Generating all efficient solutions of a rescheduling problem on unrelated parallel machines

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and stability measures. Our efficiency measure is the total flow time and stability measure is the total reassignment cost caused by the differences in the machine allocations in the initial and new schedules. We propose a branch and bound algorithm to generate all efficient solutions with respect to our efficiency and stability measures. We improve the efficiency of the algorithm by incorporating powerful reduction and bounding mechanisms. Our computational tests on large sized problem instances have revealed the satisfactory behaviour of our algorithm.     

Spread time considerations in operational fixed job scheduling

In this study, we consider the operational fixed job scheduling problem on identical parallel machines. We assume that the jobs have fixed ready times and deadlines, and spread time constraints are imposed on machines. Our objective is to select a set of jobs for processing so as to maximise the total weight. We show that the problem is strongly NP-hard, and we investigate several special polynomially solvable cases. We propose a branch and bound algorithm that employs size reduction mechanisms, dominance conditions, and powerful lower and upper bounds. The computational results reveal that the branch and bound algorithm returns optimal solutions for problem instances with up to 100 jobs in reasonable solution times.     

Scheduling about an unrestricted common due windowwith arbitrary earliness/tardiness penalty rates

We consider the NP-hard problem of scheduling jobs on a single machine about an unrestricted due window to minimize total weighted earliness and tardiness cost. Each job has an earliness penalty rate and a tardiness penalty rate that are allowed to be arbitrary. Earliness or tardiness cost is assessed when a job completes outside the due window, which may be an instant in time or a time increment defining acceptable job completion. In this paper we present properties that characterize the structure of an optimal schedule, present a lower bound, propose a two-step branch and bound algorithm, and report results from a computational experiment. We find that optimal solutions can be quickly obtained for medium-sized problem instances.     

Flexible assembly line design problem with fixed number of workstations

In the paper, we study a flexible assembly line design problem with equipment decisions. We assume the task times and equipment costs are correlated in the sense that for all tasks the cheaper equipment gives no smaller task time. Given the cycle time and number of workstations we aim to find the assignment of tasks and equipment to the workstations so as to minimise the total equipment cost. We develop a branch and bound algorithm that uses powerful lower bounds and reduction mechanisms. Our computational experiments have revealed that our algorithm can solve large-sized problem instances in reasonable solution times.     

A multi-point simulated annealing heuristic for solving multiple objective unrelated parallel machine scheduling problems

This study considers the problem of job scheduling on unrelated parallel machines. A multi-objective multi-point simulated annealing (MOMSA) algorithm was proposed for solving this problem by simultaneously minimising makespan, total weighted completion time and total weighted tardiness. To assess the performance of the proposed heuristic and compare it with that of several benchmark heuristics, the obtained sets of non-dominated solutions were assessed using four multi-objective performance indicators. The computational results demonstrated that the proposed heuristic markedly outperformed the benchmark heuristics in terms of the four performance indicators. The proposed MOMSA algorithm can provide a new benchmark for future research related to the unrelated parallel machine scheduling problem addressed in this study.     

An ant colony optimization heuristic for an integrated production and distribution scheduling problem

Make-to-order or direct-order business models that require close interaction between production and distribution activities have been adopted by many enterprises in order to be competitive in demanding markets. This article considers an integrated production and distribution scheduling problem in which jobs are first processed by one of the unrelated parallel machines and then distributed to corresponding customers by capacitated vehicles without intermediate inventory. The objective is to find a joint production and distribution schedule so that the weighted sum of total weighted job delivery time and the total distribution cost is minimized. This article presents a mathematical model for describing the problem and designs an algorithm using ant colony optimization. Computational experiments illustrate that the algorithm developed is capable of generating near-optimal solutions. The computational results also demonstrate the value of integrating production and distribution in the model for the studied problem.     

Bi criteria flexible assembly line design problem with equipment decisions

In this paper, we address the assembly line balancing and design problem of assigning tasks and equipment to work stations where there are several equipment alternatives for each task. We consider minimizing the total equipment cost and the number of work stations criteria. We aim to generate efficient solutions with respect to these criteria and propose a branch and bound algorithm whose efficiency is enhanced with powerful reduction and bounding mechanisms. We find that our algorithm is capable of solving problem instances with up to 25 tasks and five pieces of equipment.     

