Scheduling unrelated parallel batch processing machines with non-identical job sizes and unequal ready times

This research analyzes the problem of scheduling a set of n jobs with arbitrary job sizes and non-zero ready times on a set of m unrelated parallel batch processing machines so as to minimize the makespan. Unrelated parallel machine is a generalization of the identical parallel processing machines and is closer to real-world production systems. Each machine can accommodate and process several jobs simultaneously as a batch as long as the machine capacity is not exceeded. The batch processing time and the batch ready time are respectively equal to the largest processing time and the largest ready time among all the jobs in the batch. Motivated by the computational complexity and the practical relevance of the problem, we present several heuristics based on first-fit and best-fit earliest job ready time rules. We also present a mixed integer programming model for the problem and a lower bound to evaluate the quality of the heuristics. The small computational effort of deterministic heuristics, which is valuable in some practical applications, is also one of the reasons that motivates this study. The results show that the heuristic proposed in this paper has a superior performance compared to the heuristics based on ideas proposed in the literature.     

Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective

This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.     

Aggregate production planning for a continuous reconfigurable manufacturing process

Most of the research on aggregate production planning has been focused on discrete parts manufacturing models. In environments where intermediate inventory cannot be stored, and multiple products are produced simultaneously using complex configurations of production machines, these models may produce erroneous results. In this paper, we present a configuration-based formulation for one such manufacturing environment, where production may involve dissimilar machines performing similar operations at different rates and equipment can be connected together to form different production lines. The production process is continuous and no in-process inventory can be kept. We present and compare several heuristics to generate input data to solve the aggregate production-planning problems using the configuration-based formulation. Computational experiments show that large-scale real-world problems we encountered can be solved in reasonable time using our heuristics and commercial optimization software like CPLEX.     

Additive manufacturing in the spare parts supply chain

As additive manufacturing (AM) evolves to become a common method of producing final parts, further study of this computer integrated technology is necessary. The purpose of this research is to evaluate the potential impact of additive manufacturing improvements on the configuration of spare parts supply chains. This goal has been accomplished through scenario modeling of a real-life spare parts supply chain in the aeronautics industry. The spare parts supply chain of the F-18 Super Hornet fighter jet was selected as the case study because the air-cooling ducts of the environmental control system are produced using AM technology. In total, four scenarios are investigated that vary the supply chain configurations and additive manufacturing machine specifications. The reference scenario is based on the spare parts supplier's current practice and the possible future decentralization of production and likely improvements in AM technology. Total operating cost, including downtime cost, is used to compare the scenarios. We found that using current AM technology, centralized production is clearly the preferable supply chain configuration in the case example. However, distributed spare parts production becomes practical as AM machines become less capital intensive, more autonomous and offer shorter production cycles. This investigation provides guidance for the development of additive manufacturing machines and their possible deployment in spare parts supply chains. This study contributes to the emerging literature on AM deployment in supply chains with a real-world case setting and scenario model illustrating the cost trade-offs and critical requirements for technology development.     

Part-machine grouping using weighted similarity coefficients

The first step in the transition to cellular manufacturing is part-machine grouping. In this paper, grouping parts into families and machines into cells is done in two phases: by first grouping machines and then assigning parts. Limits both on the number of machines per cell and on the number of parts per family are considered. The number of cells is not fixed. A weighted sum of within-cell voids and out-of-cell operations is used to evaluate the part-machine grouping obtained. In Phase One, weighted similarity coefficients are computed and machines are clustered using a Tabu search algorithm. In Phase Two, part types are assigned to the previously formed groups using a linear minimum cost network flow model. The proposed approach is compared with three heuristics, namely ZODIAC, GRAFICS and MST, on a large number of problems.     

