General Position-dependent Processing Times Research Articles

Due-Window Assignment Methods and Scheduling with Generalized Positional-Dependent Weights

We focus on a single-machine scheduling problem with common and slack due-window assignment methods. Both the job sequence and due-windows are decision variables to be determined by the decision maker. We consider the following performance criterion: the total weighted number of early and late jobs plus the total weighted of earliness, tardiness and due-window assignment cost, where the weights depend on the position in which a job is scheduled. Some properties are established, and it is shown that the problem can be solved in [Formula: see text] time, where [Formula: see text] is the number of jobs. The extensions of the model are to cases of general position-dependent processing times and time-dependent processing times.

Due-window assignment scheduling problems with position-dependent weights on a single machine

ABSTRACTThis article deals with an integrated optimization problem of production scheduling and common due-window assignment on a single machine. The objective is to minimize the total cost, which is a weighted sum function of earliness and tardiness, due-window starting time, and due-window size, where the weights only depend on their position in a sequence (i.e. position-dependent weights). A polynomial time solution algorithm is provided for the corresponding problem. The problem can also be extended to slack due-windows assignment and general position-dependent processing times. It is proved that both these extensions remain polynomially solvable.

Comments on “Proportionate flowshops with general position dependent processing times” [Inf. Process. Lett. 111 (2011) 174–177] and “Minimizing total load on a proportionate flowshop with position-dependent processing times and job-rejection” [Inf. Process. Lett. 132 (2018) 39–43

Mosheiov [4] and Fiszman and Mosheiov [2] studied flowshop scheduling problems with position dependent job processing times and proposed algorithms which employ solving an assignment problem as a subroutine. This subroutine needs a correction. We describe such a correction. The running times of the corrected algorithms match the best known running times for the studied problems.

A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection

We study a scheduling problem with the objective of minimizing total absolute deviation of completion times (TADC). TADC is considered here in the most general form studied so far: the machine setting is that of parallel unrelated, job processing time are assumed to be position-dependent with no restrictions on the functional form, and the option of processing only a subset of the jobs (i.e., job-rejection) is allowed. We show that minimizing TADC in this very general form remains polynomially solvable in the number of jobs.

Due-window assignment and scheduling with general position-dependent processing times involving a deteriorating and compressible maintenance activity

In this paper, we consider common due-window assignment and scheduling problems with general position-dependent processing times involving deteriorating and compressible maintenance activity on a single machine. Two models associated with maintenance activity are examined in this article, in which the maintenance length is assumed to be either time-dependent and compressible or position-dependent and compressible. The objective is to find jointly the location and size of due-window, position of maintenance as well as resource amount allocated to it, and job sequence to minimise a total cost function based on earliness, tardiness, window location, window size and resource cost. We show that the problem considered in each of the two models’ setting can be optimally solved with polynomial time algorithm by reducing to assignment problem. Finally, two examples are provided to illustrate the solution procedures.

Scheduling a deteriorating maintenance activity and due-window assignment

Several papers published during the last decade dealt with scheduling a maintenance activity and considered a new setting, where the maintenance duration is assumed to be deteriorating, i.e., it requires more time or effort if it is delayed. We study a deteriorating maintenance in the context of due-window assignment, where a time interval is determined such that jobs completed within this interval are “on-time”, whereas early and tardy jobs are penalized. Thus, our paper extends known models by considering simultaneously a deteriorating maintenance and due-window. Two deterioration types are considered: time-dependent (where the maintenance time increases as a function of its starting time), and position-dependent (where it is a function of its position in the sequence). The classical assumption of position-independent processing times was considered first, and then the model is extended to general position-dependent processing times. We prove several properties of the optimal timing of the due-window and of the maintenance. Consequently, we show that all the problems studied here are solved in O(n4), where n is the number of jobs.

Single Machine Scheduling and due Date Assignment with Past-Sequence-Dependent Delivery Times and General Position-Dependent Processing Times

We studied single machine scheduling problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depended on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyzed these problems with two different due date assignment methods and conclude that the problems are polynomial time solvable.

A note on single machine scheduling and due date assignment with general position-dependent processing times

This note considers single machine scheduling and due date assignment in which a job’s processing time depends on its position in a sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and the total earliness of the scheduled jobs. We analyse these problems with three different due date assignment methods. We provide a generic polynomial-time dynamic programming algorithm to solve the problems.

Single machine scheduling problems with general position-dependent processing times and past-sequence-dependent delivery times

This paper considers single machine scheduling with past-sequence-dependent (psd) delivery times, in which the processing time of a job depends on its position in a sequence. We provide a unified model for solving single machine scheduling problems with psd delivery times. We first show how this unified model can be useful in solving scheduling problems with due date assignment considerations. We analyze the problem with four different due date assignment methods, the objective function includes costs for earliness, tardiness and due date assignment. We then consider scheduling problems which do not involve due date assignment decisions. The objective function is to minimize makespan, total completion time and total absolute variation in completion times. We show that each of the problems can be reduced to a special case of our unified model and solved in O(n 3) time. In addition, we also show that each of the problems can be solved in O(nlogn) time for the spacial case with job-independent positional function.

Minmax scheduling problems with common flow-allowance

In due-date assignment problems with a common flow-allowance, the due-date of a given job is defined as the sum of its processing time and a job-independent constant. We study flow-allowance on a single machine, with an objective function of a minmax type. The total cost of a given job consists of its earliness/tardiness and its flow-allowance cost components. Thus, we seek the job schedule and flow-allowance value that minimize the largest cost among all the jobs. Three extensions are considered: the case of general position-dependent processing times, the model containing an explicit cost for the due-dates, and the setting of due-windows. Properties of optimal schedules are fully analysed in all cases, and all the problems are shown to have polynomial time solutions.

Scheduling on parallel identical machines with job-rejection and position-dependent processing times

We solve scheduling problems which combine the option of job-rejection and general position-dependent processing times. The option of rejection reflects a very common scenario, where the scheduler may decide not to process a job if it is not profitable. The assumption of position-dependent processing time is a common generalization of classical settings, and contains the well-known and extensively studied special cases of “learning” and “aging”. The machine setting is parallel identical machines, and two scheduling measures are considered: total flow-time and total load. When the number of jobs is given, both problems are shown to be solved in polynomial time in the number of jobs. The special case of non-decreasing job-position processing times (“aging”) is shown to be solved much faster.

A short note on “Proportionate flowshops with general position-dependent processing times”

Recently, Mosheiov (2011) [1] studied a proportionate flowshop scheduling problem with general position-dependent processing times. The main result in this paper is correct. However, there is a minor error in the results of the special cases. In this short note, we show counterexamples and then offer new more strict conditions to resolve the special cases.

Minimizing the number of tardy jobs on a proportionate flowshop with general position-dependent processing times

In various real life scheduling systems job processing times vary according to the number of jobs previously processed. The vast majority of studies assume a restrictive functional form to describe job processing times. In this note, we address a scheduling problem with the most general job processing time functions. The machine setting assumed is an m-machine proportionate flowshop, and the objective function is minimum number of tardy jobs. We show that the problem can be formulated as a bottleneck assignment problem with a maximum cardinality constraint. An efficient polynomial time (O(n4logn)) solution is introduced.

Proportionate flowshops with general position-dependent processing times

Most scheduling studies assume constant (position-independent) job processing times. Most of the papers allowing position-dependent processing times consider only special cases, where the job processing times follow a specific function of the job-position. Polynomial time solutions have hardly been found for general position-dependent processing times in scheduling literature. In this note we provide one of these cases: we introduce a polynomial time solution for minimum makespan on an m-machine proportionate flowshop.