Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Question
error_outline
This textbook solution is under construction.
Students have asked these similar questions
A large paper manufacturing company, the Quality Paper Corporation, has 10 paper mills from which it needs to supply 1,000 customers. It uses three alternative types of machines and four types of raw materials to make five different types of paper. Therefore, the company needs to develop a detailed production distribution plan on a monthly basis, with an objective of minimizing the total cost of producing and distributing the paper during the month. Specifically, it is necessary to determine jointly the amount of each type of paper to be made at each paper mill on each type of machine and the amount of each type of paper to be shipped from each paper millto each customer.
The relevant data can be expressed symbolically as follows:Djk = number of units of paper type k demanded by customer j,rklm = number of units of raw material m needed to produce 1 unit of paper type k on machine type l,Rim = number of units of raw material m available at paper mill i,ckl = number of capacity units of…
A contractor owns three excavators of different capacity. He/she wants to dispatch these excavatorsinto three different jobs. The performance of the excavators is measured as the time consumed toperform each job. The data of the time tests are shown as given in the table below.
(a) Draw a network flow diagram.(b) Formulate a mathematical model to obtain the minimum time.(c) Solve this model using the Vogel’s approximation model.
Given the set of machines M = {m₁, m₂,... m₁}, each associated with a
maintenance cost c; and throughput t, where 1 ≤ i ≤n. The objective is
to determine which machines to execute in the production line so that the
total throughput is greater than or equal to a given minimum throughput
and total maintenance cost is minimized. Consider the following problems:
(a) Given the minimum total throughput T. Write an O(nT) algorithm
to determine the minimum maintenance cost such that
minimize Scri
subject to Star; ΣΤ
i=1
where x, {0, 1} for 1 ≤ i ≤n.
Knowledge Booster
Similar questions
- In this problem we have n jobs j1, j2, ..., jn, each has an associated deadline d1, d2, ..., dn and profit p1, p2, ..., pn. Profit will only be awarded or earned if the job is completed before the deadline. We assume that each job takes 1 unit of time to complete. The objective is to earn maximum profit when only one job can be scheduled or processed at any given time.Provide the pseudocode of an algorithm to find the sequence of jobs to do with the maximum total profit. Also describe the main idea of your algorithm using plain language.[Hint: You can select the jobs in a greedy way. You can use the following example to help your analysis.] Job J1 J2 J3 J4 J5 Deadline 2 1 3 2 1 Profit 60 100 20 40 20 The best job sequence would be J2 →J1 →J3.arrow_forwardA company wants to plan production for the ensuing year to minimize the combined cost of production and inventory costs. In each quarter of the year, demand is anticipated to be 130, 160, 250, and 150 units, respectively. The plant can produce a maximum of 200 units each quarter. The product can be manufactured at a cost of $15 per unit during the first quarter, however the manufacturing cost is expected to rise by $1 per quarter. Excess production can be stored from one quarter to the next at a cost of $1.50 per unit, but the storage facility can hold a maximum of 60 units. How should the production be scheduled so as to minimize the total costs? Please answer using python Formulate an LP model to minimize costs. Solve the LP (provide exact values for all variables and the optimal objective function).arrow_forward2. Consider the following problem: You have three jugs with capacities 4, 5 and 6 litters respectively. Initially all of the jugs contain 2 litters of water. At any time-step, you can either remove 1 litter of water from any 2 jugs or add 1 litter to any 1 jug. You have to continue the process until the jugs contain 8 or more litters of water in total. The target is to reach the goal within minimum number of steps. Answer the following: a. How many variables are required to mathematically represent the states of the problem? b. What is the size of the state-space? Explain your calculation. c. List any 30 goal states. d. Will a DFS find optimal solution for this problem? What about a BFS? Which one would you go for, and why?arrow_forward
- Problem 3 A truck must travel from New York to Los Angeles. As shown in the diagram, several routes are available. The number associated with each arc is the number of gallons of fuel required by the truck to traverse the arc. Use Excel model to determine the route from New York to Los Angeles that uses the minimum amount of gas. (Hint: Similar to the short-route problem). In the excel model, use a single letter or number index to denote the cities instead of typing the full city names. 