Total weighted tardiness for scheduling MapReduce jobs on parallel batch machines

In the paper, we revisit the scheduling problems with integrated production and delivery on parallel batching machines. There are n jobs and m identical and parallel batching machines. The machines have identical capacities and the jobs have identical processing time. When a job is processed and delivered to customers in time, the company earns profit; otherwise, it earns nothing. A third party logistic (3PL) provider will be used to deliver the jobs. It provides certain vehicles with identical capacities at some certain time points. In the paper [Kai Li, Zhao-hong Jia, Joseph Y.-T. Leung (2015) Integrated production and delivery on parallel batching machines, European Journal of Operational Research, 247(3), 755-763.], the authors considered the scheduling problems and designed the algorithms to deal with them. But unfortunately, there are some wrong conclusions. Specifically, we construct counterexamples to show that both of Theorem 4 and Theorem 5 are invalid. Furthermore, we provide two faster algorithms than Algorithm Sch-Id-Size.

This paper studies a multi-stage and parallel-machine scheduling problem with job splitting which is similar to the traditional hybrid flow shop scheduling (HFS) in the solar cell industry. The HFS has one common hypothesis, one job on one machine, among the research. Under the hypothesis, one order cannot be executed by numerous machines simultaneously. Therefore, multiprocessor task scheduling has been advocated by scholars. The machine allocation of each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage is determined. However, machine allocation and production sequence decisions are highly interactive. As a result, this study, motivated from the solar cell industry, is going to explore these issues. The multi-stage and parallel-machine scheduling problem with job splitting simultaneously determines the optimal production sequence, multiprocessor task scheduling and machine configurations through dynamically splitting a job into several sublots to be processed on multiple machines. We formulate this problem as a mixed integer linear programming model considering practical characteristics and constraints. A hybrid-coded genetic algorithm is developed to find a near-optimal solution. A preliminary computational study indicates that the developed algorithm not only provides good quality solutions but outperforms the classic branch and bound method and the current heuristic in practice.

This research considers a broad range of scheduling problems in the parallel machines environment. Schedules are evaluated according to two independent components of the objective function: (1) machine cost consisting of a fixed cost and a variable cost; and (2) a regular measure of performance. This study is only one of a few that take the selection of machines among those available as a decision variable. For machine cost with concave functions, we derive the general characteristics of optimal solutions with respect to decisions on the number of machines to use and the way to load the machines. Our analysis is not restricted to the machine cost criterion, but may be extended to other measures with concave functions. Furthermore, we provide a Pareto efficient perspective in understanding the tradeoff between machine cost and any regular measure of performance.

A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

This paper deals with a parallel machine scheduling problem whose objective is to minimize a regular step total cost function. A real world application of the problem is presented, and Mixed Integer Linear Programming models are described for the cases with and without release dates, as well as a dedicated constraint generation procedure. Experimental results are reported and discussed to evaluate the relevance of the different approaches on well-known special cases and the general case.

Integrated problem of soaking pit heating and hot rolling scheduling in steel plants

Nowadays, intelligent vehicles have be used for transporting jobs in many manufacturing plants; thus, routing vehicles properly is very important for processing jobs. This paper studied a job shop scheduling problem considering intelligent vehicle transport. The problem is difficult to be handled because it needs to optimize the route of a vehicle and the processing sequences of jobs on machines simultaneously. To address this problem, a multi-attribute directed graph is proposed, in which a determined vehicle path associated with the attributes of job and machine is defined as a node and an undetermined vehicle path is defined as an arc; thereby, a mixed integer linear programming model is established. Numerical experiments show the effectiveness of the proposed model.

Global warming and climate change are threatening life on earth. These changes are due to human activities resulting in the emission of greenhouse gases. This is caused by intensive industrial activities and excessive fuel energy consumption. Recently, the scheduling of production systems has been judged to be an effective way to reduce energy consumption. This is the field of green scheduling, which aims to allocate jobs to machines in order to minimize total costs, with a focus on the sustainable use of energy. Several studies have investigated parallel-machine shops, with a special focus on reducing and minimizing the total consumed energy. Few studies explicitly include the idle energy of parallel machines, which is the energy consumed when the machines are idle. In addition, very few studies have considered the elimination of idle machine times as an efficient way to reduce the total consumed energy. This is the no-idle machine constraint, which is the green aspect of the research. In this context, this paper addresses the green parallel-machine scheduling problem, including release dates, delivery times, and no-idle machines, with the objective of minimizing the maximum completion time. This problem is of practical interest since it is encountered in several industry processes, such as the steel and automobile industries. A mixed-integer linear programming (MILP) model is proposed for use in obtaining exact solutions for small-sized instances. Due to the NP-hardness of the studied problem, and encouraged by the successful adaptation of metaheuristics for green scheduling problems, three genetic algorithms (GAs) using three different crossover operators and a simulated annealing algorithm (SA) were developed for large-sized problems. A new family of lower bounds is proposed. This was intended for the evaluation of the performance of the proposed algorithms over the average percent of relative deviation (ARPD). In addition, the green aspect was evaluated over the percentage of saved energy, while eliminating the idle-machine times. An extensive experimental study was carried out on a benchmark of test problems with up to 200 jobs and eight machines. This experimental study showed that one GA variant dominated the other proposed procedures. Furthermore, the obtained numerical results provide strong evidence that the proposed GA variant outperformed the existing procedures from the literature. The experimental study also showed that the adoption of the no-idle machine time constraints made it possible to reduce the total consumed energy by 29.57%, while the makespan (cost) increased by only 0.12%.

In this paper we report two mixed integer linear programming models to resolve the malleable jobs scheduling problem with single resource. Jobs’ release dates and deadlines are taken into account. The total amount of available resource of the system is variable at different times. Numerical experimentation is conducted to evaluate the performance variability between two introduced models. The objective of this optimization problem is to minimize the total weighted completion time.

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

Cellular manufacturing systems (CMS) are production systems that typically comprise a number of manufacturing cells served by a centralized material handling system. Designing such systems includes three major decisions; cell formation (CF), group layout (GL), and group scheduling (GS). Traditionally, these three decisions have been dealt with separately, which has usually lead to less than optimal system performance. In this paper, a new mixed integer linear programming (MILP) model is proposed for the integrated CF, GL and GS problem, to efficiently design and operate CMSs. The model solves the integrated problem, taking into consideration intercellular and intracellular transportation times to determine the optimal cell formation, layout of machines and schedule of parts on the machines, simultaneously. Sequence-dependent set up times are also considered in the model. The performance of the model is tested by solving problems previously introduced in the literature considering two objectives; minimizing the makespan or minimizing the mean flow time in the system. The results show that the proposed model is efficient in solving small to medium-sized problems.

This paper presents multiple readings to solve a vehicle routing problem with pickup and delivery (VRPPD) based on a real-life case study. Compared to theoretical problems, real-life ones are more difficult to address due to their richness and complexity. To handle multiple points of view in modeling our problem, we developed three different Mixed Integer Linear Programming (MILP) models, where each model covers particular constraints. The suggested models are designed for a mega poultry company in Tunisia, called CHAHIA. Our mission was to develop a prototype for CHAHIA that helps decision-makers find the best path for simultaneously delivering the company’s products and collecting the empty boxes. Based on data provided by CHAHIA, we conducted computational experiments, which have shown interesting and promising results.

The increasing level of customer awareness and application of environmental laws by governments, on the one hand, and the increasing number of competitors, on the other hand, has obliged industry owners to include green activities in the design of the supply chain network. Green activities include any type of action that reduces environmental degradation. Hence, this study seeks to develop a bi-objective, mixed integer linear programming (MILP) model for designing a green supply chain network. In the proposed model, the minimisation of costs and detrimental environmental effects are discussed. LP metric method is used to solve the bi-objective model and the proposed model is run by using simulated data in small and medium sizes in GAMS software. Finally, the model sensitivity analysis is measured in order to evaluate the validity and performance of the proposed model by using demand-driven scenarios. The results of this model indicate the effectiveness of the proposed model.

Mixed Integer Linear Programming Model for Vehicle Routing Problem for Hazardous Materials Transportation

This paper presents a mixed integer linear programming (MILP) model to operate a dual source heat pump (DSHP) optimally. The DSHP draws environmental energy from an underground ice storage tank (IST) or wind infrared sensitive collectors (WISC). WISC are further used to regenerate the IST. Thermal energy storage (TES) stores the thermal output of the DSHP. A single-objective optimisation approach is applied to minimise the operational cost of the DSHP over a scheduling horizon of 24h. The developed framework is tested on various days, which are representative for each season of the year. Furthermore, it is investigated how the variable electricity price market data influence the dynamic behaviour of the DSHP.