All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
operations research an introduction

Questions and Answers of Operations Research An Introduction

Carry out two iterations of Problem 10-36.
Carry out the next iteration that follows the one given in Table 10.19.
Excel experiment. Use file excels-IP-Heuristic.xls to find a solution for the following ILP:Minimize z = x1 + x2 + x3 + x4 + x5 + x6 + x7 subject to x1 + x4 + x5 + x6 + x7 Ú 20 x1 + x2 + x5 + x6 +
Carry out 5 SA iterations for the following problem:Maximize z = 99x1 + 90x2 + 58x3 + 40x4 + 79x5+ 92x6 + 102x7 + 74x8 + 67x9 + 80x10 subject to 30x1 + 8x2 + 6x3 + 5x4 + 20x5 + 12x6 + 25x7 + 24x8 +
Carry out 5 iterations of Example 10.4-2 assuming cj = 1 for all j.
Excel experiment. Use excelTabu-IP-heuristc.xls to find a solution for the following problems:(a) Project selection problem of Example 9.1-1.(b) Set covering problem of Example 9.1-2.Compare the
Carry out 10 TS iterations for each of the following problems:(a) Maximize z = 4x1 + 6x2 + 2x3 subject to 4x1 - 4x2 … 5-x1 + 6x2 … 5-x1 + x2 + x3 … 5 x1, x2, x3 Ú 0 and integer(b) Maximize z =
Verify the entries in iterations 1, 2, and 3 in Table 10.15.
In the game of chess, queens move horizontally, vertically, or along a (45°) diagonal path. We need to position N queens in the 1N * N2 grid so that no queen can “take”any other queen. Design a
Consider the following problem:Maximize f1x, y2 = xsin14x2 + 1.1sin12y2, x = 0, 1, 2,c, 10, y = 0, 1, 2,c, 10 Carry out five GA iterations to estimate the optimum solution.
Repeat Problem 10-28 assuming that the wire is used to form a box with the maximum volume.
You have a piece of wire whose length is L = 107.1 inches and you would like to shape it into a rectangular frame. Use the genetic algorithm to determine the width and height that will yield the
You have a deck of ten cards numbered 1 to10. You need to divide the ten cards into two piles such that the sum of pile 1 cards is 36 and the product of the pile 2 cards is also 36. Develop a GA for
Carry out an additional iteration of Example 10.3-6.
Carry out two additional iterations of Example 10.3-5.
Suppose that GA is used to find the maximum of F(x), x = 0, 1,c, 275. Let x = 107 and x = 254 represent parents P1 and P2.(a) Represent P1 and P2 as binary codes.(b) Use uniform crossover to create
Consider the well-known six-hump camelback function:f1x, y2 = 4x2 - 2.1x4 + x6/3 + xy - 4y2 + 4y4, -3 … x … 3, -2 … y … 2 The exact global minima are 1 -.08984, .712662 and 1.08984, -.712662
Scheduling conflicting classroom courses. A simplified version of college course scheduling calls for assigning eight courses (1, 2, . . . , 8) in the least possible number of time periods. Table
Map-coloring problem. The coloring problem deals with determining the least number of colors for painting the regions of a map such that no two adjacent regions will have the same color. Figure
Timetable scheduling. Consider a case of developing a timetable of teaching 5 classes(C) by 5 teachers (T). The teachers provide the following preferences for teaching classes (first of the list is
Carry out four additional iterations of the job sequencing problem in Example 10.3-4.
Solve Example 10.3-3 to estimate the maximum solution point. Use x0 = 2 and t = 3.
Carry out five additional iterations in Example 10.3-3.
Cartographic label placement, Yamamoto and Associates (2002). Unambiguous placement of the names of cities, streets, lakes, and rivers on printed maps has long been a time-consuming manual process.