1800 Cleveland Phoenix 400 400 900 1100 900 950 600 1300 New York St. Louis Dallas Los Angeles 800 600 1000 600 1200 Nashville Salt Lake City 3arrow_forward3. National Disc Corp. produces the discs used in producing Xbox and PlayStation discs. Their local plant runs 24 hours a day, 7 days a week. In a given day, there are requirements for the total number of employees that must be at the plant. These are given below. Employees Needed Hours 12am - 4am 4am - 8am 8am-12pm 12pm - 4pm 4pm - 8pm 8pm-12am 8 10 16 21 18 12 Employees can either work 8-hour or 12-hour shifts, starting at the times stated above (12- hour shifts can start only at 12 am/pm or 8 am/pm). Those working 8-hour shifts cost the company $40 per hour in benefits, and those working 12-hour shifts cost the company $60 per hour. Develop a linear program that can be used to determine how National should staff the local plant so as to minimize labor costs (you do not need to solve the model). Be sure to clearly identify your variables.arrow_forwardBig Lots Services (BLS) would like to develop a model that will help allocate their technician’s time between service calls to regular contract customers and new customers. A maximum of eighty hours of technician time is available over the two-week planning period. To satisfy cash flow requirements, at least eight hundred dollars in revenue (per technician) must be generated during the two-week period. Technician time for regular customers generates twenty-five dollars per hour. However, technician time for new customers only generates an average of eight dollars per hour. To ensure that new customer contracts are being maintained, the technician time spent on new customer contracts must be at least sixty percent of the time spent on regular customer contracts. Given these revenue and policy requirements, (BLS) would like to determine how to allocate technician time between regular customers and new customers so that the total number of customers contracted during the two week period…arrow_forward
- (a) Consider 6 jobs having the processing times Pj, the due-dates d; and the weights w; of the jobs j=1, ..., 6, given in the table: Jobs 1 2 3 4 6 3 2 4 1 1 Pi d 7 12 18 6. 7 W; 2 5 3 1 3 Calculate the total weighted completion time, the maximum lateness, and the total weighted tardiness of the following schedule: 4, 2, 6, 3, 1, 5.arrow_forward1. for October 19–20, starting with a reception on the evening of October 18. The conference consists of all-day meetings that the entire sales force, numbering 120 sales representatives and their 16 managers, must attend. Each sales representative requires his or her own room, and the company needs two common meeting rooms, one large enough to hold the entire sales force plus a few visitors (200) and the other able to hold half the force. Management has set a budget of $195,000 for the representatives' room rentals. The company would like to hold the conference in either Miami or Marco Island, Florida, at a Hilton- or Marriott-owned hotel. The Foremost Composite Materials Company is planning a two-day sales conference Use the Hilton and Marriott websites to select a hotel in whichever of these cities would enable the company to hold its sales conference within its budget and meet its sales conference requirements. Then locate flights arriving the afternoon prior to the conference.…arrow_forwardDe anza is looking to hire teachers and TAs to fill its staffing needs for its summer program at minimum cost. The average monthly salary of a teacher is $2400 and the average monthly salary of a TA is $1100. The program can accommodate up to 45 staff members, needs at least 30 to run properly, and must have teachers (they will NOT employee only TAs). They must have at least 10 TAs and may have up to 3 TA’s for every 2 teachers. How many teachers and TAs the should the program hire to minimize costs. What is the minimum cost? use python code & explain each steparrow_forward
- Problem 5. An Electricity board charges the following rates mentioned in the table for the use of electricity. All users are charged Taka 50 as a meter charge for every month. If any user wants to change/replace his meter, he will be charged taka 2000. The monthly bill will be generated based on ● Customer Category ● Consumed Units ● Phase ● For Category 3 and 5 along with other parameters, you need to also consider flat rate, peak time, and off-peak time. Take input from the user, how many units were consumed during flat rate, peak, or off-peak time. ● Meter Charge Write a program to read the name of the user, Customer Category, Phase, number of units consumed and print out the monthly bill. Note that ● Phase, flat rate, peak time and off-peak time will be appeared based on the customer category. ● The monthly bill will be calculated following the number of Days in a montharrow_forwardDe anza is looking to hire teachers and TAs to fill its staffing needs for its summer program at minimum cost. The average monthly salary of a teacher is $2400 and the average monthly salary of a TA is $1100. The program can accommodate up to 45 staff members, needs at least 30 to run properly, and must have teachers (they will NOT employee only TAs). They must have at least 10 TAs and may have up to 3 TA’s for every 2 teachers. How many teachers and TAs the should the program hire to minimize costs. What is the minimum cost? use code & explain each steparrow_forwardVandelay Industries has 275 sales reps in order to sell its latex products, each to be assigned to one of four marketing teams. If the first team is to have four times as many members as the second team and the third team is to have five times as many members as the fourth team, how can the members be distributed among the teams?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole