Branch and Bound Method to Solve The Sum of Two Objective Functions

In this paper, the problem of sequencing a set of n jobs on single machine was considered to minimize multiple objectives function (MOF). The objective  is to find the optimal  solution (scheduling) for n independent jobs to minimize the objective function consists of a sum  of  weighted number  of  early  jobs  and  total  weighted of completion time. This problem is strongly NP-hard and to resolve it we derived two lower bounds (LB1, LB2) and heuristic method to get an upper bound which are used in root node of branch and bound tree. Some special cases  and dominance rule were proposed and proved. Results of extensive computational tests show that the proposed (BAB) algorithm effective in solving problems with up to (30)  jobs in time less than or equal to (30) minutes

Local search Methods to Solve The Sum of Two Objective Functions

In this paper, the problem of sequencing a set of n jobs on single machine was considered to minimize theobjective function. The aim  is to find the optimal or near optimal  solution  (scheduling) for the objective function consists of a  sum  of  total late work and maximum lateness. This problem is strongly NP-hard. Simulated Annealing, Ant colony Algorithm, and usagea hybridization as a tool to solved the problem approximatelywith up to  100000 jobs in a reasonable time 10 minutes

Branch and Bound Method to Solve Multi Objectives Function

This paper  presents  a  branch  and  bound  algorithm  for  sequencing  a  set  of  n independent  jobs  on  a single  machine  to  minimize sum of the discounted total weighted completion time and maximum lateness,  this problems is NP-hard. Two lower bounds were proposed and heuristic method to get an upper bound. Some special cases were  proved and some dominance rules were suggested and proved, the problem solved with up to 50 jobs

Solving Machine Scheduling Problem under Fuzzy Processing Time using the Simulated Annealing Method

In this paper, we describe the problem of sequencing a set of n jobs on single machine was considered to minimize multiple objectives function (MOF). The objective is to find the approximate solutions for scheduling n independent jobs to minimize the objective function consists from a sum of weighted number of early jobs and the weighted number of tardy jobs with fuzzy processing time. This problem is denoted by: (1/ / ). To resolve it we proposed the Average High Ranking (AHR) method to obtain a processing time generated from fuzzy processing time, calculate the costs and reach to total penalty cost. Since our problem is Strongly NP-hard in normal form, we used Simulated Annealing. It solved the problem with up to 12000 jobs in 30 seconds