FLOW SHOP SCHEDULING ALGORITHM TO MINIMIZE COMPLETION TIME FOR -JOBS -MACHINES PROBLEM n m

In a shop floor of the industry, the routings which are based upon the jobs that need to be processed on different machines are one among the major activities and therefore the resource requirements are not based upon the quantity as in a flow shop but rather the routings for the products being produced. However, both job shop and flow shop production cope with a scheduling problem to find a feasible sequence of jobs on given machines with the objective of minimising some function of the job completion times. Job completion time (make-span) can be defined as the time span from material availability at the first processing operation to the completion at the last operation [1]. Johnson [2] has shown that, in a 2-machines flow shop, an optimal sequence can be constructed. It was demonstrated later that -machine flow shop scheduling problem (FSSP) is strongly NP-hard for 3 [3]. FSSPs can be divided into two main categories: dynamic and static. The dynamic flow shop considered is one where jobs arrive continuously over time. The static flow shop-sequencing and scheduling problem denotes the problem of determining the best sequence of jobs on each machine in the flow shop. The criterion of optimality in a flow shop sequencing problem is usually specified as minimization of make-span that is defined as the total time to ensure that all jobs are completed on all machines. If there are no release times for the jobs then the total completion time equals the total flow time. In some cases for calculating the completion times specific constraints are assumed. For example, such a situation in the FSSP arises when no idle time is allowed at machines. This constraint creates an important practical situation that arises when expensive machinery is employed [4]. The general scheduling problem for a classical shop