Operations Research Algorithms In Linear Programming Transportation Modelling And Assignment Modelling

The assignment model is indeed a special case of the transportation model. In the assignment model, the objective is to assign a set of resources to a set of tasks, while minimizing the total cost or maximizing the total profit. This can be seen as a transportation problem, where the resources can be considered as supply points and the tasks as demand points. Therefore, the assignment model can be seen as a simplified version of the transportation model, focusing on a specific type of allocation problem.

The objective function is considered a linear function when it can be expressed as a linear equation, meaning it consists only of variables that are raised to the power of 1 and are multiplied by constant coefficients. This means that the function does not contain any terms with exponents or other non-linear operations. Therefore, if the given objective function satisfies these conditions, the correct answer is true.

In the shortest path method, the objective is to find the minimum possible distance between two points. Therefore, the correct answer is true.

When dealing with maximal flow, the cut should come from the upper left downward because it follows the direction of the flow. In a flow network, the upper left represents the source of the flow, and the flow is directed towards the lower right, which represents the sink. Therefore, the cut should be made in a way that separates the source from the sink, and this is achieved by cutting from the upper left downward.

Variables "X, Y, Z, ..." are called decision variables. Decision variables are the variables that are used to represent the choices or decisions that need to be made in a mathematical model or optimization problem. These variables are typically used to represent the values that need to be determined or optimized in order to achieve the desired objective. Therefore, the correct answer is decision variable.

Transportation modeling can be used to help resolve distribution and location decisions. By utilizing transportation modeling techniques, such as route optimization and capacity planning, businesses can effectively determine the most efficient and cost-effective ways to distribute their products and make location decisions. This allows them to minimize transportation costs, optimize delivery routes, and ensure timely and efficient distribution, ultimately improving overall operational efficiency and customer satisfaction.

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

The Northwest-Corner Rule is a method used in transportation problems to allocate shipments from sources to destinations. It starts by allocating shipments from the northwest corner (top-left) of the matrix and moves horizontally or vertically to the next available cell until all shipments are allocated. In this case, the total cost obtained using this method is $460.

The optimal value refers to the largest or smallest value of the objective function in a mathematical optimization problem. It represents the best possible solution or outcome that can be achieved based on the given constraints and decision variables. The optimal value is the ultimate goal of the optimization process, as it represents the most favorable result that can be obtained.

start with the least number.

The explanation for the given correct answer is that in order to determine the shortest path route, you need to list down all possible routes and then evaluate the distances between them. This process allows you to compare the distances and ultimately find 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.

Maximal Flow is not called the Cutting Algorithm. The Cutting Algorithm is a different algorithm used to find the minimum cut in a flow network. Maximal Flow, on the other hand, is an algorithm used to find the maximum flow in a flow network. Therefore, the statement "Maximal Flow is also called the Cutting Algorithm" is false.

Its the nodes that represent the destination

The Shortest Path Method is used to find the shortest distance between two points in a graph or network. In this case, the person used the Shortest Path Method to calculate a total distance of 15 km. This method is commonly used in transportation and logistics to determine the most efficient route or path.

its terminal meaning, the end.

The given correct answer is "all of the above" because all three terms - linear programming, LP, and linear optimization - refer to the same problem of maximizing or minimizing a linear function in the presence of linear inequality and/or equality constraints. These terms are used interchangeably to describe the same mathematical optimization technique.

Its the Maximal Flow

Its the arcs that represent the distnace

The total minimum cost of assigning the four men to each job is $78. This can be determined by finding the minimum cost for each job and summing them up. In this case, the minimum cost for each job is $20 (A to job 1), $18 (B to job 2), $20 (C to job 3), and $20 (D to job 4). Adding these costs together gives a total of $78.

you start at the northwest cell not northeast cell.

In a typical assignment problem, three different machines are to be assigned to three different jobs with the restriction that exactly one machine is allowed for each job. The associated costs are given, but the question does not explicitly state the cost associated with machine C. However, since the question asks for the job to which machine C should be assigned, and the only available option is job number 3, the correct answer is 3.

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

The shortest path that would give the shortest distance possible is O-B-F-I-T. This path only includes the necessary nodes to reach the destination (T) while minimizing the distance traveled. The other paths (O-C-G-T, O-A-D-H-T, O-B-G-F-I-T) include additional nodes that are not needed to reach the destination, resulting in a longer distance.