SOLVING THE MULTIPLE-MACHINE WEIGHTED FLOW TIME PROBLEM USING TABU SEARCH

In this paper we discuss the development and application of a new and more powerful method for solving the muldple-machine weighted flow time problem using a basic tabu search (TS) approach. Previous methods of solution used branch and bound and are computationally limited to problems of about 25 jobs. In a set of previously published problems with IS to 30 jobs, the new method achieved optimality in at least an order of magnitude less computation time than branch and bound first achieved the optimum. Studies of larger problems indicate that the new method maintains its ability to achieve superior solutions with only a modest growth in computational effort.     

Minimizing the Total Flow Time of n Jobs on a Network

This paper addresses the problem of determining a sequence for processing jobs on a machine, with sequence dependent setup times, such that the total flow time is minimized. The paper includes a branch and bound algorithm to find the optimal tour sequence.     

考虑有限可用性可控的两批次并行机调度研究

构建了一个考虑有限可用性可控的两批次并行机调度模型.每台机器在考虑周期内可实施一次关机操作,由此形成一个不可用的时间段,关机开始时间和长度都不确定,需要在决策过程中决定,目标是最小化由完成时间和关机时间组成的总成本.先证明了问题最优解的一些性质,然后采用了基于列生成的分支定界法来求解,并结合了动态规划法来提高方法的效率...     

Lagrangian relaxation and cut generation for sequence-dependent setup time flowshop scheduling problems to minimise the total weighted tardiness

The Lagrangian relaxation and cut generation technique is applied to solve sequence-dependent setup time flowshop scheduling problems to minimise the total weighted tardiness. The original problem is decomposed into individual job-level subproblems that can be effectively solved by dynamic programming. Two types of additional constraints for the violation of sequence-dependent setup time constraints are imposed on the decomposed subproblems in order to improve the lower bound. The decomposed subproblem with the additional setup time constraints on any subset of jobs is also effectively solved by a novel dynamic programming. Computational results show that the lower bound derived by the proposed method is much better than those of CPLEX and branch and bound for problem instances with 50 jobs and five stages with less computational effort.     

Design of flexible assembly line to minimize equipment cost

In this paper we develop an optimal and a heuristic algorithm for the problem of designing a flexible assembly line when several equipment alternatives are available. The design problem addresses the questions of selecting the equipment and assigning tasks to workstations, when precedence constraints exist among tasks. The objective is to minimize total equipment costs, given a predetermined cycle time (derived from the required production rate). We develop an exact branch and bound algorithm which is capable of solving practical problems of moderate size. The algorithm's efficiency is enhanced due to the development of good lower bounds, as well as the use of some dominance rules to reduce the size of the branch and bound tree. We also suggest the use of a branch-and-bound-based heuristic procedure for large problems, and analyze the design and performance of this heuristic.     

An integer concave minimization approach for the minimum concave cost capacitated flow problem on networks

Formulating the minimum concave cost capacitated network flow problem as an integer concave minimization problem, we establish finite branch and bound algorithms, in which the branching operation is the so–called integral rectangular partition and the bounding procedure is performed by the classical minimum linear cost flow problem on subnetworks. For the special case that the flow cost function is concave on a fixed number of arcs and linear on the others, an upper bound of the running time is given. Received: 19 July 1996 / Accepted: 8 July 1997     

A weighted approach for assembly line design with station paralleling and equipment selection

This paper studies the problem of assembly line design, focusing on station paralleling and equipment selection. Two problem formulations, minimizing the number of stations, and minimizing the total cost, are discussed. The latter formulation is demonstrated by several examples, for different assembly system conditions: labor intensive or equipment intensive, and with task times that may exceed the required cycle time. It is shown that the problem of assembly system design with parallel stations can be treated as a special case of the problem of equipment selection for an assembly line. A branch and bound optimal algorithm developed for the equipment selection problem is adapted to solve the parallel station problem. Experiments are designed to investigate and demonstrate the influence of system parameters, such as assembly sequence flexibility and cycle time, on the balancing improvement due to station paralleling. An ILP formulation is developed for the combined problem of station paralleling with equipment selection, and an optimal solution of an example problem is presented.     

