This paper presents a simulated annealing algorithm to minimize makespan of single machine scheduling problem with uniform parallel machines. The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, which are to be scheduled on m parallel machines with different speeds. Since, this scheduling problem is a combinatorial problem; usage o...

We design a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints. We show that designing such an algorithm is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0-1 linear program. Also, we show that upon t...

In the field of robust optimization, the goal is to provide solutions to combinatorial problems that hedge against variations of the numerical parameters. This constitutes an effort to design algorithms that are applicable in the presence of uncertainty in the definition of the instance. We study the single machine scheduling problem with the objective to minimize the weighted sum of completion...

In this paper, the minimization of the maximum aggregate inventory of all products for the common cycle time approach to the scheduling problem of a multi-products single machine system is considered. In the case of non-zero set up time and limited resources, a simply and easy to apply rule has been obtained for this optimization problem. Using this rule, one can obtain the optimal production s...

  This paper deals with minimization of tardiness in single machine scheduling problem when each job has two different due-dates i.e. ordinary due-date and drop dead date. The drop dead date is the date in which jobs’ weights rise sharply or the customer cancels the order. A linear programming formulation is developed for the problem and since the problem is known to be NP-hard, three heuristic...

We discuss the problem of sequencing precedence-constrained jobs on a single machine to minimize the average weighted completion time. This problem has attracted much attention in the mathematical programming community since Sidney’s pioneering work in 1975 (Sidney, J. B. 1975. Decomposition algorithms for single machine scheduling with precedence relations and deferral costs. Operations Resear...

A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by precedence delays, i.e., a task can start its execution only after any of its predecessors has completed and the delay between the two tasks has elapsed. In the case of unit executi...

We consider the problem of scheduling jobs on a single machine. Given a nonlinear cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each job is defined as the cost function value at the job’s completion time. Throughout the past decades, great effort has been made to develop fast optimal branch-and-bound algorithms for the case of quadratic costs....

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completiontime formulation. We show their equivalence by proving that a O(n logn) greedy algorithm leads to optimal solutions to both relax...