, 100 customers arrive per hour at the restaurant. Each server can handle an average of 50 customers per hour. A server costs $8 per hour, and the cost of a customer waiting in line for
On average, 100 customers arrive per hour at the Gotham City Bank. The average service time for each customer is one minute. Service times and inter-arrival times are exponentially distributed. The manager wants to ensure that no more than 1% of all customers will have to wait in line for more than
The limited source model can often be used to approximate the behavior of a computer’s CPU (central processing unit). Suppose that 20 terminals (assumed to always be busy) feed the CPU. After the CPU responds to a user, the user takes an average of 80 seconds before sending another request to the
Consider an airport where taxis and customers arrive (exponential inter-arrival times) with respective rates of one and two per minute. No matter how many other taxis are present, a taxi will wait. If an arriving customer does not find a taxi, the customer immediately leaves.a. Model this
A bank is trying to determine which of two machines to rent for check processing. Machine 1 rents for $10,000 per year and processes 1000 checks per hour. Machine 2 rents for $15,000 per year and processes 1600 checks per hour. Assume that machines work eight hours a day, five days a week, 50 weeks
A worker at the State Unemployment Office is responsible for processing a company’s forms when it opens for business. The worker can process an average of four forms per week. Last year, an average of 1.8 companies per week submitted forms for processing, and the worker had a backlog of 0.45
For the M/M/1 queueing model, why do the following results hold? (Remember that 1/µ is the mean service time. Then think how long a typical arrival must wait in the system or in the queue.)a. W = (L +1)/µb. WQ = L/µ
The manager of a bank wants to use an M/M/s queueing model to weigh the costs of extra tellers against the cost of having customers wait in line. The arrival rate is 60 customers per hour, and the average service time is four minutes. The cost of each teller is easy to gauge at the $11.50 per hour
On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of two minutes to serve a customer. Inter-arrival and service times are exponentially distributed. The bank currently has four tellers working. The bank manager wants to compare the following two systems
Two one-barber shops sit side by side in Dunkirk Square. Each shop can hold a maximum of four people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges $15 per haircut and takes an average of 15 minutes to complete a haircut. Barber 2 charges $11 per
The small mail-order firm Sea’s Beginning has one phone line. An average of 60 people per hour call in orders, and it takes an average of one minute to handle a call. Time between calls and time to handle calls are exponentially distributed. If the phone line is busy, Sea’s Beginning can put up
How long does it take to reach steady state? Use simulation, with the Multi-server Simulation.xlsm file, to experiment with the effect of warm-up time and run time on the key outputs. For each of the following, assume a five-server system with a Poisson arrival rate of one per minute and
Simulate the system in Problem 10. Make any assumptions about the warm-up time and run time you believe are appropriate. Try solving the problem with exponentially distributed copying times. Then try it with gamma-distributed copying times, where the standard deviation is 3.2 minutes. Do you get
In Example 13.4 of section 13.5, we examined whether an M/M/1 system with a single fast server is better or worse than an M/M/s system with several slow servers. Keeping the same inputs as in the example, use simulation to see whether you obtain the same type of results as with the analytical
US Airlines receives an average of 500 calls per hour from customers who want to make reservations, where the times between calls follow an exponential distribution. It takes an average of three minutes to handle each call. Each customer who buys a ticket contributes $100 to US Airlines profit. It
On average, 50 customers arrive per hour at a small post office. Inter-arrival times are exponentially distributed. Each window can serve an average of 25 customers per hour. Service times are exponentially distributed. It costs $25 per hour to open a window, and the post office values the time a
On average, 300 customers arrive per hour at a huge branch of Bank 2. It takes an average of two minutes to serve each customer. It costs $10 per hour to keep a teller window open, and the bank estimates that it will lose $50 in future profits for each hour that a customer waits in line. How many
Ships arrive at a port facility at an average rate of two ships every three days. On average, it takes a single crew one day to unload a ship. Assume that inter-arrival and service times are exponential. The shipping company owns the port facility as well as the ships using that facility. The
On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distributed. The factory can process an average of 42 jobs per day, and the time to process a job is exponentially distributed.a. On average, how long does it take before a job is completed (measured
On average, 90 patrons arrive per hour at a hotel lobby (inter-arrival times are exponential) waiting to check in. At present there are five clerks, and patrons wait in a single line for the first available clerk. The average time for a clerk to service a patron is three minutes (exponentially
The mail order firm of L. L. Pea receives an average of 200 calls per hour, where times between calls are exponentially distributed. It takes an L. L. Pea operator an average of three minutes to handle a call. If a caller gets a busy signal, L. L. Pea assumes that he or she will call a competing
Bloomington Hospital knows that insurance companies are going to reduce the average length of stay of many types of patients. How can queueing models be used to determine how changes in insurance policies will influence the hospital?
