A bicriteria approach to minimize the total weighted number of tardy jobs with convex controllable processing times and assignable due dates

We study a single-machine scheduling problem in a flexible framework where both job processing times and due dates are decision variables to be determined by the scheduler. The model can also be applied for quoting delivery times when some parts of the jobs may be outsourced. We analyze the problem for two due date assignment methods and a convex resource consumption function. For each due date assignment method, we provide a bicriteria analysis where the first criterion is to minimize the total weighted number of tardy jobs plus due date assignment cost, and the second criterion is to minimize total weighted resource consumption. We consider four different models for treating the two criteria. Although the problem of minimizing a single integrated objective function can be solved in polynomial time, we prove that the three bicriteria models are NP\mathcal{NP}-hard for both due date assignment methods. We also present special cases, which frequently occur in practice, and in which all four models are polynomially solvable.     

Energetic reasoning revisited: application to parallel machine scheduling

We consider the problem of minimizing makespan on identical parallel machines subject to release dates and delivery times. We present several new feasibility tests and adjustment techniques that consistently improve the classical energetic reasoning approach. Computational results carried out on a set of hard instances provide strong evidence that the performance of a state-of-the-art exact branch-and-bound algorithm is substantially improved through embedding the proposed enhanced energetic reasoning.     

Benchmarks for scheduling on a single machine against restrictive and unrestrictive common due dates

We consider the NP-hard problem of scheduling jobs on a single machine against common due dates with respect to earliness and tardiness penalties. The paper covers two aspects: Firstly, we develop a problem generator and solve 280 instances with two new heuristics to obtain upper bounds on the optimal objective function value. Secondly, we demonstrate computationally that our heuristics are efficient in obtaining near-optimal solutions for small problem instances. The generated problem instances in combination with the upper bounds can be used as benchmarks for future approaches in the field of common due-date scheduling.Scope and purposeIn connection with just-in-time production and delivery, earliness as well as tardiness penalties are of interest. Thus scheduling against common due dates has received growing attention during the last decade. Many algorithms have been developed to solve the different variants of this problem. But whenever a new algorithm for scheduling against common due dates is proposed, its quality is assessed only on a few self-generated examples. Hence it is difficult to evaluate the various approaches, particularly in comparison with each other. Therefore the goal of this paper is to present numerous benchmark problems together with some upper bounds on the optimal objective function value.     

Pre-Emptive Scheduling Problems with Controllable Processing Times

We consider a range of single machine and identical parallel machine pre-emptive scheduling models with controllable processing times. For each model we study a single criterion problem to minimize the compression cost of the processing times subject to the constraint that all due dates should be met. We demonstrate that each single criterion problem can be formulated in terms of minimizing a linear function over a polymatroid, and this justifies the greedy approach to its solution. A unified technique allows us to develop fast algorithms for solving both single criterion problems and bicriteria counterparts.     

Using a branch-and-bound and a genetic algorithm for a single-machine total late work scheduling problem

Scheduling with learning effects has received a lot of research attention lately. On the other hand, it is commonly seen that time restrictions are usually modeled by due dates or deadlines and the quality of schedules is estimated with reference to these parameters. One of the performance measures involving due dates is the late work criterion, which is relatively unexplored. Thus, we study a single-machine scheduling problem with a position-based learning effect. The objective is to minimize the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. We attempt to develop a branch-and-bound algorithm incorporating with some dominance rules and a lower bound for the optimal solution. For saving computational time, we also propose three heuristic-based genetic algorithms for the near-optimal solution. Finally, the computational results of proposed algorithms are also provided.     

Preemptive Scheduling on Uniform Parallel Machines with Controllable Job Processing Times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan.     

Integrated production and outbound distribution scheduling problems with job release dates and deadlines

In this paper, we study an integrated production and outbound distribution scheduling model with one manufacturer and one customer. The manufacturer has to process a set of jobs on a single machine and deliver them in batches to the customer. Each job has a release date and a delivery deadline. The objective of the problem is to issue a feasible integrated production and distribution schedule minimizing the transportation cost subject to the production release dates and delivery deadline constraints. We consider three problems with different ways how a job can be produced and delivered: non-splittable production and delivery (NSP–NSD) problem, splittable production and non-splittable delivery problem and splittable production and delivery problem. We provide polynomial-time algorithms that solve special cases of the problem. One of these algorithms allows us to compute a lower bound for the NP-hard problem NSP–NSD, which we use in a branch-and-bound (B&B) algorithm to solve problem NSP–NSD. The computational results show that the B&B algorithm outperforms a MILP formulation of the problem implemented on a commercial solver.     

On the exact solution of the no-wait flow shop problem with due date constraints

This paper deals with the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, the jobs should be completed before their respective due dates; due date constraints are dealt with as hard constraints. The considered performance criterion is makespan. The problem is strongly NP-hard. This paper develops a number of distinct mathematical models for the problem based on different decision variables. Namely, a mixed integer programming model, two quadratic mixed integer programming models, and two constraint programming models are developed. Moreover, a novel graph representation is developed for the problem. This new modeling technique facilitates the investigation of some of the important characteristics of the problem; this results in a number of propositions to rule out a large number of infeasible solutions from the set of all possible permutations. Afterward, the new graph representation and the resulting propositions are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the mathematical models and to compare them with the developed exact algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.     

A bicriterion approach to time/cost trade-offs in scheduling with convex resource-dependent job processing times and release dates

This paper presents a bicriterion analysis of time/cost trade-offs for the single-machine scheduling problem where both job processing times and release dates are controllable by the allocation of a continuously nonrenewable resource. Using the bicriterion approach, we distinguish between our sequencing criterion, namely the makespan, and the cost criterion, the total resource consumed, in order to construct an efficient time/cost frontier. Although the computational complexity of the problem of constructing this frontier remains an open question, we show that the optimal job sequence is independent of the total resource being used; thereby we were able to reduce the problem to a sequencing one. We suggest an exact dynamic programming algorithm for solving small to medium sizes of the problem, while for large-scale problems we present some heuristic algorithms that turned out to be very efficient. Five different special cases that are solvable by using polynomial time algorithms are also presented.     

A bicriteria two-machine flow-shop serial-batching scheduling problem with bounded batch size

We consider the two-machine flow-shop serial-batching scheduling problem where the machines have a limited capacity in terms of the number of jobs. Two criteria are considered here. The first criterion is the number of batches to be minimized. This criterion reflects situations where processing of any batch induces a fixed cost, which leads to a total cost proportional to the number of batches. The second criterion is the makespan. This model is relevant in different production contexts, especially when considering joint production and inbound delivery scheduling. We study the complexity of the problem and propose two polynomial-time approximation algorithms with a guaranteed performance. The effectiveness of these algorithms is evaluated using numerical experiments. Exact polynomial-time algorithms are also provided for some particular cases.     

Heuristics for hybrid flow shops with controllable processing times and assignable due dates

This paper considers a generalization of the permutation flow shop problem that combines the scheduling function with the planning stage. In this problem, each work center consists of parallel identical machines. Each job has a different release date and consists of ordered operations that have to be processed on machines from different machine centers in the same order. In addition, the processing times of the operations on some machines may vary between a minimum and a maximum value depending on the use of a continuously divisible resource. We consider a nonregular optimization criterion based on due dates which are not a priori given but can be fixed by a decision-maker. A due date assignment cost is included into the objective function. For this type of problems, we generalize well-known approaches for the heuristic solution of classical problems and propose constructive algorithms based on job insertion techniques and iterative algorithms based on local search. For the latter, we deal with the design of appropriate neighborhoods to find better quality solution. Computational results for problems with up to 20 jobs and 10 machine centers are given.Scope and purposeTraditional research to solve multi-stage scheduling problems has focused on regular measures of performance based on a single criterion and assumes that several decisions related to due dates and processing times have already been made. However, in many industrial scheduling practices, managers develop schedules based on multicriteria and have to decide the due dates and processing times as part of the scheduling activities. Further, in practical scheduling situations, there are multiple machines at each stage and the objective function often reflects the total cost of processing, earliness and tardiness. Such scheduling problems require significantly more effort in finding acceptable solutions and hence have not received much attention in the literature. For this reason, this paper considers one such hybrid flow shop scheduling problem involving nonregular measures of performance, controllable processing times, and assignable due dates. We combine and generalize the existing approaches for the classical flow shop problem to the problem under consideration. Computational experiments are used to evaluate the utility of the proposed algorithms for the generalized scheduling problems. Brah and Hunsucker (European Journal of Operational Research 1991;51:88–99) and Nowicki and Smutnicki (European Journal of Operational Research 1998;106:226–253) describe branch and bound and tabu search algorithms for the approach used in the development of heuristic algorithms can also be adapted to several other complex practical scheduling problems.     

Beam-PSO优化算法在多行程车辆路径问题的应用

针对城市物流配送系统，研究了一类带时间窗和释放时间约束的多行程车辆路径问题。首先，对该运输调度问题进行了描述，构建了以总配送时长最小化为目标的数学模型。其次，为了快速获得问题的满意解，提出了Beam-PSO优化算法。在算法设计中，结合该问题的性质，构建了基于随机键的编解码方法，以克服标准粒子群算法无法直接适用于求解离散问题的不足。同时，设计了基于Beam search优化技术的局部搜索流程，用于强化算法的优化性能。最后，进行了仿真实验，实验结果表明了Beam-PSO优化算法的可行性和有效性。     

New Solution Approaches to the General Single- Machine Earliness-Tardiness Problem

This paper addresses the general single-machine earliness-tardiness problem with distinct release dates, due dates, and unit costs. The aim of this research is to obtain an exact nonpreemptive solution in which machine idle time is allowed. In a hybrid approach, we formulate and then solve the problem using dynamic programming (DP), while incorporating techniques from branch-and-bound (BB). This approach (DP-BB) has been proven to be effective in solving certain types of scheduling problems. We further propose a new adaptation of the approach to a general problem with a nonregular objective function. To address some shortcomings of DP-BB, we also apply a BB approach in which partial dynamic programming dominance (BB-PDP) is exploited. Computational experiments were conducted with randomly generated test instances in order to evaluate the effectiveness of the two approaches. The results clearly showed that our new approaches can solve all the instances with up to 40 jobs and most of the instances with 50 jobs, which outperforms those frequently used approaches in scheduling research.     