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 by making the column minimums equal to zero. By subtracting the minimum value from each entry in the column, the problem of finding the optimal assignment can be simplified. This step is crucial in determining the initial assignments and finding the optimal solution in the subsequent steps of the Hungarian method.

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The given answer is False. Maximum Spanning Tree is not an algorithm of linear programming. It is a graph algorithm used to find a spanning tree with the maximum possible total weight or cost. Linear programming, on the other hand, is a mathematical optimization technique used to find the best possible outcome in a linear mathematical model.

The correct answer is Machine A should be assigned to Job 1 and Machine B should be assigned to Job 2. This is because the associated costs for Machine A-Job 1 and Machine B-Job 2 are not given, so we cannot determine which assignment would have the lowest cost.

The least-cost method is used to determine the optimal allocation of goods from multiple sources to multiple destinations based on cost. In this case, the question asks for the number of units of toy cars that should be supplied from factory A to warehouse 1. To determine this, we compare the costs of supplying from factory A to each warehouse. The cost of supplying from factory A to warehouse 1 is 15, which is the highest among all the options. Therefore, the optimal allocation is to supply 15 units of toy cars from factory A to warehouse 1.

The Northeast-Corner Rule is not a method of transportation modeling. 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 goal is to minimize airfare, so we need to choose the routes with the lowest cost. Looking at the table, the cost of flying from Austin to Edmonton is the lowest among the options for Austin. Similarly, the cost of flying from Boston to Denver is the lowest among the options for Boston, and the cost of flying from Chicago to Fargo is the lowest among the options for Chicago. Therefore, the answer is Austin (Edmonton), Boston (Denver), Chicago (Fargo).

The correct answer is O-A-B-D-T because it follows the path that goes through points A, B, D, and finally T, which is the terminal point. This path is the shortest because it has the fewest number of points to go through compared to the other options.

The Hungarian Method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time. It is known for its efficiency and accuracy in finding the optimal solution for the assignment problem. The method was developed by Hungarian mathematicians and was one of the earliest algorithms to solve this problem. It uses a primal-dual approach and has been widely used in various fields such as operations research, computer science, and economics.

Based on the information provided, crane #2 should be placed at construction site 3 because it has the shortest distance from that site compared to the other sites.

In the assignment model, there is not a one-to-one correspondence. This model allows for multiple tasks to be assigned to a single individual or multiple individuals to be assigned to a single task. Therefore, the correct answer is false.

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The Hungarian Method involves what is called as Matrix Reduction. Matrix reduction is a technique used to simplify a matrix by subtracting the smallest element in each row or column from all the other elements in that row or column. This process helps in finding the optimal assignment of tasks or resources in a bipartite graph by reducing the matrix to a more manageable size. By performing matrix reduction, the Hungarian Method efficiently solves assignment problems by finding the minimum cost or maximum profit assignment.

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The total distance would be 21. The Cutting Algorithm involves making a series of cuts to a given object, and the total distance is the sum of the lengths of all the cuts made. In this case, there are four options given, and the option with the total distance of 21 is the correct answer.

The Assignment Model is a type of Allocation Problem. It involves allocating a set of resources to a set of tasks in the most efficient way possible. In this model, each task is assigned to exactly one resource, and each resource is assigned to exactly one task. The goal is to minimize the total cost or maximize the total benefit of the allocation. Therefore, the correct answer is Allocation Problem.

The assignment model is a special form of linear programming that is similar to transportation modeling. It is used to determine the optimal assignment of tasks or resources to individuals or machines, taking into consideration various constraints and objectives. In this model, the goal is to minimize the total cost or maximize the total profit of the assignments. It is commonly used in operations research and management science to solve allocation problems efficiently.

Bulldozer 3 should be moved to garage B. This is because the question asks for the garage where bulldozer 3 should be moved, and the answer states "B".

VAM stands for Vogel's Approximation Model, which is a method used in transportation modeling. This model is used to find an initial feasible solution for transportation problems by considering the costs and supplies/demands of different routes. Vogel's Approximation Model takes into account the penalties for unbalanced transportation, such as penalties for unused capacity or unmet demand. By using this model, transportation planners can optimize the allocation of resources and minimize costs in transportation systems.

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