Two-machine flow shop problem with unit-time operations and conflict graph

This paper addresses the problem of scheduling, on a two-machine flow shop, a set of unit-time operations subject to the constraints that some conflicting jobs cannot be scheduled simultaneously on different machines. In the context of our study, these conflicts are modelled by general graphs. The problem of minimising the maximum completion time (makespan) is known to be NP-hard in the strong sense. We propose a mixed-integer linear programming (MILP) model. Then, we develop a branch and bound algorithm based on new lower and upper bound procedures. We further provide a computer simulation to measure the performance of the proposed approaches. The computational results show that the branch and bound algorithm outperforms the MILP model and can solve instances of size up to 20,000 jobs.     

An improved branching scheme for the branch and bound procedure of scheduling n jobs on m parallel machines to minimize total weighted flowtime

A branch and bound procedure to solve the n job, m parallel machine problem for the weighted flowtime criterion has been developed by Elmaghraby and Park (1974) and further modified by Barnes and Brennan (1977). This paper proposes a branching scheme different from theirs and shows its superiority. Also, some new and simple results are presented which are easy to implement to obtain an efficient branch-and-bound algorithm. In addition, a new and improved lower bound is developed which is easy to compute.     

Simulated annealing based parallel genetic algorithm for facility layout problem

The facility layout problem (FLP), a typical combinational optimisation problem, is addressed in this paper by implementing parallel simulated annealing (SA) and genetic algorithms (GAs) based on a coarse-grained model to derive solutions for solving the static FLP with rectangle shape areas. Based on the consideration of minimising the material flow factor cost (MFFC), shape ratio factor (SRF) and area utilisation factor (AUF), a total layout cost (TLC) function is derived by conducting a weighted summation of MFFC, SRF and AUF. The evolution operations (including crossover, mutation, and selection) of GA provide a population-based global search in the space of possible solutions, and the SA algorithm can lead to an efficient local search near the optimal solution. By combing the characteristics of GA and SA, better solutions will be obtained. Moreover, the parallel implementation of simulated annealing based genetic algorithm (SAGA) enables a quick search for the optimal solution. The proposed method is tested by performing a case study simulation and the results confirm its feasibility and superiority to other approaches for solving FLP.     

Scheduling parallel machines to minimize weighted flowtime with family set-up times

We describe and evaluate several branch-and-bound algorithms for an identical parallel machine scheduling problem with family set-up times and an objective of minimizing total weighted flowtime. The algorithms differ by choice of lower bound method. Computational results suggest conditions favourable to a particular algorithm as well as the range of problem sizes that can be optimally solved in reasonable CPU time.     

Single-machine scheduling for minimizing total cost with identical,asymmetrical earliness and tardiness penalties

Costs of flowtime, earliness and tardiness should be incorporated in real production scheduling. This paper constructs a single-machine scheduling model with a common due date to minimize the total cost including an identical, asymmetric earliness-tardiness cost. Several dominance conditions necessary for an optimal schedule are derived. A branch and bound algorithm exploiting the conditions is proposed to find an optimal schedule for an unconstrained version of the scheduling problem. Numerical experiments are demonstrated to show the effectiveness of the proposed method.     

Parallel machine scheduling with limited controllable machine availability

Most machine scheduling models assume that either the machines are available all the time, or the time of their unavailability is fixed as a constraint. In this paper, we study the problem that neither the unavailability length nor the start time of machine unavailability is fixed. Instead, they would be determined in order to minimise the total cost involved with the completion time and the unavailable time. This model could represent a more realistic and complex situation, in which jobs and machines’ availability operations should be optimised simultaneously. After the model is formulated, some properties of the problem are presented. Then a branch and bound algorithm based on column generation approach is proposed to solve the problem. The computation results show that, within a reasonable computation time, the proposed algorithm can solve medium sized problems optimally.