Scheduling with job release dates, delivery times and preemption penalties

We consider in this paper the single-machine preemptive scheduling problem with job release dates, delivery times and preemption penalties, where each time a job is started, whether initially or after preemption, a job-dependent setup must take place. First, we prove that the problem is strongly NP-hard. Then, we present a dynamic programming algorithm and a polynomial time approximation scheme.     

Deteriorating job scheduling to minimize the number of late jobs with setup times

Deteriorating jobs scheduling problems have been widely studied recently. However, research on scheduling problems with deteriorating jobs has rarely considered explicit setup times. With the current emphasis on customer service and meeting the promised delivery dates, we consider a single-machine scheduling problem to minimize the number of late jobs with deteriorating jobs and setup times in this paper. We derive some dominance properties, a lower bound, and an initial upper bound by using a heuristic algorithm to speed up the search process of the branch-and-bound algorithm. Computational experiments show that the algorithm can solve instances up to 1000 jobs in a reasonable amount of time.     

The One-Machine Problem with Earliness and Tardiness Penalties

We address the one-machine problem in which the jobs have distinct due dates, earliness costs, and tardiness costs. In order to determine the minimal cost of such a problem, a new lower bound is proposed. It is based on the decomposition of each job in unary operations that are then assigned to the time slots, which gives a preemptive schedule. Assignment costs are defined so that the minimum assignment cost is a valid lower bound. A branch-and-bound algorithm based on this lower bound and on some new dominance rules is experimentally tested.     

Inverse scheduling with maximum lateness objective

We study a range of counterparts of the single-machine scheduling problem with the maximum lateness criterion that arise in the context of inverse optimization. While in the forward scheduling problem all parameters are given and the objective is to find the optimal job sequence for which the value of the maximum lateness is minimum, in inverse scheduling the exact values of processing times or due dates are unknown, and they should be determined so that a prespecified solution becomes optimal. We perform a fairly complete classification of the corresponding inverse models under different types of norms that measure the deviation of adjusted parameters from their given estimates.     

Modeling realistic hybrid flexible flowshop scheduling problems

This paper aims to contribute to the recent research efforts to bridge the gap between the theory and the practice of scheduling by modelizing a realistic manufacturing environment and analyzing the effect of the inclusion of several characteristics in the problem formulation. There are several constraints and characteristics that affect the scheduling operations at companies. While these constraints are many times tackled in the literature, they are seldom considered together inside the same problem formulation. We propose a formulation along with a mixed integer modelization and some heuristics for the problem of scheduling n jobs on m stages where at each stage we have a known number of unrelated machines. The jobs might skip stages and, therefore, we have what we call a hybrid flexible flowshop problem. We also consider per machine sequence-dependent setup times which can be anticipatory and non-anticipatory along with machine lags, release dates for machines, machine eligibility and precedence relationships among jobs. Manufacturing environments like this appear in sectors like food processing, ceramic tile manufacturing and several others. The optimization criterion considered is the minimization of the makespan. The MIP model and the heuristics proposed are tested against a comprehensive benchmark and the results evaluated by advanced statistical tools that make use of decision trees and experimental designs. The results allow us to identify the constraints that increase the difficulty.     

An improved estimate of the robust stability bound of time-delay systems with norm-bounded uncertainty

The robust stability problem of linear time-delay systems with norm-bounded uncertainty is further investigated by using a refined discretized Lyapunov functional approach. A new stability criterion is derived. The computational requirement is reduced for the same discretization mesh. Examples show that the results obtained by this new criterion significantly improve the estimate of the stability limit over some existing results in the literature.     

The pickup and delivery problem with time windows and handling operations

This paper introduces the pickup and delivery problem with time windows and handling operations. In this problem, the loading compartment of a vehicle is modeled as a linear LIFO stack. When an item is picked up, it is positioned on top of the stack. When it is on top of the stack, it can be delivered without additional handling. Otherwise, items on top must be unloaded before the delivery and reloaded afterwards, which requires time. We define two rehandling policies. For both policies, rehandling is only allowed at delivery locations and there is no specific reloading order for the rehandled items. Under the first policy, only compulsory rehandling is allowed. Under the second policy, in addition to compulsory rehandling, preventive rehandling is allowed. For each policy, we propose a branch-price-and-cut algorithm with an ad hoc dominance criterion for the labeling algorithm used to generate routes. Computational results are reported on benchmark instances for the pickup and delivery problem with time windows.