Optimal Due-date Research Articles

Research on position-dependent weights scheduling with delivery times and truncated sum-of-processing-times-based learning effect

<p style='text-indent:20px;'>This paper considers single-machine position-dependent weights scheduling problem with past-sequence-dependent delivery times and truncated sum-of-processing-times-based learning effect. The objective is to minimize the weighted sum of due date, and the number of early jobs and tardy jobs, where the weights are position-dependent weights. Under the common due date, slack due date and different due date assignments, the optimal properties are given, and the corresponding optimal solution algorithms are respectively proposed to obtain the optimal sequence and optimal due dates of jobs.</p>

A Bicriterion Approach to Due Date Assignment Scheduling in Single-Machine with Position-Dependent Weights

We study single-machine bicriteria scheduling problems with position-dependent weights. Due date costs and penalty costs can affect the decision-maker’s profit. Therefore, how to optimize the benefits and balance of these costs for decision-makers is the focus of this research. This paper discusses three models: weighted-sum scheduling problem, constrained scheduling problem, Pareto scheduling problem. It analyzes the properties of bicriteria schedule, determines the optimal due dates (usually referred to as different due dates: DIF), and gives the corresponding polynomial solvable algorithms.

Due date assignment scheduling with positional-dependent weights and proportional setup times.

In this paper, we investigate the single-machine scheduling problem that considers due date assignment and past-sequence-dependent setup times simultaneously. Under common (slack and different) due date assignment, the objective is to find jointly the optimal sequence and optimal due dates to minimize the weighted sum of lateness, number of early and delayed jobs, and due date cost, where the weight only depends on it's position in a sequence (i.e., a position-dependent weight). Optimal properties of the problem are given and then the polynomial time algorithm is proposed to obtain the optimal solution.

Minmax common due-window assignment and scheduling on a single machine with two competing agents

We study the classical method of common due-date assignment and focus on minmax objective functions. In due-date assignment problems, the objective is to find the optimal due-date and job sequence that minimize the total earliness, tardiness and due-date-related costs. We extend the single-agent problem to a setting involving two competing agents and to a setting of multi-agent. In the two-agent setting (herein agents A and B), the scheduler needs to minimize the maximum cost of the agent A, subject to an upper bound on the maximal cost of the agent B. In the general model of multi-agent scheduling, the scheduler needs to minimize the cost among all A-type agents, subject to an agent-dependent upper bound on the maximal cost of the B-type agents. We further generalize the problems to the method of common due-window assignment. For all studied problems, we introduce efficient polynomial time solutions.

Two-agent single-machine scheduling with unrestricted due date assignment

We address two scheduling problems arising when two agents (agents A and B), each with a set of jobs, compete to perform their respective jobs on a common machine, where the due dates of agent A’s jobs are decision variables to be determined by the scheduler. Specifically, the objective is to determine the optimal due dates for agent A’s jobs and the job sequence for both agents’ jobs simultaneously to minimize the total cost associated with the due date assignment and weighted number of tardy jobs of agent A, while keeping the maximum of regular functions (associated with each B-job) or the number of tardy jobs of agent B below or at a fixed threshold. We prove that both problems are NP-hard in the strong sense and develop polynomial or pseudo-polynomial solutions for some important special cases.

Scheduling a Single Machine with Job Rejection and Multiple Common due Dates Assignment

This paper studies a single machine scheduling with job rejection and multiple common due dates assignment. A job is either rejected, in which a rejection penalty has to be paid, or accepted and processed on the machine. There is a cost if the job is completed prior or after the due date. The objective is to determine the optimal due dates, the set of jobs assigned to each due date and the optimal sequence of jobs to minimize a total costs based on earliness, tardiness, multiple common due dates and rejection cost. We provide dynamic programming algorithms and show that the problem is solvable in polynomial time.

Setting optimal due dates in a basic safe-scheduling model

We examine a basic stochastic sequencing model with due dates as decisions. The objective is to make due dates as tight as possible while meeting service level constraints. We develop an optimizing procedure using branch and bound, and we evaluate the performance of heuristic procedures as well.