Zerox has 16 service centers throughout the United States. Zerox is trying to determine how many technicians it should assign to each service center. How would you approach this problem?
Based on Quinn et al. (1991). Winter Riggers handles approximately $400 million in telephone orders per year. Winter Riggers’ system works as follows. Callers are connected to an agent if one is avail-able. Otherwise, they are put on hold (if a trunk line is available). A customer can hang up at
Suppose that annually an average of λ library patrons want to borrow a book. A patron borrows the book for an average of 1/µ years. Suppose we observe that the book is actually borrowed an average of R times per year. Explain how we can estimate λ, which is an un-observable quantity. (Let U be
Excessive delays have recently been noted on New York City’s 911 system. Discuss how you would use queueing models to improve the performance of the 911 system.
The Newcoat Painting Company has for some time been experiencing high demand for its automobile repainting service. Because it has had to turn away business, management is concerned that the limited space available to store cars awaiting painting has cost them in lost revenue. A small vacant lot
The manager of a large group of employees must decide whether she needs another photocopying machine. The cost of a machine is $40 per eight-hour day regardless of whether the machine is in use. On average, four people need to use the copying machine per hour. Each person uses the copier for an
At the Franklin Post Office, patrons wait in a single line for the first open window. On average, 100 patrons enter the post office per hour, and each window can serve an average of 45 patrons per hour. The post office estimates a cost of $0.10 for each minute a patron waits in line and believes
A bank is attempting to determine where its assets should be invested during the current year. At present,$500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rates of return on each type of investment are known to be the following: bonds, 10%; home
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 70% chemical 1, and drug 2 must be at least 60% chemical 2. Up to 50,000 ounces of drug 1 can be sold at $30 per ounce; up to 60,000 ounces of drug 2 can be sold at $25 per ounce. Up to 45,000 ounces of
A coal company produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in the file P04_57.xlsx. The number of tons of coal demanded by each
A chemical company produces three products, A, B, and C, and can sell these products in unlimited quantities at the following unit prices: A, $10; B, $55; and C, $100. Producing a unit of A requires one hour of labor; a unit of B, two hours of labor plus two units of A; and a unit of C, three hours
Abotte Products produces three products, A, B, and C. The company can sell up to 300 pounds of each product at the following prices (per pound): product A, $10; product B, $12; and product C, $20. Abotte purchases raw material at $5 per pound. Each pound of raw material can be used to produce
An investor has $100,000 to invest right now (the beginning of year 1). The cash flows associated with five available investments are listed in the file P04_61.xlsx. For example, every dollar invested in A in year 1 yields $1.40 in year 4. In addition to these investments, the investor can invest
An oil company processes oil into aviation fuel and heating oil. It costs $65,000 to purchase each 1000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels of heating oil. Output from the distillation can be sold directly or processed in the catalytic
All steel manufactured by Allied Steel must meet the following requirements: between 3.2% and 3.5% carbon; between 1.8% and 2.5% silicon; between 0.9% and 1.2% nickel; tensile strength of at least 45,000 pounds per square inch (psi). The company manufactures steel by combining two alloys. The cost
United Steel manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differ for each mill, as listed in the
United Steel manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differ for each mill, as listed in the
Federated Oil has refineries in Los Angeles and Chicago. The Los Angeles refinery can refine up to two million barrels of oil per year, and the Chicago refinery up to three million. After the oil is refined, it is shipped to two distribution points, Houston and New York City. Federated Oil
A feed company produces two types of cattle feed, both consisting totally of wheat and alfalfa. Feed 1 must contain at least 80% wheat, and feed 2 must contain at least 60% alfalfa. Feed 1 sells for $1.50 per pound, and feed 2 sells for $1.30 per pound. The company can purchase up to 1000 pounds of
Based on Thomas (1971). A toy company produces toys at two plants and sells them in three regions. The current demands at these regions are given in the file P04_72.xlsx. Each plant can produce up to 2500 units. Each toy sells for $10, and the cost of producing and shipping a toy from a
A bank needs exactly two employees working each hour from 9 a.m. to 5 p.m. Workers can work the shifts and are paid the wages listed in the file P04_74.xlsx. For example, a worker working 9 a.m. to 2 p.m. is paid $42.00. Find an assignment of workers that provides enough workers at minimum cost.
