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Add Optimal Job Scheduling (#3868)

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src/main/java/com/thealgorithms/dynamicprogramming/OptimalJobScheduling.java Normal file
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package com.thealgorithms.dynamicprogramming;
/**
* This class refers to the Optimal Job Scheduling problem with the following constrains:
* - precedence relation between the processes
* - machine pair dependent transportation delays
*
* https://en.wikipedia.org/wiki/Optimal_job_scheduling
*
* @author georgioct@csd.auth.gr
*/
public class OptimalJobScheduling {
private final int numberProcesses;
private final int numberMachines;
private final int[][] Run;
private final int[][] Transfer;
private final int[][] Cost;
/**
* Constructor of the class.
* @param numberProcesses ,refers to the number of precedent processes(N)
* @param numberMachines ,refers to the number of different machines in our disposal(M)
* @param Run , N*M matrix refers to the cost of running each process to each machine
* @param Transfer ,M*M symmetric matrix refers to the transportation delay for each pair of machines
*/
public OptimalJobScheduling(int numberProcesses, int numberMachines, int[][] Run, int[][] Transfer) {
this.numberProcesses = numberProcesses;
this.numberMachines = numberMachines;
this.Run = Run;
this.Transfer = Transfer;
this.Cost = new int[numberProcesses][numberMachines];
}
/**
* Function which computes the cost of process scheduling to a number of VMs.
*/
public void execute(){
this.calculateCost();
this.showResults();
}
/**
* Function which computes the cost of running each Process to each and every Machine
*/
private void calculateCost(){
for (int i=0; i < numberProcesses; i++){ //for each Process
for (int j=0; j < numberMachines; j++) { //for each Machine
Cost[i][j] = runningCost(i, j);
}
}
}
/**
* Function which returns the minimum cost of running a certain Process to a certain Machine.In order for the Machine to execute the Process ,he requires the output
* of the previously executed Process, which may have been executed to the same Machine or some other.If the previous Process has been executed to another Machine,we
* have to transfer her result, which means extra cost for transferring the data from one Machine to another(if the previous Process has been executed to the same
* Machine, there is no transport cost).
*
* @param process ,refers to the Process
* @param machine ,refers to the Machine
* @return the minimum cost of executing the process to the certain machine.
*/
private int runningCost(int process, int machine) {
if (process==0) //refers to the first process,which does not require for a previous one to have been executed
return Run[process][machine];
else {
int[] runningCosts = new int[numberMachines]; //stores the costs of executing our Process depending on the Machine the previous one was executed
for (int k=0; k < numberMachines; k++) //computes the cost of executing the previous process to each and every Machine
runningCosts[k] = Cost[process-1][k] + Transfer[k][machine] + Run[process][machine]; //transferring the result to our Machine and executing the Process to our Machine
return findMin(runningCosts); //returns the minimum running cost
}
}
/**
* Function used in order to return the minimum Cost.
* @param cost ,an Array of size M which refers to the costs of executing a Process to each Machine
* @return the minimum cost
*/
private int findMin(int[] cost) {
int min=0;
for (int i=1;i<cost.length;i++){
if (cost[i]<cost[min])
min=i;
}
return cost[min];
}
/**
* Method used in order to present the overall costs.
*/
private void showResults(){
for (int i=0; i < numberProcesses; i++){
for (int j=0; j < numberMachines; j++) {
System.out.print(Cost[i][j]);
System.out.print(" ");
}
System.out.println();
}
System.out.println();
}
/**
* Getter for the running Cost of i process on j machine.
*/
public int getCost(int process,int machine) {
return Cost[process][machine];
}
}

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src/test/java/com/thealgorithms/dynamicprogramming/OptimalJobSchedulingTest.java Normal file
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package com.thealgorithms.dynamicprogramming;
import org.junit.jupiter.api.Test;
import static org.junit.jupiter.api.Assertions.assertEquals;
/**
* @author georgioct@csd.auth.gr
*/
public class OptimalJobSchedulingTest {
@Test
public void testOptimalJobScheduling1(){
int numberProcesses = 5;
int numberMachines = 4;
int[][] Run = {
{5, 1, 3, 2},
{4, 2, 1, 3},
{1, 5, 2, 1},
{2, 3, 4, 2},
{1, 1, 3, 1}};
int[][] Transfer = {
{0, 1, 2, 4},
{1, 0, 2, 3},
{2, 2, 0, 1},
{4, 3, 1, 0}};
OptimalJobScheduling opt = new OptimalJobScheduling(numberProcesses,numberMachines,Run,Transfer);
opt.execute();
int[][] costs = {
{5, 1, 3, 2},
{6, 3, 4, 5},
{5, 8, 6, 6},
{7, 9, 10, 8},
{8, 9, 12, 9}};
for (int i=0; i < numberProcesses; i++){
for (int j=0; j < numberMachines; j++){
assertEquals(costs[i][j],opt.getCost(i,j));
}
}
}
@Test
public void testOptimalJobScheduling2(){
int numberProcesses = 3;
int numberMachines = 3;
int[][] Run = {
{5, 1, 3},
{4, 2, 1},
{1, 5, 2}};
int[][] Transfer = {
{0, 1, 2},
{1, 0, 2},
{2, 2, 0}};
OptimalJobScheduling opt = new OptimalJobScheduling(numberProcesses,numberMachines,Run,Transfer);
opt.execute();
int[][] costs = {
{5, 1, 3},
{6, 3, 4},
{5, 8, 6}};
for (int i=0; i < numberProcesses; i++){
for (int j=0; j < numberMachines; j++){
assertEquals(costs[i][j],opt.getCost(i,j));
}
}
}
@Test
public void testOptimalJobScheduling3(){
int numberProcesses = 6;
int numberMachines = 4;
int[][] Run = {
{5, 1, 3, 2},
{4, 2, 1, 1},
{1, 5, 2, 6},
{1, 1, 2, 3},
{2, 1, 4, 6},
{3, 2, 2, 3},
};
int[][] Transfer = {
{0, 1, 2, 1},
{1, 0, 2, 3},
{2, 2, 0, 2},
{1, 3, 2, 0},
};
OptimalJobScheduling opt = new OptimalJobScheduling(numberProcesses,numberMachines,Run,Transfer);
opt.execute();
int[][] costs = {
{5, 1, 3, 2},
{6, 3, 4, 3},
{5, 8, 6, 9},
{6, 7, 8, 9},
{8, 8, 12, 13},
{11, 10, 12, 12}};
for (int i=0; i < numberProcesses; i++){
for (int j=0; j < numberMachines; j++){
assertEquals(costs[i][j],opt.getCost(i,j));
}
}
}
}