A modeling technique for loading and scheduling problems in FMS

In recent years, due to highly competitive market conditions, it has become necessary for manufacturing systems to have quick response times and high flexibility. Flexible manufacturing systems (FMS's) have gained attention in response to this challenge. FMS has the ability to produce a variety of parts using the same system. However this flexibility comes at the price, which is the development of efficient and effective methods for integrated production planning, and control.In this paper, we analyze the production planning problem in flexible manufacturing systems. We address the problems of part loading, tool loading, and part scheduling. We assume that there is a set of tools with known life and a set of machines that can produce a variety of parts. A batch of various part types is routed through this system with the assumption that the processing time and cost vary with the assignment of parts to different machines and assignment of various tool sets to machines. We developed a mathematical model to select machines and assign operations and the required tools to machines in order to minimize the summation of maximum completion time, material handling time, and total processing time.We first integrate and formulate loading, and routing, two of the most important FMS planning problems, as a 0–1 mixed integer programming problem. We then take the output from the integrated planning model and generate a detailed operations schedule. The results reported in this paper demonstrate the model efficiency and examine the performance of the system with respect to measures such as production rate and utilization.     

Flow shops with WIP and value added costs

A new deterministic flow shop problem is studied where the objective is to minimize the total WIP (work-in-process) cost. Based on a value added model, the unit time WIP cost increases as a job passes through various stages in the production process. The recognition version is unary NP-Complete even for two machines. Several simple and intuitive heuristics are presented. For each heuristic, we determine asymptotically attainable upper bounds on the relative error. Finally, the heuristics are empirically evaluated.     

Parallel machine scheduling problems in green manufacturing industry

Manufacturing companies are now more conscious about the environment. As such, there are more concerns in reducing the consumption of energy and the production of pollutants. Reduced consumption of energy will save cost, while reduction of pollutants will decrease the cost of cleaning up the environment. This paper considers scheduling problems that arise in green manufacturing companies. Suppose the manufacturing company has a set of parallel machines. Each machine has a cost per unit time that differs from machine to machine. The cost here is the sum of the energy cost and the clean up cost. A set of jobs is to be processed by these machines. Our goal is to find a schedule that minimizes the makespan (schedule length) or the total completion time, subject to the constraint that the total cost is not more than a given threshold value. We propose efficient heuristics and show, by computational experiments, that they perform very well in practice.     

Bicriteria robotic cell scheduling

This paper considers the scheduling problems arising in two- and three-machine manufacturing cells configured in a flowshop which repeatedly produces one type of product and where transportation of the parts between the machines is performed by a robot. The cycle time of the cell is affected by the robot move sequence as well as the processing times of the parts on the machines. For highly flexible CNC machines, the processing times can be changed by altering the machining conditions at the expense of increasing the manufacturing cost. As a result, we try to find the robot move sequence as well as the processing times of the parts on each machine that not only minimize the cycle time but, for the first time in robotic cell scheduling literature, also minimize the manufacturing cost. For each 1-unit cycle in two- and three-machine cells, we determine the efficient set of processing time vectors such that no other processing time vector gives both a smaller cycle time and a smaller cost value. We also compare these cycles with each other to determine the sufficient conditions under which each of the cycles dominates the rest. Finally, we show how different assumptions on cost structures affect the results.     

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.     

Two-stage hybrid flowshop scheduling with simultaneous processing machines

Simultaneous processing machines, common in processing industries such as steel and food production, can process several jobs simultaneously in the first-in, first-out manner. However, they are often highly energy-consuming. In this paper, we study a new two-stage hybrid flowshop scheduling problem, with simultaneous processing machines at the first stage and a single no-idle machine with predetermined job sequence at the second stage. A mixed integer programming model is proposed with the objective of minimizing the total processing time to reduce energy consumption and improve production efficiency. We give a sufficient and necessary condition to construct feasible sequencing solutions and present an effective approach to calculate the time variables for a feasible sequencing solution. Based on these results, we design a list scheduling heuristic algorithm and its improvement. Both heuristics can find an optimal solution under certain conditions with complexity O(nlogn), where n is the number of jobs. Our experiments verify the efficiency of these heuristics compared with classical heuristics in the literature and investigate the impacts of problem size and processing times.     

The sustainable cell formation problem: manufacturing cell creation with machine modification costs

An approach for manufacturing cell formation with machine modification is presented. In cell formation it is often important in practice to be able to reassign parts to additional machine types in order to create better cell configurations. This involves extending the set of parts that certain individual machines can process. Such extensions may be cheaper than simply purchasing additional machines. Thus, there is the possibility of machine modification to reduce inter-cell travel. The cost of such modifications must be balanced by the consequent reduction in inter-cell travel cost. The extended machine cell formation problem to be described involves the specification of which individual machines should be modified to enable them to process additional part types, part-machine assignment, and the grouping of individual machines for cell formation. The objective is to minimize the sum of the machine modification costs and the inter-cell travel. We call this the sustainable cell formation problem (SCFP). As far as the authors are aware, there have not been any solution procedures for this important problem reported in the open literature. It is our purpose to fill this gap by presenting a mixed integer programming model of the SCFP. We also propose and analyze greedy and tabu search heuristics for the design of large-scale systems related to the SCFP. Computational experience with the solution procedures indicates that they are likely to be useful additions to the production engineer's toolkit.     

Bicriteria robotic operation allocation in a flexible manufacturing cell

Consider a manufacturing cell of two identical CNC machines and a material handling robot. Identical parts requesting the completion of a number of operations are to be produced in a cyclic scheduling environment through a flow shop type setting. The existing studies in the literature overlook the flexibility of the CNC machines by assuming that both the allocation of the operations to the machines as well as their respective processing times are fixed. Consequently, the provided results may be either suboptimal or valid under unnecessarily limiting assumptions for a flexible manufacturing cell. The allocations of the operations to the two machines and the processing time of an operation on a machine can be changed by altering the machining conditions of that machine such as the speed and the feed rate in a CNC turning machine. Such flexibilities constitute the point of origin of the current study. The allocation of the operations to the machines and the machining conditions of the machines affect the processing times which, in turn, affect the cycle time. On the other hand, the machining conditions also affect the manufacturing cost. This study is the first to consider a bicriteria model which determines the allocation of the operations to the machines, the processing times of the operations on the machines, and the robot move sequence that jointly minimize the cycle time and the total manufacturing cost. We provide algorithms for the two 1-unit cycles and test their efficiency in terms of the solution quality and the computation time by a wide range of experiments on varying design parameters.     

Goal distance estimation for automated planning using neural networks and support vector machines

Many of today’s most successful planners perform a forward heuristic search. The accuracy of the heuristic estimates and the cost of their computation determine the performance of the planner. Thanks to the efforts of researchers in the area of heuristic search planning, modern algorithms are able to generate high-quality estimates. In this paper we propose to learn heuristic functions using artificial neural networks and support vector machines. This approach can be used to learn standalone heuristic functions but also to improve standard planning heuristics. One of the most famous and successful variants for heuristic search planning is used by the Fast-Forward (FF) planner. We analyze the performance of standalone learned heuristics based on nature-inspired machine learning techniques and employ a comparison to the standard FF heuristic and other heuristic learning approaches. In the conducted experiments artificial neural networks and support vector machines were able to produce standalone heuristics of superior accuracy. Also, the resulting heuristics are computationally much more performant than related ones.     

Decomposition heuristic to minimize total cost in a multi-level supply chain network

In this paper, the distribution planning model for the multi-level supply chain network is studied. Products which are manufactured at factory are delivered to customers through warehouses and distribution centers for the given customer demands. The objective function of suggested model is to minimize logistic costs such as replenishment cost, inventory holding cost and transportation cost. A mixed integer programming formulation and heuristics for practical use are suggested. Heuristics are composed of two steps: decomposition and post improving process. In the decomposition heuristics, the problems are solved optimally only considering the transportation route first by the minimum cost flow problem, and the replenishment plan is generated by applying the cost-saving heuristic which was originally suggested in the manufacturing assembly line operation, and integrating with the transportation plan. Another heuristic, in which the original model is segmented due to the time periods, and run on a rolling horizon based method, is suggested. With the post-improving process using tabu search method, the performances are evaluated, and it was shown that solutions can be computed within a reasonable computation time by the gap of about 10% in average from the lower bound of the optimal solutions.     

Characterization of the iterative application of makespan heuristics on non-makespan machines in a heterogeneous parallel and distributed environment

Heterogeneous computing (HC) is the coordinated use of different types of machines, and networks to process a diverse workload in a manner that will maximize the combined performance and/or cost effectiveness of the system. Heuristics for allocating resources in an HC system are based on some optimization criterion. A common optimization criterion is to minimize the completion time of the machine that finishes last (makespan). In this study, we consider an iterative approach that repeatedly runs a mapping heuristic to minimize the makespan of the considered machines and tasks. For each successive iteration, the makespan machine of the previous iteration and the tasks assigned to it are removed from the set of considered machines and tasks. This study focuses on understanding the different mathematical characteristics of resource allocation heuristics that cause them to behave differently when combined with this iterative approach. This paper has three main contributions. The first contribution is the study of an iterative technique used in conjunction with resource allocation heuristics. The second contribution is the definition and mathematical characterization of “iteration invariant” heuristics. The third contribution is to determine the characteristics of a heuristic that will cause the mapping to change across iterations.     

Effect of machining time in the duplication process of machine cells formation

After the assignment of parts and machines to manufacturing cells are made, it would be advantages to consider duplicating bottleneck machines, as in the long run significant savings in material handling costs can be realized. In this paper, we consider the effect of machining time saved over and above the savings in material handling costs in the development of the model. Comparative results obtained from solving an example problem demonstrate that this effect could indeed be significant under certain levels of budgetary restrictions.     

A two-stage hybrid flowshop scheduling problem with a function constraint and unrelated alternative machines

This article addresses a two-stage hybrid flowshop scheduling problem with unrelated alternative machines. The problem to be studied has m unrelated alternative machines at the first machine center followed by a second machine center with a common processing machine in the system. The objective is to minimize the makespan of the system. For the processing of any job, it is assumed that the operation can be partially substituted by other machines in the first center, depending on its machining constraints. Such scheduling problems occur in certain practical applications such as semiconductors, electronics manufacturing, airplane engine production, and petrochemical production. We demonstrate that the addressed problem is NP-hard and then provide some heuristic algorithms to solve the problem efficiently. The experimental results show that the combination of the modified Johnson's rule and the First-Fit rule provides the best solutions within all proposed heuristics.Scope and purpose     

Simulated annealing heuristics for the dynamic facility layout problem

In today's economy, manufacturing plants must be able to operate efficiently and respond quickly to changes in product mix and demand. Therefore, this paper considers the problem of arranging and rearranging (when there are changes between the flows of materials between departments) manufacturing facilities such that the sum of the material handling and rearrangement costs is minimized. This problem is known as the dynamic facility layout problem (DFLP). In this paper, two simulated annealing (SA) heuristics are developed for the DFLP. The first SA heuristic (SA I) is a direct adaptation of SA to the DFLP. The second SA heuristic (SA II) is the same as SA I with a look-ahead/look-back strategy added. To test the performance of the heuristics, a data set taken from the literature is used in the analysis. The results obtained show that the proposed heuristics are very effective for the dynamic facility layout problem.     

Parallel machine match-up scheduling with manufacturing cost considerations

Many scheduling problems in practice involve rescheduling of disrupted schedules. In this study, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules considering the manufacturing cost implications in response to disruptions. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain manufacturing cost, which is a convex function of the compression on the processing time. In rescheduling it is highly desirable to catch up the original schedule as soon as possible by reassigning the jobs to the machines and compressing their processing times. On the other hand, one must also keep the manufacturing cost due to compression of the jobs low. Thus, one is faced with a tradeoff between match-up time and manufacturing cost criteria. We introduce alternative match-up scheduling problems for finding schedules on the efficient frontier of this time/cost tradeoff. We employ the recent advances in conic mixed-integer programming to model these problems effectively. We further provide a fast heuristic algorithm driven by dual prices of convex subproblems for generating approximate efficient schedules.