We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems. Zusam...

The single-machine scheduling problems with position and sum-of-processing-time based processing times are considered. The actual processing time of a job is defined by function of its scheduled position and total normal processing time of jobs in front of it in the sequence. We provide optimal solutions in polynomial time for some special cases of the makespan minimization and the total comple...

Operations flexibility refers to production environments where there are more tasks than workstations and any task can be assigned to any workstation. This article investigates the advantages of operations flexibility in a flowshop when the objectives are to minimize the makespan and workstation utilization. The proposed heuristic framework consists of two phases, allocation of operations to wo...

We describe a simple online heuristic for scheduling job shops. We assume there is a fixed set of routes for the jobs, and many jobs, say N , on each route. The heuristic uses safety stocks and keeps the bottleneck machine busy at almost all times, while the other machines are paced by the bottleneck machine. We perform a probabilistic analysis of the heuristic, under some assumptions on the di...

we study the nonpreemptive parallel machines scheduling problem where some of the machines are planned to be shutdown. We apply LPT algorithm to the problem and analyze its performance. Our analysis shows that the makespan of the LPT schedule is bounded by twice the optimum makespan if no more than half of the machines are allowed to be shutdown simultaneously. We also show that this bound ls t...

We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fix...

Approximation algorithms have been used to design polynomial time algorithms for intractable problems that provide solutions within the bounded proximity of the optimal solution. Load balancing problem on Heterogeneous Distributed Computing System (HDCS) deals with allocation of tasks to computing nodes, so that computing nodes are evenly loaded. Load-balancing algorithms are attempts to comput...