Add Optimal Job Scheduling (#3868)

Author: georgioct

src/main/java/com/thealgorithms/dynamicprogramming/OptimalJobScheduling.java

@@ -0,0 +1,122 @@
+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 [email protected]
+ */
+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];
+    }
+}

src/test/java/com/thealgorithms/dynamicprogramming/OptimalJobSchedulingTest.java

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+package com.thealgorithms.dynamicprogramming;
+
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+/**
+ * @author [email protected]
+ */
+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));
+            }
+        }
+    }
+}