A rock company uses five types of rocks to fill four orders. The phosphate content, availability of each type of rock, and the production cost per pound for each rock are listed in the file P04_76.xlsx, as well as the size of each order and the minimum and maxi-mum phosphate percentage in each
An automobile manufacturer needs to plan its production for the next year. Demands for the next 12 months are forecasted to be 940, 790, 360, 720, 270, 130, 160, 300, 990, 290, 280, and 790. Other relevant information is as follows:■ Workers are paid $5000 per month.■ It costs $500 to hold a
You want to take out a $300,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 6%. Twenty years from now, you will need to make a $40,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the
Suppose you are planning for retirement. At the beginning of this year and each of the next 39 years, you plan to contribute some money to your retirement fund. Each year, you plan to increase your retirement contribution by $500. When you retire in 40 years, you plan to withdraw $100,000 at the
Based on Brams and Taylor (2000). Suppose that Eli Lilly and Pfizer are going to merge. Merger negotiations must settle the following issues:■ What will the name of the merged corporation be?■ Will corporate headquarters be in Indianapolis (Lilly wants this) or New York (Pfizer wants this)?■
AdminaStar processes Medicare claims. At the beginning of month 1 they have a backlog of 40,000 difficult claims and 60,000 easy claims. The predicted claim volume for months 1 through 8 is listed in the file P04_85.xlsx. At the beginning of month 1, AdminaStar has 70 experienced claim processors.
Based on Charnes and Cooper (1955). A small company is trying to determine employee salary based on the following attributes: effectiveness, responsibility, initiative, experience, education, self-expression, planning ability, intelligence, and the ability to get things done. Each of the
You can calculate the risk index of an investment by taking the absolute values of percentage changes in the value of the investment for each year and averaging them. Suppose you are trying to determine the percentages of your money to invest in several potential investments. The file
Based on Magoulas and Marinos-Kouris (1988). An oil company produces two products: regular and premium gasoline. Each product contains 0.15 gram of lead per liter. The two products are produced from these six in-puts: reformate, fluid catalytic cracker gasoline (FCG), isomerate (ISO),
Capsule Drugs manufactures two drugs. The drugs are produced by blending two chemicals. By weight, drug 1 must contain at least 65% chemical 1, and drug 2 must contain at least 55% chemical 1. Drug 1 sells for $6 per ounce, and drug 2 sells for $4 per ounce. Chemicals 1 and 2 can be produced by one
Molecular Products produces three chemicals: B, C, and D. The company begins by purchasing chemical A for a cost of $650 per 100 liters. For an additional cost of $320 and the use of three hours of skilled labor, 100 liters of A can be transformed into 40 liters of C and 60 liters of B. Chemical C
Bexter Labs produces three products: A, B, and C. Bexter can sell up to 3000 units of product A, up to 2000 units of product B, and up to 2000 units of product C. Each unit of product C uses two units of A and three units of B and incurs $5 in processing costs. Products A and B are produced from
An automobile manufacturing company has a $1,500,000 advertising budget. To increase its auto-mobile sales, the company is considering advertising in newspapers and on television. The more the company uses a particular medium, the less effective each additional ad is. The file P04_96.xlsxlists the
Broker Sonya Wong is currently trying to maximize her profit in the bond market. Four bonds are available for purchase and sale at the bid and ask prices shown in the file P04_97.xlsx. Sonya can buy up to 1000 units of each bond at the ask price or sell up to 1000 units of each bond at the bid
Budget Auto produces inexpensive cars. Each car is sold for $7900. The raw material in a car costs $5000. Labor time and robot time are needed to produce cars. A worker can do the needed labor on, at most, 100 cars per month; a robot can complete the needed work on, at most, 200 cars per month. The

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