Scheduling Due Dates Assignment with Simultaneous Considerations of Time-Dependent and Position-Dependent Deterioration Effects and Deteriorating Maintenance on a Single Machine

The due date assignment has been popular issues related to the interaction between various participants of the supply chain. In this paper, we investigate single machine due dates assignment scheduling problems with deterioration effects and deteriorating maintenance simultaneously. In the proposed model, the actual processing time of a job is not only dependent on the job's scheduled position, it also depends on the time expended by the jobs already processed. To counteract the deterioration effects of the machine, we assume that at most one maintenance is allowed throughout the scheduling horizon. The common due date assignment model and the slack due date assignment model are examined, respectively. The goal is to determine jointly the optimal due dates, the optimal maintenance position, and the optimal schedule to minimize the total penalty function based on earliness, tardiness and due dates. We show that all the problems studied can be optimally solved in polynomial time algorithms.

Unrelated parallel-machine scheduling simultaneously with rate-modifying activities and earliness and tardiness penalties

In this paper, we consider a scheduling problem simultaneously with rate-modifying activities and earliness and tardiness penalties on an unrelated parallel-machine setting. We assume that each machine has at most one rate-modifying activity to improve its production efficiency during the scheduling horizon and all the jobs have a common due-date. The objective is to determine jointly the optimal positions of rate-modifying activities, the optimal common due-date of all jobs, and the optimal schedule to minimize the sum of earliness and tardiness costs. We show that the problem can be optimally solved in polynomial time.

Supplier risk management: An economic model of P-chart considered due-date and quality risks

Abstract We present a quality risk management model for a supplier–assembler structure supply chain. To mitigate quality risks, supply chain members are coordinated by sharing their information. A good example of such supply chain is the keiretsu of Japanese automobile industries. To be able to quick respond to the assembler's feedback (e.g., quality problems) has become a key point of a supplier's competitive edge. This ability is also useful for removing bottlenecks among a supply chain. In the setting of a due-date to treat an assignable cause, because idle risk and delay risk have a trade-off relationship, find out the optimal due-date becomes a problem of great interest to the supplier. We develop a P-chart solution model to help suppliers find out the optimal due-date that minimizes the total cost. We also clarify the relations among various risks by analyzing proposed model. We find that a longer due-time should be set when either the sampling interval is longer or a high quality is demanded.

Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine

This paper considers the problem of scheduling deteriorating jobs and due date assignment on a single machine. The actual processing time of a job is a linear increasing function of its starting time. The problem is to determine the optimal due dates and the processing sequence simultaneously to minimize costs for earliness, due date assignment and weighted number of tardy jobs. We present polynomial-time algorithms to solve the problem in the case of two popular due date assignment methods: CON and SLK.

Single machine multiple common due dates scheduling with learning effects

In this paper, we consider the problem of simultaneous determination of optimal due dates and optimal schedule for the single machine problem with multiple common due dates. The penalty for a job is assumed to be a linear function of the due date and the earliness/tardiness for the job. The objective function is to minimize the total penalty for all jobs. We show that with the introduction of learning to job processing times the problem remains polynomially solvable for a given number of multiple common due dates.

Single-machine scheduling with waiting-time-dependent due dates

We consider a single-machine scheduling problem in which due dates are linear functions of the job waiting-times and the objective is to minimize the maximum lateness. An optimal sequence is constructed by implementing an index-based priority rule for a fixed value of the due date normalizing constant k. We determine in polynomial time all the k value ranges so that the optimal sequence remains the same within each range. The optimal due dates are computed as linear functions of the global optimal value of k. The overall procedure is illustrated in a numerical example.

A Production Planning Model for an Unreliable Production Facility: Case of Finite Horizon and Single Demand

We study a two-level inventory system that is subject to failures and repairs. The objective is to minimize the expected total cost so as to determine the production plan for a single quantity demand. The expected total cost consists of the inventory carrying costs for finished and unfinished items, the backlog cost for not meeting the demand due-date, and the planning costs associated with the ordering schedule of unfinished items. The production plan consists of the optimal number of lot sizes, the optimal size for each lot, the optimal ordering schedule for unfinished items, and the optimal due-date to be assigned to the demand. To gain insight, we solve special cases and use their results to device an efficient solution approach for the main model. The models are solved to optimality and the solution is either obtained in closed form or through very efficient algorithms.

