An improved ant colony optimization for scheduling identical parallel batching machines with arbitrary job sizes

In this paper we consider the problem of scheduling parallel batching machines with jobs of arbitrary sizes. The machines have identical capacity of size and processing velocity. The jobs are processed in batches given that the total size of jobs in a batch cannot exceed the machine capacity. Once a batch starts processing, no interruption is allowed until all the jobs are completed. First we present a mixed integer programming model of the problem. We show the computational complexity of the problem and optimality properties. Then we propose a novel ant colony optimization method where the Metropolis Criterion is used to select the paths of ants to overcome the immature convergence. Finally, we generate different scales of instances to test the performance. The computational results show the effectiveness of the algorithm, especially for large-scale instances.     

Scheduling of parallel machines with sequence-dependent batches and product incompatibilities in an automotive glass facility

This application is motivated by a complex real-world scheduling problem found in the bottleneck workstation of the production line of an automotive safety glass manufacturing facility. The scheduling problem consists of scheduling jobs (glass parts) on a number of parallel batch processing machines (furnaces), assigning each job to a batch, and sequencing the batches on each machine. The two main objectives are to maximize the utilization of the parallel machines and to minimize the delay in the completion date of each job in relation to a required due date (specific for each job). Aside from the main objectives, the output batches should also produce a balanced workload on the parallel machines, balanced job due dates within each batch, and minimal capacity loss in the batches. The scheduling problem also considers a batch capacity constraint, sequence-dependent processing times, incompatible product families, additional resources, and machine capability. We propose a two-phase heuristic approach that combines exact methods with search heuristics. The first phase comprises a four-stage mixed-integer linear program for building the batches; the second phase is based on a Greedy Randomized Adaptive Search Procedure for sequencing the batches assigned to each machine. We conducted experiments on instances with up to 100 jobs built with real data from the manufacturing facility. The results are encouraging both in terms of computing time—5 min in average—and quality of the solutions—less than 10 % relative gap from the optimal solution in the first phase and less than 5 % in the second phase. Additional experiments were conducted on randomly generated instances of small, medium, and large size.     

Annual production budget in the beverage industry

Driven by a real-world application in the beverage industry, this paper provides a design of a new VNS variant to tackle the annual production budget problem. The problem consists of assigning and scheduling production lots in a multi-plant environment, where each plant has a set of filling lines that bottle and pack drinks. Plans also consider final product transfers between the plants. Our algorithm fixes setup variables for family of products and determines production, inventory and transfer decisions by solving a linear programming (LP) model. As we are dealing with very large problem instances, it is inefficient and unpractical to search the entire neighborhood of the incumbent solution at each iteration of the algorithm. We explore the sensitivity analysis of the LP to guide the partial neighborhood search. Dual-reoptimization is also used to speed-up the solution procedure. Tests with instances from our case study have shown that the algorithm can substantially improve the current business practice, and it is more competitive than state-of-the-art commercial solvers and other VNS variants.     

A decision support system for production scheduling in an ion plating cell

Production scheduling is one of the major issues in production planning and control of individual production units which lies on the heart of the performance of manufacturing organizations. Traditionally, production planning decision, especially scheduling, was resolved through intuition, experience, and judgment. Machine loading is one of the process planning and scheduling problems that involves a set of part types and a set of tools needed for processing the parts on a set of machines. It provides solution on assigning parts and allocating tools to optimize some predefined measures of productivity. In this study, Ion Plating industry requires similar approaches on allocating customer's order, i.e. grouping production jobs into batches and arrangement of machine loading sequencing for (i) producing products with better quality products; and (ii) enabling to meet due date to satisfy customers. The aim of this research is to develop a Machine Loading Sequencing Genetic Algorithm (MLSGA) model to improve the production efficiency by integrating a bin packing genetic algorithm model in an Ion Plating Cell (IPC), such that the entire system performance can be improved significantly. The proposed production scheduling system will take into account the quality of product and service, inventory holding cost, and machine utilization in Ion Plating. Genetic Algorithm is being chosen since it is one of the best heuristics algorithms on solving optimization problems. In the case studies, industrial data of a precious metal finishing company has been used to simulate the proposed models, and the computational results have been compared with the industrial data. The results of developed models demonstrated that less resource could be required by applying the proposed models in solving production scheduling problem in the IPC.     

Parallel-identical-machine job-shop scheduling with different stage-dependent buffering requirements

The neglect of buffering requirements in a classical job shop scheduling system often results in inapplicability in many complex real-world applications. To overcome this inapplicability, a new and more generalised scheduling problem is proposed under different stage-dependent buffering requirements and parallel use of identical-function machine units at each processing stage in job shop environments. The problem is formulated as a mixed integer programming model that can be exactly solved by ILOG-CPEX for small-size instances. Moreover, a hybrid metaheuristic algorithm embedded with a state-of-the-art constructive algorithm is developed. The computational experiment shows that the proposed metaheuristic can efficiently solve large-size instances. The result analysis indicates that the proposed approach can provide better configuration of real-world scheduling systems. The proposed DBPMJSS methodology has a potential to analyse, model and solve many industrial systems with the requirements of buffering conditions, particularly for manufacturing, railway, healthcare and mining industries.     

Multi-degree cyclic scheduling of two robots in a no-wait flowshop

This paper addresses multi-degree cyclic scheduling of two robots in a no-wait flowshop, where exactly r(r > 1) identical parts with constant processing times enter and leave the production line during each cycle, and transportation of the parts between machines is performed by two robots on parallel tracks. The objective is to minimize the cycle time. The problem is transformed into enumeration of pairs of overlapping moves that cannot be performed by the same robot. This enumeration is accomplished by enumerating intervals for some linear functions of decision variables. The algorithm developed is polynomial in the number of machines for a fixed r, but exponential if r is arbitrary. Computational results with benchmark instances are reported. Note to Practitioners-This paper was motivated by the problem of cyclic scheduling of a no-wait production line, where a part must be processed without any interruption either on or between machines due to characteristics of the processing technology itself or the absences of storage capacity between operations of a part. Multi-degree schedules, in which multiple parts enter and leave the line during a cycle, usually have larger throughput rate than simple ones. This paper proposes an algorithm for multi-degree cyclic scheduling of a no-wait flowshop with two robots. Computational results show that the throughput rate can be really improved by using multi-degree schedules with two robots. However, we have not addressed the decision of the optimal value of the degree of the cycle. Furthermore, since we consider that the two robots travel along parallel tracks, the collision-avoidance constraints have been relaxed in the algorithm. In future research, we will address the two problems and generalize the algorithm to multi-robot cases.     

Flow shop batching and scheduling with sequence-dependent setup times

This paper addresses the flow shop batching and scheduling problem where sequence-dependent family setup times are present and the objective is to minimize makespan. We consider violating the group technology assumption by dividing product families into batches. In order to reduce setup times, inconsistent batches are formed on different machines, which lead to non-permutation schedules. To the best of our knowledge, this is the first time that the splitting of job families into inconsistent batches has been considered in a flow shop system. A tabu search algorithm is developed which contains several neighbourhood functions, double tabu lists and a multilevel diversification structure. Compared to the state-of-the-art meta-heuristics for this problem, the proposed tabu search algorithm achieves further improvement when the group scheduling assumption is dropped. Also, various experiments conducted on the benchmark problem instances confirm the benefits of batching. Therefore, it will be prudent for the practitioners to consider adopting inconsistent batches and non-permutation schedules to improve their operational efficiency within a reasonable amount of computational effort.     

Multihoist Cyclic Scheduling With Fixed Processing and Transfer Times

In this paper, we study the no-wait multihoist cyclic scheduling problem, in which the processing times in the tanks and the transfer times between tanks are constant parameters, and develop a polynomial optimal solution to minimize the production cycle length. We first analyze the problem with a fixed cycle length and identify a group of hoist assignment constraints based on the positions of and the relationships among the part moves in the cycle. We show that the feasibility of the hoist scheduling problem with fixed cycle length is consistent with the feasibility of this group of constraints which can be solved efficiently. We then identify all of the special values of the cycle length at which the feasibility property of the problem may change. Finally, the whole problem is solved optimally by considering the fixed-cycle-length problems at these special values. Note to Practitioners-Automated electroplating lines are commonly used in the production of many products, such as printed-circuit boards. The productivity of these systems depends heavily on effective scheduling of the material handling hoists that move the products between the processing tanks. This paper studies the hoist scheduling problem in systems where the processing times in the tanks and the intertank move times are fixed parameters. An efficient optimal algorithm is developed to solve the problem with any number of hoists. The resulting schedule can be programmed as programmable logic controller codes to directly control the hoist operations. The algorithm can also be used to develop heuristic solutions for multihoist scheduling in systems where the processing times may vary in given intervals.     

Color-Coating Production Scheduling for Coils in Inventory in Steel Industry

This paper studies a large-scale scheduling problem in iron and steel industry, called Color-Coating Production Scheduling for Coils in Inventory (CCPSCI). The problem is to select steel coils from those in the coil yard and to create a production schedule so that the productivity and product quality are maximized, while the production cost and other penalties are minimized. A tabu search (TS) algorithm is proposed for this problem. Results on real production instances show that the proposed method is much more effective and efficient than manual scheduling.      

求解考虑机器调整时间的并行机分批优化调度问题

基于目前车间调度问题是以单个或整批进行生产加工的并行机调度模型已不再符合实际工况下的车间生产。提出以最小化最大完工时间为优化目标,对遗传差分进化混合算法,灰狼差分进化混合算法进行了比较。为提高加工工件进行分批及分批之后子批的分配与排序效率,该问题是对不同规模的经典并行机调度问题进行求解并展示两种算法的求解,证明了灰狼差分进化混合算法在寻优性能上优于遗传差分进化混合算法,不仅具有更好的解的稳定性,而且具有更高的寻优精度。     

Order acceptance and scheduling to maximize total net revenue in permutation flowshops with weighted tardiness

The order acceptance and scheduling (OAS) problem is important in make-to-order production systems in which production capacity is limited and order delivery requirements are applied. This study proposes a multi-initiator simulated annealing (MSA) algorithm to maximize the total net revenue for the permutation flowshop scheduling problem with order acceptance and weighted tardiness. To evaluate the performance of the proposed MSA algorithm, computational experiments are performed and compared for a benchmark problem set of test instances with up to 500 orders. Experimental results reveal that the proposed heuristic outperforms the state-of-the-art algorithm and obtains the best solutions in 140 out of 160 benchmark instances.     

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.     

Development of hybrid evolutionary algorithms for production scheduling of hot strip mill

A hot strip mill (HSM) produces hot rolled products from steel slabs, and is one of the most important production lines in a steel plant. The aim of HSM scheduling is to construct a rolling sequence that optimizes a set of given criteria under constraints. Due to the complexity in modeling the production process and optimizing the rolling sequence, the HSM scheduling is a challenging task for hot rolling production schedulers. This paper first introduces the HSM production process and requirements, and then reviews previous research on the modeling and optimization of the HSM scheduling problem. According to the practical requirements of hot rolling production, a mathematical model is formulated to describe two important scheduling sub-tasks: (1) selecting a subset of manufacturing orders and (2) generating an optimal rolling sequence from the selected manufacturing orders. Further, hybrid evolutionary algorithms with integration of genetic algorithm (GA) and extremal optimization (EO) are proposed to solve the HSM scheduling problem. Computational results on industrial data show that the proposed HSM scheduling solution can be applied in practice to provide satisfactory performance.     

Minimizing maximum tardiness and delivery costs in a batched delivery system

High delivery costs usually urge manufacturers to dispatch their jobs in batches. However, dispatching the jobs in batches can have profound negative effects on important scheduling objective functions such as minimizing maximum tardiness. This paper considers a single machine scheduling problem with the aim of minimizing the maximum tardiness and delivery costs in a single-machine scheduling problem with batched delivery system. A mathematical model is developed for this problem which can serve to solve it with the help of a commercial solver. However, due to the fact that this model happens to be a mixed integer nonlinear programming model the solver cannot guarantee to reach the global solution. For this reason, a branch and bound algorithm (B&B) is presented to obtain the global solution. Besides, a heuristic algorithm for calculation of the initial upper bound is introduced. Computational results show that the algorithm can be beneficial for solving this problem, especially for large size instances.     

Minimising makespan for two batch-processing machines with non-identical job sizes in job shop

In this article, the job shop scheduling problem with two batch-processing machines is considered. The machines have limited capacity and the jobs have non-identical job sizes. The jobs are processed in batches and the total size of each batch cannot exceed the machine capacity. The processing times of a job on the two machines are proportional. We show the problem of minimising makespan is NP-hard in the strong sense. Then we provide an approximation algorithm with worst-case ratio no more than 4, and the running time of the algorithm is O(n?log?n). Finally, the performance of the proposed algorithm is tested by different levels of instances. Computational results demonstrate the effectiveness of the algorithm for all the instances.     

A heuristic algorithm for the distributed and flexible job-shop scheduling problem

The distributed manufacturing takes place in a multi-factory environment including several factories, which may be geographically distributed in different locations, or in a multi-cell environment including several independent manufacturing cells located in the same plant. Each factory/cell is capable of manufacturing a variety of product types. An important issue in dealing with the production in this decentralized manner is the scheduling of manufacturing operations of products (jobs) in the distributed manufacturing system. In this paper, we study the distributed and flexible job-shop scheduling problem (DFJSP) which involves the scheduling of jobs (products) in a distributed manufacturing environment, under the assumption that the shop floor of each factory/cell is configured as a flexible job shop. A fast heuristic algorithm based on a constructive procedure is developed to obtain good quality schedules very quickly. The algorithm is tested on benchmark instances from the literature in order to evaluate its performance. Computational results show that, despite its simplicity, the proposed heuristic is computationally efficient and promising for practical problems.     

Modeling and Solving Lot-Splitting Scheduling Problem Based on Process

In flexible job-shop batch scheduling problem, the optimal lot-size of different process is not always the same because of different processing time and set-up time. Even for the same process of the same workpiece, the choice of machine also affects the optimal lot-size. In addition, different choices of lot-size between the constrained processes will impact the manufacture efficiency. Considering that each process has its own appropriate lot-size, we put forward the concept of scheduling with lot-splitting based on process and set up the scheduling model of lot-splitting to critical path process as the core. The model could update the set of batch process and machine selection strategy dynamically to determine processing route and arrange proper lot-size for different processes, to achieve the purpose of optimizing the makespan and reducing the processing batches effectively. The experiment results show that, comparing with lot-splitting scheduling scheme based on workpiece, this model optimizes the makespan and improves the utilization efficiency of the machine. It also greatly decreases the machined batches(42%) and reduces the complexity of shop scheduling production management.     

A bi-layer optimization approach for a hybrid flow shop scheduling problem involving controllable processing times in the steelmaking industry

A steelmaking-continuous casting (SCC) scheduling problem is an example of complex hybrid flow shop scheduling problem (HFSSP) with a strong industrial background. This paper investigates the SCC scheduling problem that involves controllable processing times (CPT) with multiple objectives concerning the total waiting time, earliness/tardiness and adjusting cost. The SCC scheduling problem with CPT is seldom discussed in the existing literature. This study is motivated by the practical situation of a large integrated steel company in which the just-in-time (JIT) and cost-cutting production strategy have become a significant concern. To address this complex HFSSP, the scheduling problem is decomposed into two subproblems: a parallel machine scheduling problem (PMSP) in the last stage and an HFSSP in the upstream stages. First, a hybrid differential evolution (HDE) algorithm combined with a variable neighborhood decomposition search (VNDS) is proposed for the former subproblem. Second, an iterative backward list scheduling (IBLS) algorithm is presented to solve the latter subproblem. The effectiveness of this bi-layer optimization approach is verified by computational experiments on well-designed and real-world scheduling instances. This study provides a new perspective on modeling and solving practical SCC scheduling problems.     

A memetic algorithm to solve an unrelated parallel machine scheduling problem with auxiliary resources in semiconductor manufacturing

In this paper, we propose a metaheuristic for solving an original scheduling problem with auxiliary resources in a photolithography workshop of a semiconductor plant. The photolithography workshop is often a bottleneck, and improving scheduling decisions in this workshop can help to improve indicators of the whole plant. Two optimization criteria are separately considered: the weighted flow time (to minimize) and the number of products that are processed (to maximize). After stating the problem and giving some properties on the solution space, we show how these properties help us to efficiently solve the problem with the proposed memetic algorithm, which has been implemented and tested on large generated instances. Numerical experiments show that good solutions are obtained within a reasonable computational time.     

Single machine batch scheduling to minimize total completion time and resource consumption costs

In this paper we study the single-machine batch scheduling problem under batch availability, where both setup and job processing times are controllable by allocating a continuously divisible nonrenewable resource. Under batch availability a set of jobs is processed contiguously and completed together, when the processing of the last job in the batch is finished. We present polynomial time algorithms to find the job sequence, the partition of the job sequence into batches and the resource allocation, which minimize the total completion time or the total production cost (inventory plus resource costs).