Crislaire Jay L. Barcenal

Barcenal, Clarisse ACC 421 (11428) June 29, 2021 Let’s Check 1. Describe the branch and bound method in integer programming Based on my understanding, the branch and bound approach is a solution method that divides the possible solution space into smaller subsets. These smaller subsets can be systematically evaluated until the optimal option is discovered. The branch and bound strategy is used in conjunction with the conventional noninteger solution approach while solving an integer programming issue. According to my research the branch and bound method uses a tree diagram of nodes and branches to organize the solution partitioning. There are optimal integer solution as well which will always be between the upper bound of the relaxed solution and a lower bound of the rounded-down integer solution. Branch of the variable with the solution value with the greatest fractional part. 2. What are the three information needs of the transportation model? The 3 information we need to consider are: (1) the origin points and the capacity or supply per period at each. (2) the destination points and the demand per period at each. (3) The cost of shipping one unit from each origin to each destination. The transportation model is a type of linear programming model, which is an iterative technique for solving issues that involves minimizing the cost of delivering things from a number of different sources to a number of different destinations. 3. Identify the three “steps” in the northwest-corner rule Starting at the upper left-hand cell of a table specifically the northwest corner and systematically allocating units to shipping routes is a procedure in the transportation model we should consider the three steps: (1) Exhaust the supply (factory capacity) of each row before moving down to the next row. (2) Exhaust the (warehouse) requirements of each column before moving to the next column on the right. (3) Check to ensure that all supplies and demands are met. 4. How to find the optimal solution to the linear programming problem model with the integer restrictions relaxed? An optimal solution is one in which the objective function obtains its maximum (or minimum) value, i.e. the highest profit or lowest cost. According to the following linear programming problem, the values of x and y are optimal solutions if the objective function z = ax + by is minimum or maximum. However, there are a variety of approaches for determining the best solution to an LP problem, such as the graphical method, the simplex method, and so on. 5. Suppose you are using the Hungarian Algorithm to minimize cost. After creating a matrix with people as rows and activities as columns, you have 8 rows and 7 columns. What do you have to do before you can start the steps of the algorithm? To start, I think subtract the smallest entry in each row from each entry in that row to find the row minimal. Subtract the smallest entry in each column from each entry in that column to find the column minimal. 6. For Company Z, the amount shipped to three out of four destinations must not exceed 45 tons. This is an example of what kind of constraint? Based on my understanding I think this is an example of k out of n constraint however I think that using a solution with built-in support for this constraints is sometimes more efficient than manually stating it. 7. The more sources and destinations there are for a transportation problem, the smaller the percentage of all cells that will be used in the optimal solution. Explain Transportation changes impacted the flow of goods from various sources to various destinations, with the general goal of lowering transportation costs. Physical distribution of commodities and services from a variety of supply centres to demand centres. 8. All of the transportation examples appear to apply to long distances. Is it possible for the transportation model to apply on a much smaller scale, for example, within the departments of a store or the offices of a building? Discuss; create an example or prove the application impossible. It is possible, with regards to transportation model to use on a way smaller scale because location of a replacement industrial plant, warehouse, or distribution center could be a strategic issue with substantial price implications, example of this are system requires that orders processed in The United States will be shipped in containers to customers in the Philippines using a combination of river barge, rail, and truck. As a result, (1) all inland terminals will eventually abolish repackaging, (2) material handling costs and capacities at Gulf and East Coast port facilities will be considerably lowered, and (3) repackaging at all inland terminals will finally be eliminated and (3) orders will be delivered directly with little or no increase in order response time and only a little increase in total inventory in the system due to the increased frequency of departures of ocean-going container barges from factories. 9. What is meant by an unbalanced transportation problem, and how would you balance it? If supply and demand are not equal, a transportation situation is said to be uneven. There are two possibilities: 1. If supply exceeds demand, a dummy supply variable is put into the equation to equalize supply. 2. To make demand equal to supply, a dummy demand variable is put into the equation. When supply exceeds demand, the excess supply is assumed to go to inventory. A column of slack variables is added to the transportation table which represents dummy destination with a requirement equal to the amount of excess supply and the transportation cost equal to zero. When demand exceeds supply, balance is restored by adding a dummy origin. The row representing it is added with an assumed total availability equal to the difference between total demand & supply and with each cell having a zero unit cost. 10. Explain what is meant by the term degeneracy within the context of transportation modelling. When the values of certain fundamental variables are zero and the Replacement ratio is the same, degeneracy in a linear programming problem is said to arise when a basic feasible solution comprises a fewer number of non-zero variables than the number of independent constraints. If number of allocations, N = m + n – 1, then degeneracy does not exist. If number of allocations, N ¹ m + n – 1, then degeneracy does exist.