Rule 8.5

The longest expected processing time first (LEPT) rule minimizes the expected makespan in the class of nonpreemptive static list policies as well as in the class of nonpreemptive dynamic policies.

Rule 8.6

Let us consider the stochastic version of , where job  has an exponential distributed processing time with a rate of  and a deterministic due date, . Thus it leads to the concept of weighted discounted shortest processing time first (WDESPT), under which one can minimize the expected weighted number of tardy jobs in the classes of nonpreemptive static list policies, nonpreemptive dynamic policies as well as preemptive dynamic policies.

Now let us consider some simple rules with examples as applicable for problems which have release dates which are stochastic

Rule 8.7

Let us consider the stochastic version of , where there is preemption for processing, and we also know that the highest preemptive rule is already defined. Then the optimal preemptive policy is the preemptive weighted discounted shortest processing time first (WDESPT) rule. Hence at any point of time, amongst jobs available, the one with highest  must be processed.

Rule 8.8

Under the optimal nonpreemptive dynamic policy, the decision maker selects whenever the machine is free, from among the waiting jobs one with the highest value of . This implies that the jobs are scheduled according to the weighted discounted shortest processing time first (WDESPT) rule.

Now let us consider some simple rules with examples as applicable for problems which have parallel machines

Rule 8.9

If there are two machines in parallel and the processing times are exponentially distributed, then the longest expected job processing time (LEPT) rule minimizes the expected makespan in the class of nonpreemptive static list policies.

Rule 8.10

The nonpreemptive shortest expected job processing time (SEPT) policy minimizes the total expected completion time in the class of preemptive dynamic policies.