Constrained Minimal Spanning Tree, Glover (1990). Section 6.2 presents an optimum algorithm for finding the minimal spanning tree that links all the nodes of a network(by definition, a tree contains
Warehouse allocation. Consider the case of 4 warehouses and 5 stores. The fixed cost of opening a warehouse is 20 ($ thousand). The transportation cost, cij, of shipments between the warehouses and
Repeat Problem 10-12 for the following Boolean expressions:(B1 and B5) or (B3 and B9) and (B2 or B10)B3 or B6 and (B7 or B9 and B10)B4 and B7 and B8 B2 or B3 and B4 and B5 or B8 and (B1 or B6)(B3 and
Consider 10 Boolean variables, Bi, i = 1, 2,c, 10. Each variable assumes the value T (true) or F (false). Next, consider the following six expressions (the notation Bi defines not Bi):(B1 and B3 and
Apply TS with t = 3 iterations to solve the 5-job sequencing problem using the data in Table 10.20. (Hint: You may find it convenient to use file excelJobSequencing.xls to compute the cost functions.)
Consider the following function:f1x2 = .01172x6 - .3185x5 + 3.2044x4 - 14.6906x3 + 29.75625x2 - 19.10625x The function has multiple maxima and minima in the range x = 1, 2,c, 10. Apply 10 TS
Solve Example 10.2-1 to estimate the maximum solution point. Use x0 = 8 and t = 2.
The height of a cylindrical water tank must be at least twice as much as its base diameter. Neither the diameter nor the height can exceed 10 ft. The volume of the tank must be at least 300 ft3. The
Apply the uniform sampling heuristic to estimate the minimum solution of the following two-variable function: f1x2 = 3x2 + 2y2 - 4xy - 2x - 3y, 0 … x … 5, 0 … y … 5.
Consider the problem of forming a maximum-area rectangle out of a piece of wire of length 100 inches.(a) Excel experiment. Use excelContVarHeuristic.xls with uniform sampling to generate 5 iterations
Excel experiment. Consider the following function:f1x2 = .01172x6 - .3185x5 + 3.2044x4 - 14.6906x3 + 29.75625x2 - 19.10625x The function has multiple maxima and minima in the range 0 … x … 10.
Re-solve the problem of Example 10.2-3 to estimate the maximum value of F(x) using uniform sampling. Next, use the solution from uniform sampling as a starting solution for the application of normal
Re-solve the problem of Example 10.2-2 to estimate the maximum value of F(x).
Re-solve the problem of Example 10.2-1 to estimate the maximum value of F(x).Repeat the calculations using x = 7 as a starting solution.
Solve the following problems by the fractional cut, and compare the true optimum integer solution with the solution obtained by rounding the continuous optimum.*(a) Maximize z = 4x1 + 6x2 + 2x3
Show that, even though the following problem has a feasible integer solution in x1 and x2, the fractional cut would not yield a feasible solution unless all the fractions in the constraint were
In Example 9.2-2, derive cut II from the x3-row. Use the new cut to complete the solution of the example.
Express cuts I and II of Example 9.2-2 in terms of x1 and x2, and show that they are the same ones used graphically in Figure 9.6.
In Example 9.2-2, show graphically how the following two (legitimate) cuts can lead to the optimum integer solution:x1 + 2x2 … 10 1Cut I2 3x1 + x2 … 15 1Cut II2
In Example 9.2-2, show graphically whether or not each of the following constraints can form a legitimate cut:*(a) x1 + 2x2 … 10(b) 2x1 + x2 … 10(c) 3x2 … 10(d) 3x1 + x2 … 15
AMPL Experiment. In the following 0-1 ILP, use interactive AMPL to generate the associated search tree. In each case, show how the z-bound is used to fathom subproblems.Maximize z = 3x1 + 2x2 - 5x3 -
Convert the problem into an equivalent 0-1 ILP, then solve it with TORA’s automated option. Compare the size of the search trees in the two problems.
TORA Experiment. Reconsider Problem
TORA Experiment. Consider the following ILP:Maximize z = 18x1 + 14x2 + 8x3 subject to 15x1 + 12x2 + 7x3 … 43 x1, x2, x3 nonnegative integers Use TORA’s B&B user-guided option to generate the
TORA/Solver/AMPL Experiment. The following problem is designed to demonstrate the bizarre behavior of the B&B algorithm even for small problems. In particular, note how many subproblems are examined
Convert the following problem into a mixed ILP, and find the optimum solution:Maximize z = x1 + 2x2 + 5x3 subject to -x1 + 10x2 - 3x3 Ú 15 2x1 + x2 + x3 … 10 x1, x2, x3 Ú 0
Solve the following problems by B&B:Maximize z = 18x1 + 14x2 + 8x3 + 4x4 subject to 15x1 + 12x2 + 7x3 + 4x4 + x5 … 37 x1, x2, x3, x4, x5 = 10, 12
Show graphically that the following ILP has no feasible solution, and then verify the result using B&B.Maximize z = 2x1 + x2 subject to 10x1 + 9x2 … 8 8x1 + 6x2 Ú 1 x1, x2 Ú 0 and integer
Repeat Problem 9-56, assuming that x1 is continuous.
