In this video, I have solved a non-smooth job sequencing non-linear problem using the Evolutionary solver in Excel. I have also explained the GRG solver is not very helpful in this context. Before solving the problem, I have explained the INDEX function operation and the all DIFFERENT constraint in Excel. The objective was to minimize the average tardiness for the jobs. The concepts of tardiness and lateness were also explained in this video.
In this video, I have solved a smooth non-linear problem using the GRG solver in Excel. I have also explained how to choose the Convergence size and the Multi-start option in GRG. The multi-start option is like mimicking the genetic algorithm of the Evolutionary solver in that it chooses various starting points in anticipation of the fact that the objective value will eventually find its global optima.
In this video, useful concepts were discussed related to non-linear programming. The idea was to deliver an introduction to non-linear problems and non-linear solvers before starting to use them. Linear vs. Non-linear; Convexity vs. Concavity; Continuity vs. Discontinuity; and Smoothness vs. Non-smoothness were discussed. Also, how the two solver engines – GRG and Evolutionary work is also explained.
This is the 18th video of the lecture series Optimization using Excel. Here we have discussed how to solve a Travelling Salesman Problem (TSP) problem using Integer Programming. A TSP is a specific type of network where the flow unit will start from a node and terminate the journey at the same node after visiting all the other nodes of the network only once. The objective is to minimize the total distance traveled.
Here we have discussed how to solve a minimum spanning tree problem using Prim’s algorithm. The objective is to find a minimum spanning tree network from a given network arrangement of nodes. Spanning Tree and Minimum Spanning Tree What are the steps of Prim’s algorithm? The steps for implementing Prim’s algorithm are as follows: Initialize the minimum spanning tree with a vertex chosen at random. Find all the edges that connect the tree to new vertices, find the minimum and add it to the tree. Keep repeating step 2 until we get a minimum spanning tree.
This is the 16th video of the lecture series Optimization using Excel. Here we have discussed how to solve a minimum spanning tree problem using Kruskal’s algorithm. The objective is to find a minimum spanning tree network from a given network arrangement of nodes.
Here we have solved the Travelling Salesman Problem (TSP) problem once again using the non-linear approach. A TSP is a specific type of network where the flow unit will start from a node and terminate the journey at the same node after visiting all the other nodes of the network only once. The objective is to minimize the total distance traveled. Setting up a TSP using a non-linear approach is easier compared to integer programming. However, the solving time is worse compared to integer programming.
Here we have discussed how to formulate and solve a maximum flow (Maxflow) network problem. The objective is to maximize the total flow from the source to the destination node given the capacity constraints of the different routes of the network. Both algebraic formulation and Excel solver setup have been explained in the video.
In this video, we have described how to solve a specific type of network flow model – The Shortest Path Problem using Excel. Viewers are required to watch the previous video (i.e., 13. Network Flow Models) in order to appreciate the use of the =SUMIF() function used in this model. In the shortest path problem, the goal is to find the shortest distance between a source and a sink node. The distances given in the network diagram can be either time or cost. The objective is to minimize the total cost. This is a specific example of a binary integer program.
This is the thirteenth video of the lecture series Optimization using Excel. In this video, we have discussed theoretically various types of network models available to use. This video is an introduction to these network flow models. The actual models will be discussed using separate videos. At the end of the video, we have used the SUMIF function of Excel because we would be using the same while solving the Shortest path and Maximal flow problems in the subsequent videos.