A note on due-date assignment and single-machine scheduling with deteriorating jobs

In this note, we study a single-machine scheduling problem with deteriorating jobs whose processing times are an increasing function of their start times. The objective is to determine the optimal due-date and schedule simultaneously to minimize the total of due-date, earliness and tardiness penalties. We give a concise analysis of the problem and provide a polynomial time algorithm to solve the problem. Moreover, the algorithm can be easily applied to the ‘mirror’ scheduling problem in which the actual processing time of a job is a decreasing function of its starting time.

Optimal Due Date Assignment and Resource Allocation to Minimize the Weighted Number of Tardy Jobs on a Single Machine

With the increased emphasis on the effective management of operational issues in supply chains, the timely delivery of products has become even more important. Companies have to quote attainable delivery dates and then meet these, or face large tardiness penalties. We study systems that can be modeled by single-machine scheduling problems with due date assignment and controllable job-processing times, which are either linear or convex functions of the amount of a continuously divisible and nonrenewable resource that is allocated to the task. The due date assignment methods studied include the common due date, the slack due date, which reflects equal waiting time allowance for the jobs, and the most general method of unrestricted due dates, when each job may be assigned a different due date. For each combination of due date assignment method and processing-time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes the weighted number of tardy jobs, and due date assignment, makespan, and total resource consumption costs.

A production planning model for an unreliable production facility: Case of finite horizon and single demand

We study a two-level inventory system that is subject to failures and repairs. The objective is to minimize the expected total cost so as to determine the production plan for a single quantity demand. The expected total cost consists of the inventory carrying costs for finished and unfinished items, the backlog cost for not meeting the demand due-date, and the planning costs associated with the ordering schedule of unfinished items. The production plan consists of the optimal number of lot sizes, the optimal size for each lot, the optimal ordering schedule for unfinished items, and the optimal due-date to be assigned to the demand. To gain insight, we solve special cases and use their results to device an efficient solution approach for the main model. The models are solved to optimality and the solution is either obtained in closed form or through very efficient algorithms.

Harmonization simulation model for managing several stochastic projects

A highly complicated project management system including several simultaneously realized PERT-COST type network projects, is considered. The projects are of different importance and significance; for each project its corresponding priority index is pre-given. The total budget at the project management disposal to carry out all the projects, is limited. Given for each project its priority value, the problem is to determine optimal budget assignments and optimal due dates of accomplishing each project, to maximize the weighted sum of the projects’ utilities. The problem centers on maximizing the system’s utility by implementing the harmonization model for each single project, which has been outlined in our previous publication [Math. Comput. Simul. (2002)]. Thus, the paper under consideration is an essential extension of that publication. The system’s harmonization model comprises two levels. At the upper level a high-speed lookover search algorithm is implemented, together with a partial harmonization model to determine the projects’ reliability values. At the lower level a linear programming model is imbedded under certain assumptions.

Economic due-date setting in job-shops based on routing and workload dependent flow time distribution functions

The trade-off between the length of the lead times quoted to the customers and the delivery reliability has been investigated by many authors. However, only a few studies do this in an economic setting. In this study, the setting of cost optimal due dates taking into account lead-time related and tardiness related costs is investigated. More specifically, in setting the internal due dates, which are used for determining the priorities on the shop floor, and in determining the expected order flow time probability density functions which are used for setting the external due dates, the work load is taken into account. From this study, it follows that this approach leads to (much) lower costs as compared to the situation with workload independent order flow time p.d.f.'s.

Sequencing and due-date determination in the stochastic single machine problem with earliness and tardiness costs

Abstract This paper studies the problem of simultaneous due-date determination and sequencing of a set of n jobs on a single machine where processing times are random variables and job earliness and tardiness costs are distinct. The objective is to determine the optimal sequence and the optimal due-dates which jointly minimize the expected total earliness and tardiness cost. We present an analytical approach to determine optimal due-dates, and propose two efficient heuristics of order O(n log n) to find candidates for the optimal sequence. It is demonstrated that variations in processing times increase cost and affect sequencing and due-date determination decisions. Our illustrative examples as well as computational results show that the proposed model produces optimal sequences and optimal due-dates that are significantly different from those provided by the classical deterministic single machine models. Furthermore, our computational experiments reveal that the proposed heuristics perform well in providing either optimal sequences or good candidates with low overcosts.