Develop the B&B tree for each of the following problems. For convenience, always select x1 as the branching variable at node 0.*(a) Maximize z = 3x1 + 2x2 subject to 2x1 + 5x2 … 18 4x1 + 2x2 … 18
Solve the ILP of Example 9.2-1 by the B&B algorithm starting with x2 as the branching variable. Start the procedure by solving the subproblem associated with x2 … [x2 * ].11
Give the binary variables y1, y2, . . . , yn, such that if xi = 1, then xi - 1 or xi + 1 must equal 1, i = 1, 2, . . . , n, where y0 and yn + 1 define the variable yn.
Consider the following objective function Minimize z = min52x1 + x2, 4x1 - 3x2 x1 Ú 1, x2 Ú 06 Use auxiliary binary variables to convert the objective function z into an analytically manageable
In the following constraint, the right-hand side may assume one of values, b1, b2, . . . , and bm.g1x1, x2,c, xn2 … 1b1, b2 ,c, or bm2 Show how this condition is represented.
Suppose that it is required that any k out of the following m constraints must be active:gi1x1, x2,c , xn2 … bi, i = 1, 2,c , m Show how this condition may be represented.
Consider the binary variable yi, i = 1, 2,c, n. Express the following condition as a set of simultaneous ILP constraints: If i = k, then yk = 1, and all the remaining variables equal zero.
Given the binary variables x1, x2, x3, x4, and x5, if x1 = 1 and x2 = 0, then x3 = 1, x4 = 1, and x5 = 1. Formulate the condition as simultaneous constraints.*9-49. Suppose that product zw occurs in
Show how the nonconvex shaded solution spaces in Figure 9.8 can be represented by a set of simultaneous constraints. Find the optimum solution that maximizes z = 2x1 + 3x2 subject to the solution
A manufacturing process uses four interchangeable raw materials. The raw materials differ in properties, which leads to different output units per unit of raw material. They also differ in cost and
N queens problem. In the game of chess, queens attack by moving horizontally, vertically, or diagonally. It is desired to place N queens on an (N * N)-grid so that no queen can“take” any other
UPak is a subsidiary of an LTL transportation company. Customers bring their shipments to the UPak terminal to be loaded on the trailer and can rent space up to 36 ft.The customer pays for the exact
Jaco owns a plant in which three products are manufactured. The labor and raw material requirements for the three products are given in the following table.Product Required daily
In Problem 9-41, suppose that job 4 cannot be processed until job 3 has been completed.Also, machine settings for jobs 7 and 8 necessitate processing them one right after the other (i.e., job 7
Jobco Shop has 10 outstanding jobs to be processed on a single machine. The following table provides processing times and due dates. All times are in days, and due time is measured from time 0:Job
Gapco manufactures three products, whose daily labor and raw material requirements are given in the following table.Product Required daily labor(hr/unit)Required daily raw material(lb/unit)1 3 4 2 4
A machine is used to produce two interchangeable products. The daily capacity of the machine can produce at most 20 units of product 1 and 40 units of product 2. Alternatively, the machine can be
Barnett (1987). Professor Yataha needs to schedule eight round-trips between Boston and Washington, D.C. The route is served by three airlines, Eastern, US Air, and Continental, and there is no
A household uses at least 3000 minutes of long-distance telephone calls monthly and can choose to use the services of any of three companies: A, B, and C. Company A charges a fixed monthly fee of $10
A company uses four special tank trucks to deliver four different gasoline products to customers. Each tank has five compartments with different capacities: 500, 750, 1200, 1500, and 1750 gallons.
