Minimizing the sum of absolute deviations under a common due date for a single-machine scheduling problem with availability constraints

Abstract

This paper investigates a single-machine scheduling problem with a planned maintenance period. The objective is to minimize the sum of absolute deviations (SAD) of job completion times under a common due date. It appears to be the first attempt to schedule jointly the SAD criterion and machine availability constraints. The problem is first mathematically formulated as a mixed integer linear programming model and is then solved optimally. Subsequently, we present some optimality conditions and describe the special cases of the problem which are polynomially solvable. As the computational complexity associated with the formulation makes it difficult for standard solvers address large-sized problems in reasonable solution time, we propose an ant colony optimization algorithm based on the results of our analysis. Computational results for different problem sizes demonstrate that our application of the suggested algorithm is efficient in obtaining near-optimal solutions.

Minimizing Total Earliness and Tardiness for Common Due Date Single-Machine Scheduling with an Unavailability Interval

“…Let the binary variables equal 1 if job is processed during period ∈ Ψ and 0 otherwise, where Ψ = ⋃ ( \ { }) represents the set of time units in which the machine is available. The following formulation is originally proposed in Low et al [41]. A major drawback of this formulation is its size.…”

“…With current emphasis on the JIT production strategy, these classical measures may no longer be applicable. So far, only Low et al [41] addressed the problem of minimizing common due date TET in the presence of availability constraints. They developed an ant colony optimization algorithm for the single-machine model in which one maintenance task had to be performed and analyzed some special cases that are polynomial-time solvable.…”

“…Nevertheless, such heuristic approaches offer no guarantees to the optimality of the obtained solutions and do not define how close the obtained solutions are to the optimal ones. Furthermore, it should be noted that the matching algorithm suggested by Low et al [41] only can be used to deal with the cases when the due date falls within the unavailability interval and certain conditions are satisfied. In practical scheduling environments, the production schedulers always expect to come up with an optimal schedule in reasonable time.…”

Determining Order Delivery Date by Revenue Approach: A Case Study With Nonwoven Textile Manufacturers in Trc1 Region

“…To obtain realistic results, planned maintenance periods and production setup times of the enterprises were also included in the time calculations. In a single-machine planning environment, a study was conducted with the intention of reducing the absolute deviations of completion times of jobs for a common delivery date, considering scheduled maintenance periods [13]. It was aimed to reduce the total delay to the minimum by using the setup-by-task duration feature in another study [14].…”

Single-machine common due date total earliness/tardiness scheduling with machine unavailability

“…Jobs are nonresumable, and a single machine is unavailable periodically for a fixed maintenance duration. In this stream of research, Low et al (2015) incorporate a single fixed planned maintenance period with non-resumable jobs into their problem of minimizing the sum of the absolute deviations of the job completion times from a common due date on a single machine. A mixed-integer programming formulation of the problem at hand is followed by the development of an ant colony heuristic for large-scale instances.…”