Big M method for continuous variables

Is there any way to model the big M method for continuous variables? Something similar to this but B,C∈R≥0 and A∈{0,1}. Due to the precision problem, when the B and C are close I do not get the correct answer. Let pi,j∈R≥0, for i=1,…,n,j=1,…,m. As one of the constraints of my problem, I am looking … Read more

Optimizing library dimensions

Say I have a library that looks like that: 123cm <——–> |________| |________| |________| |________| |________| |________| |________| |________| | | Its width is (here) 123cm, its height is 231.9cm, the number of book shelves (horizontal lines) is 8. I can put books on the floor so there are effectively 8+1=9 compartments where I can … Read more

Disk Scheduling for a Fragmented Hard-Drive

Recently In class I have been learning about simple disk scheduling algorithms such as FCFS, STTF, LOOK, LOOK-SCAN etc. From my understanding these algorithms schedule I/O requests depending on which cylinder number needs to be read and a process will produce only one I/O request whenever it needs to access a file. This is confusing … Read more

Does Quadratically-Constrainted Quadratic Programming get easier if all constraints are equalities?

A Quadratically-Constrainted Quadratic Program consists of optimizing a quadratic objective function while imposing quadratic constraints, which can be inequalities or equalities. Obviously, describing the problem with inequalities alone can suffice, as a≤b and a≥b is equivalent to just a=b. For this reason, a lot of literature just focuses on the inequalities. However, I only have … Read more

Let G be a graph directed without circles. Suggest a method to find a minimum set of vertices So that all the vertices in the graph can be reached

Let G be a graph directed without circles. Suggest a method to find a minimum set of vertices So that all the vertices in the graph can be reached. I thought to run an SCC algorithm to find binding components and then return them. This is true? Or is there a better algorithm? Answer Considering … Read more

Solving the Size-Constrained Weighted Set Cover Problem

I’m wondering if anyone has experience trying to solve a weighted set cover problem over the power set (i.e. all possible subsets) of an n-element ground set where the number of sets included in the cover is limited by some constant k. This post indicates that the problem is in P with running time O(mk) … Read more

Finding the best state for chain graph with cycles

I have a chain graph like in the picture. Each node of the graph has finite possible labels, i.e. states, which define the node’s weight(non-negative) as well as the internode weight(also non-negative). Each node is connected to m previous ones. The internode weight is shown as edge and node weight as node itself. Is there … Read more

nn machines, nn types of jobs with qjq_j jobs, minimizing the cost

I have this problem A firm has qj jobs of type j, where 1≤j≤n. It also has [n]=1,2,…n machines. Machine i can service any job of type j where j≤i. The cost of running machine i is fi+mi·q where fi is the fixed cost of running the machine and mi is the marginal cost of … Read more