New Rule with Local One Step Ahead Prediction: WLS Rule

Along with an observation to improve the performance measure of the system, a dynamic posteriori rule, the WLS that is weighted loss of slack rule used.

The weighted loss of slack rule evaluates the condition of all other operations in the respective queue whether operation j would be scheduled. This decision will reason a loss of slack for all the other operations waiting in the queue.  It is most crucial, whether an operation would have negative slack t_si after scheduling of operation j. Hence, the unsafe loss of slack of operation i because of the scheduling of operation j before i is:

In Eq. (6), the differences of the exponentially weighted slack after and before the scheduling of operation j are totaling up.  The  exponential  weighting  offers  an incentive to prefer long operations (that reason larger losses of slack than short ones) while their slack reduces and therefore assists to maintain the maximal tardiness same whereas still providing minute throughput times on the middle.

The queue is further divided into two subsequences. The high priority queue consists of those operations for that t_sj < max_J  o_j  o_i, that is the operations such have negative slack or might acquire negative slack because of the scheduling of several other operations before operation j. These dangerous operations are ordered as per to the above Eq. (6). The uncritical operations are scheduled as per to the ODD rule.

This is obvious that the WLS rule is an extremely good compromise among the two classes of rules. For extensive queues and high pressure, this dominates SL/OPN both in T_mean and T_rms,

and it performs well in all situations while avoiding extreme values of Tmax. Thus, it can be  said  that  it  is  prime  candidate  for  a  good  simple  priority  rule  especially  in decentralized scheduling.