Jarvis and Associates (1978). Seven cities are being considered as potential locations for the construction of at most four wastewater treatment plants. The following table provides the data for the
Liberatore and Miller (1985). A manufacturing facility uses two production lines to produce three products over the next 6 months. Backlogged demand is not allowed. However, a product may be
Repeat Problem 9-31 assuming that the demands at each of customers 2 and 3 are changed to 800.
Three industrial sites are considered for locating manufacturing plants. The plants send their supplies to three customers. The supply at the plants, the demand at the customers, and the unit
Oilco is considering two potential drilling sites for reaching four targets (possible oil wells). The following table provides the preparation costs at each of the two sites and the cost of drilling
Jobco is planning to produce at least 2000 widgets on three machines. The minimum lot size on any machine is 600 widgets. The following table gives the pertinent data of the situation.Machine Setup
Leatherco is contracted to manufacture batches of pants, vests and jackets. Each product requires a special setup of the machines needed in the manufacturing processes. The following table provides
Solve Problem 9-26 if, additionally, each receiver can handle at most 4 meters and receiver 8 can handle meters 1, 4, 8, and 10.
Gavernini and Associates (2004). Modern electric networks use automated electric utility meter reading in place of the more costly manual meter reading. In the automated system, meters from several
Guéret and Associates (2002), Section 12.6. MobileCo is budgeting $15 million to construct as many as 7 transmitters to cover as much population as possible in 15 contiguous geographical
Walmark Stores is in the process of expansion in the western United States. During next year, Walmark is planning to construct new stores that will serve 10 geographically dispersed communities. Past
Bill has just completed his exams for the academic year and wants to celebrate by seeing every movie showing in theaters in his town and in six other neighboring cities. If he travels to another
The great treasures of King Tut are on display in the Giza Museum in Cairo. The layout of the museum is shown in Figure 9.7, with the different rooms joined by open doors. A guard standing at a door
Washington County includes six towns that need emergency ambulance service. Because of the proximity of some of the towns, a single station may serve more than one community. The stipulation is that
The U of A is in the process of forming a committee to handle students’ grievances. The administration wants the committee to include at least one female, one male, one student, one administrator,
ABC is an LTL (less-than-truckload) trucking company that delivers loads on a daily basis to five customers. The following list provides the customers associated with each route:Route Customers
The world-renowned logic puzzle, Sudoku, deals with a 9 * 9 grid subdivided into 9 nonoverlapping 3 * 3 subgrids. The puzzle calls for assigning the numerical digits 1 through 9 to the cells of the
A widely circulated puzzle requires assigning a single distinct digit (0 through 9) to each letter in the equation SEND + MORE = MONEY. Formulate the problem as an integer program, and find the
Given i = 1, 2,c, n, formulate a general ILP model (for any n) to determine the smallest number y that, when divided by the integer amount 2 + i, will always produce a remainder equal to i; that is,
A street vendor selling electronic gadgets was robbed of all his possessions. When reporting the matter to the police, the vendor did not know the number of gadgets he had but stated that when
You have a 4 * 4 grid and a total of 10 tokens. Use ILP to place the tokens on the grid such that each row and each column will have an even number of tokens.
You have three currency denominations with 11 coins each. The total worth (of all 11 coins) is 12 bits for denomination 1, 14 bits for denomination 2, and 20 bits for denomination 3. You need to buy
Graves and Associates (1993). Ulern University uses a mathematical model that optimizes student preferences taking into account the limitation of classroom and faculty resources. To demonstrate the
In Problem 9-10, suppose that the nature of the melodies dictates that songs 3 and 4 cannot be recorded on the same CD. Formulate the problem as an ILP. Would it be possible to use a 30 MB CDs to
The Record-a-Song Company has contracted with a rising star to record eight songs. The sizes in MB of the different songs are 8, 10, 8, 7, 9, 6, 7, and 12, respectively. Record-a-Song uses two CDs
Weber (1990). Consider the following two groups of words:Group 1 Group 2 AREA ERST FORT FOOT HOPE HEAT SPAR PAST THAT PROF TREE STOP All the words in groups 1 and 2 can be formed from the nine
Solve Problem 9-7 given that, in addition to the total sum being the largest, the sum of column 1 and the sum of column 2 will be the largest as well. Find the optimum solution.

Showing 400 - 500 of 4620

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved