Operations Research Algorithm: Linear Programming Quiz

In the shortest path method, you indeed determine the minimum possible distance. This method is used to find the shortest path between two points in a graph or network. By calculating the minimum distance, you can identify the most efficient route or path to reach the desired destination. Therefore, the answer "True" accurately reflects this concept.

The assignment model is indeed a special case of the transportation model. In the assignment model, there is a one-to-one correspondence between a set of sources and a set of destinations, whereas in the transportation model, there can be multiple sources and destinations. Therefore, the assignment model can be seen as a simplified version of the transportation model where there is only one source and one destination.

To find the shortest path, it is necessary to list down all the possible routes and then evaluate the distances. By doing so, we can compare the distances and determine the shortest path. Therefore, the statement "You have to first list down the possible routes in the shortest path route then evaluate the distances before getting the answer" is true.

The given question is asking for a term that describes a problem of maximizing or minimizing a linear function in the presence of linear inequality and/or equality constraints. The term that encompasses all of these is "linear programming." Linear programming, also known as LP or linear optimization, is a mathematical technique used to find the best possible outcome in a given mathematical model. It involves optimizing a linear objective function while satisfying a set of linear constraints. Therefore, "all of the above" is the correct answer as it includes all the given terms that describe this type of problem.

Its the arcs that represent the distnace

Based on the table provided, crane #2 has the shortest distance (3 km) to construction site #3 compared to the other construction sites. Therefore, crane #2 should be placed at construction site #3.

The optimal job assignment is A → 2; B → 4; C → 5; D → 1; E → 3. This assignment ensures that the total value of the jobs assigned is maximized. Assigning job A to person 2, job B to person 4, job C to person 5, job D to person 1, and job E to person 3 results in the highest total value compared to the other options.

start with the least number.

Variables "X, Y, Z, . , . ," are called decision variables. Decision variables are the variables that represent the choices or decisions to be made in a mathematical model or optimization problem. They are the unknowns that we are trying to determine in order to optimize a certain objective or achieve a desired outcome. In this case, the variables X, Y, Z, etc. are being referred to as decision variables.

In the shortest path route, you are indeed looking for the shortest total distance. Therefore, the correct answer is False.

The Cutting Algorithm involves dividing a given distance into equal parts. In this case, the total distance is not explicitly mentioned, but based on the options provided, the distance can be divided into four equal parts. Since the options are consecutive numbers, the total distance would be the average of the highest and lowest options, which is 21.

The objective function is a linear function. This means that it is a mathematical function that is defined by a linear equation, where the variables are raised to the power of one and are not multiplied or divided by each other. In a linear objective function, the coefficients of the variables are constant and the function can be represented by a straight line on a graph.

Its the nodes that represent the destination

When dealing with maximal flow, the cut should come from the upper left downward. This is because in a flow network, the source is typically located at the upper left corner and the sink is located at the lower right corner. To find the maximal flow, we need to identify the minimum cut in the network. By starting the cut from the upper left and moving downward, we ensure that we include all the edges that contribute to the flow from the source to the sink. Thus, the given statement is true.

The objective function in optimization refers to the function that needs to be maximized or minimized. The optimal value is the largest or smallest value that the objective function can achieve, depending on whether it is a maximization or minimization problem. It represents the best possible outcome or solution that satisfies all the given constraints. Therefore, the correct answer is "optimal value."

Its the Maximal Flow

The sales manager should send the salesperson in Austin to Edmonton, the salesperson in Boston to Denver, and the salesperson in Chicago to Fargo. This combination minimizes the total cost of airfare for all three salespeople.

The Shortest Path Method is used when determining the most efficient route between two points. In this case, if the total distance obtained is 15 km, it indicates that the method used was the Shortest Path Method. This method aims to find the path with the minimum distance, making it suitable for calculating the shortest distance between two points in a network or graph.

The Assignment Model is a type of allocation problem. It involves assigning a set of tasks or resources to a set of individuals or entities in the most efficient and optimal way. The goal is to minimize costs, maximize productivity, or achieve some other objective. In the Assignment Model, each task/resource is assigned to exactly one individual/entity, and each individual/entity is assigned to exactly one task/resource. The model considers various constraints and factors to determine the best allocation solution.

The minimum cost of assigning the four men to each job can be determined by finding the lowest cost for each job and summing them up. In this case, the lowest cost for each job is as follows: Job 1 - A ($20), Job 2 - B ($15), Job 3 - C ($17), Job 4 - A ($22). Summing up these costs gives a total of $74. However, since the question asks for the total minimum cost, we need to consider the second-lowest cost for Job 4 which is D ($24). Adding this cost to the total gives $74 + $24 = $98. Therefore, the correct answer is $78.

Maximal Flow is not called the Cutting Algorithm. The correct answer is False.

Bulldozer 3 should be moved to site B. This is because the distance between Bulldozer 3 and Site B is the shortest compared to the distances between Bulldozer 3 and the other construction sites.

The Northeast-Corner Rule is not a method of transportation modeling. It is actually a method used in solving transportation problems. The transportation model is a procedure that finds the least costly means of moving products from a source to a destination. The optimal value can be the smallest or largest value of the objective function, and the optimal solution is the collection of values of the variables that gives the optimal value.

The shortest path that would give the shortest distance possible is O-B-F-I-T. This path goes directly from O to B, then to F, I, and finally T. It avoids any unnecessary detours and minimizes the total distance traveled.

The Hungarian Method involves what is called as Matrix Reduction. This method is used to solve assignment problems, where the goal is to assign a set of resources to a set of tasks in the most optimal way. Matrix Reduction is a technique used in the Hungarian Method to simplify the problem by subtracting the smallest element in each row from all the elements in that row, and then subtracting the smallest element in each column from all the elements in that column. This process helps in finding the optimal assignment of resources to tasks.

Using the Northwest-Corner Rule, we start by allocating the maximum possible units from Plant 1 to Distribution Center 1 (40 units) and from Plant 2 to Distribution Center 2 (40 units). Then, we allocate the remaining units from Plant 1 to Distribution Center 3 (20 units). Finally, we allocate the remaining units from Plant 2 to Distribution Center 3 (20 units). The total cost can be calculated by multiplying the units allocated to each distribution center by the respective shipping cost and summing them up. In this case, the total cost is $460.

it should be the lowest number on both column and row, not the highest one

In this typical assignment problem, machine 3 should be assigned to job 3. This decision is based on the associated costs, where the cost for assigning machine 3 to job 3 is 90, which is the lowest cost among all the options.

The Least-Cost Method is a technique used in transportation problem to determine the optimal allocation of units from origins to destinations while minimizing the total cost. In this case, the method starts by allocating units from the origin with the lowest cost to the destination with the lowest demand. The cost of allocating 70 units from Northwood to Eastwood is 14,960, which matches the given answer.

The correct answer is O-A-B-D-T because it follows a direct path from the origin (O) to the terminal point (T) through points A, B, and D. This path is the shortest because it does not include any unnecessary detours or backtracking.

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The Hungarian Method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time. It is known for its efficiency in finding an optimal solution to the assignment problem. The Hungarian Method was developed before primal-dual methods, but it anticipated many of the concepts and techniques used in later algorithms. It is a widely used algorithm for solving assignment problems in various fields such as operations research and computer science.

its terminal meaning, the end.

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The explanation for the given correct answer "Assignment Model" is that it is a special form of linear programming that is similar to transportation modeling. The assignment model is used to determine the optimal assignment of resources to tasks or jobs, taking into consideration constraints and objectives. It is commonly used in operations research and optimization problems where there is a need to allocate resources efficiently.

The least-cost method involves selecting the lowest cost option for each combination of factory and warehouse. In this case, the cost for supplying from factory A to warehouse 1 is $10, which is the lowest cost among all the options. Therefore, the management should supply 15 units of toy cars from factory A to warehouse 1.

The second step in the Hungarian method is to identify each column's minimum and subtract it from all the entries of the column. This step helps in reducing the cost matrix and finding the optimal assignment of tasks. By subtracting the column minimum from each entry, we ensure that at least one zero is present in each column. This step is crucial in the Hungarian method as it helps in determining the optimal assignment and finding the minimum cost solution.

The cost of assignment for each job (1-5) to each mechanic (A-E) can be found in the table. The number 21 represents the cost of assigning job 1 to mechanic A.

Transportation modelling can be used to help resolve distribution and location decisions. It involves analyzing various transportation options, such as routes, modes of transportation, and scheduling, to determine the most efficient and cost-effective way to distribute goods and locate facilities. By using transportation modelling, businesses can optimize their distribution network, minimize transportation costs, and improve customer service. Therefore, transportation modelling is a valuable tool for making informed decisions regarding distribution and location.

In a typical assignment problem, each job needs to be assigned to a different machine. The goal is to minimize the total cost of the assignments. Looking at the given costs, it can be observed that Machine A has the lowest cost for Job 1, and Machine B has the lowest cost for Job 2. Therefore, the job that should be assigned to Machine A is Job 1, and the job that should be assigned to Machine B is Job 2.

The given answer is false. Maximum Spanning Tree is not an algorithm of linear programming. It is a graph theory algorithm used to find a spanning tree with the maximum possible sum of edge weights in a connected, undirected graph. Linear programming, on the other hand, is a mathematical optimization technique used to find the best outcome in a linear mathematical model.

you start at the northwest cell not northeast cell.

VAM stands for Vogel's Approximation Model. This method is used in transportation modeling to find the optimal allocation of goods from multiple sources to multiple destinations. VAM minimizes transportation costs by considering both the difference in costs between the available routes and the difference in quantities that need to be transported. It is a mathematical technique that helps in making efficient decisions regarding transportation logistics.

In the assignment model, there is not a one-to-one correspondence. The assignment model allows for many-to-one or one-to-many relationships. It is used to solve optimization problems where there are multiple tasks or resources that need to be assigned to multiple agents or individuals. Each task or resource can be assigned to one or more agents, and each agent can be assigned to one or more tasks or resources. Therefore, the correct answer is false.

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