Job Sequence with 2 machine-Operation research-problem-By Prof. Mihir Shah

okay today we will be solving some related to job sequencing problem with n number of jobs and two machines okay now in order to solve the sum okay we will first go through the question and see what is the question all about okay so in the question we have five jobs one two three four and five we have two machines a and B and these are all the values okay about the number of hours taken by machine a and machine B in order to complete the respective job now in this sum we need to find two things one the idle time and second the total you know elapsed time the total time taken by both the machine to complete the jobs now in order to solve that will start by one by one of them will go in this particular procedure and complete the so step number one we first need to find the optimal job sequence now in order to find the optimal job sequence okay we need to create a table now check there are five jobs available so we will create a table which will have five columns now remember if there are two machine the left side okay the left side of the table will represent a of machine a and the right side will represent machine B now we will start finding the optimal job sequence by taking the least you know taking the machine are you taking the job which has the least number of hours okay now if the particular R appears in machine a we will load from the left side and if that least are appears in machine B then we'll note it from the right side okay so let us see how to do this in by actually solving in to them now in this entire question we'll find try to find out the least are taken under the most lowest number so the lowest number at the lowest are which is given as 1 this is the least amount raising now the Machine corresponding to this one is machine a now if it is machine a we'll have to note from the left side now machine a has least one R and it is representing job number two so we'll note down your job number two now since I have already used this this particular Collins is of no use now let us find the second least now the second least R is to us and that is under machine B so now that appears on the right side okay it represents OP number one so will note down job number one I mean this is done after to the next least is the third on three yards okay it is represented by job a it will be presented by Java soap it will start from the left side okay and it represents odd number for the next least number is four and this is again over so four okay it is under job B ok machine B and job number five so since it is machine B will note it out on the right side okay and lastly we have number seven and only one spot available so we can note it directly so it's optimal job sequences first you know job number two will be done then job number four job number three job number five and lastly job number one now let us see how we need to calculate out what is the format of calculation of idle time and the elapsed time so now this is the table that we need to create the first column will have jobs now since there are two machines will have machine air and second will be machine B and we'll have the idle time now in machine a we need to find the in time and out time similarly for beam in time and out time in idle time we have to find for machine a and machine B so this is a basic format for solving job sequencing problem so first step we need to find the optimal job sequence and secondly we need to do the calculation so this is I can say second step we are going to do the actual calculation now under job we have to note down the optimal job Stickle that we have gone so here it will be job number 2 4 3 5 and 1 ok now let us see how we to solve this okay now always remember keep the first machine job the impact will always be zero matter from zero as you're going to start your work now check in machine a under job - how many hours did it take so for Machine a under job - it has taken one hour so my out time will be zero plus 1 which is 1 so it has taken 1 are now for one job whatever is the out time for the second it will become the in time so we cross it we bring one down so now next job will job number 4 in job number 4 for machine a it has taken 3 hours so my out time will be 1 plus 3 which is equal to 4 we bring 4 down ok so my next out time will be 4 under job number three is nine hours gonna take so 9 plus 4 is 13 I'm going to bring 13 down next will be Plus in job number firestick antennas so your it will become 23 okay we bring 23 down and lastly it'll be 23 plus job number one mistake and fibers so total is 28 okay so we first start with zero and then we keep adding the number of hours that have been taken by the respected number of John that also machine a the first machine now let's see we start how to start the second machine always remember first machine first out time will be equal to the end time for the second machine so whatever is the out time under your first machine that will become your in time for the second machine and now we have to follow the almost similar procedure but you have to be careful in one point that we will see ok machine be under job to has taken six hours so the out time will be one plus six which is equal to seven okay again the rule was whatever is out time will become the intent but now you have to be very careful if the out time is more than you know if the outcome of machine B is more than that of machine a then it has no issues you can directly bring it down so here it becomes seven okay but if it would have been less than that you know the out time of machine a then there will be one small effect that will have to do do you see that ahead but your as of now it is greater sorry bring it down so out and for the next job will be now this job number four which is eight those 7 plus 8 is 15 again this is 15 this is 13 15 is more than 13 so 3 bringing down 15 as it is job number 3 email it has taken seven hours so it will become 15 plus 7 which is equal to 22 now this is 22 okay the next out time of machine is 23 so you cannot get 22 down simple logic machine a need 23 hours to complete job number five machine B cannot start the 22 us it will be usually have to start after 23 hours or at 23 hours so if if the number okay if the total out time is less than that of the first machine we bring the same number down okay we carry the out time 23 hours okay we'll bring it here now you're what happened is machine B had already finished it was at 22 us but it cannot start because machine a will take 23 hours to finish that job only after that machine B can start so here machine B had to actually wait for one arm so the idle time of machine B under this case became one or thereafter we can directly saw no further 23 plus no job number five was for us so it became very seven now again 27 I could have bring it down directly but you had is already given as 28 us so you can all start the job B at 27 also you'll have to start it at 28 are again one our idle time will be recorded lastly 28 plus job number one it has taken to us so total begin 30 okay now let's take you know see her machine it took 23 28 hours to complete a job whereas machine B took 30 years to complete the job it means machine a had to wait how many years mayor it had to wait two hours so that was the idle time the machine a had though otherwise it was all in normal coincidence zero one one four four thirteen thirteen twenty three twenty three twenty so there's no gap between that the only gap between us the 28 to 30 so two was idle time now machine B started with you know after one are the in time was after one are so winning from zero to one it had to wait so another idle time that appears your so in total he had an idle time of 2 hours whereas B had of idle time of three hours okay so come to conclude this number one we need to first find the idle time so the idle time four machine a is equal to two hours idle time for machine B is equal to three hours so the total idle time the total idle time that the machine was idle is fibers and finally the total elapsed time that is the total time taken to complete all the job by both the machinist the total is 30 ours okay so this is how we have to solve job sequencing problems some where there are n number of jobs and two machines

Channel: Mihir Shah

Views: 104,104

Keywords: Sequencing, Problem, Operation, Research, Techniques, N jobs, and two, machines, Job Sequence, with 2 machine, method, to solve, the sum, Sequence, Idle time, Elapsed Time, 2 machines, Johnson's, algorithm, operations research, B.com, Bms, Baf, CA, MBA, M.com, NET, UGC

Id: qzUODlPEnxI

Length: 12min 13sec (733 seconds)

Published: Wed Apr 15 2020