The LEPT strategy is a stochastic scheduling strategy that processes jobs in decreasing order with respect to the expected processing time.
This paper proposes a heuristic approach that combines the modified analytic hierarchy process (MAHP), bandwidth aware divisible scheduling (BATS) + BAR optimization, longest expected processing time preemption (LEPT), and divide-and-conquer methods to perform task scheduling and resource allocation.
Our main results are that the expected processing time, O Nk2logw/α), depends on the following factors: Linear O(N) dependency on the size of data.
The expected processing time is derived accordingly multiplying (14) by αN: hat{t}left( {N,k} right) le log, w cdot frac{{k^{2} }}{{alpha^{2} }} cdot alpha N = {rm O}left( {frac{{ - { log }left( w right) cdot Nk^{2} }}{alpha }} right) (16).
Shortest Expected Processing Time (SEPT): The SEPT approach is similar to the LEPT strategy.
Four strategies for solving the problem are applied and compared: an exact approach, using the mixed integer programming solver SCIP; and three heuristic strategies, namely the longest expected processing time, the shortest expected processing time, and random choice.
The assignment order of the patients is determined by the following strategies: Longest Expected Processing Time (LEPT): The LEPT approach sorts the patients in descending order solely according to their expected LoS.
In addition, scheduling theory (23 ) implies that aggregate waiting time for reoccupants can be minimized by remediating the least-contaminated buildings first (i.e., use the shortest expected processing time priority rule).
Stochastic scheduling has been applied to the task of maximizing operating room utilization, which bears considerable similarity to the bed assignment problem: Arnaout developed and evaluated an approach [ 20] based on the Longest Expected Processing Time first (LEPT) strategy [ 21].
