Improved evolutionary algorithm for parallel batch processing machine scheduling in additive manufacturing

With the increasing prosperity of additive manufacturing, the 3D-printing shop scheduling problem has presented growing importance. The scheduling of such a shop is imperative for saving time and cost, but the problem is hard to solve, especially for simultaneous multi-part assignment and placement. This paper develops an improved evolutionary algorithm for application to additive manufacturing, by combining a genetic algorithm with a heuristic placement strategy to take into account the allocation and placement of parts integrally. The algorithm is designed also to enhance the optimisation efficiency by introducing an initialisation method based on the characteristics of the 3D printing process through the development of corresponding time calculation model. Experiments show that the developed algorithm can find better solutions compared with state-of-the-art algorithms such as simple genetic algorithm, particle swarm optimisation and heuristic algorithms.     

Determination of batch size at a bottleneck machine in manufacturing systems

In manufacturing systems, there often exists a bottleneck machine whose capacity is equal to or less than the market demand. Any idle or waste time at the bottleneck machine directly impacts the output of the entire plant because it results in a loss of throughput. In order to maximize the capacity utilization by less setup losses at the bottleneck machine, the parts are often produced in batches. Traditionally, most batch sizing decisions are made based on the economic order quantity model where setup and inventory holding costs are considered. This paper presents an alternative method to determine batch size at a bottleneck machine. We present a new objective function and cost factors for batch sizing and investigate queuing and throughput models. A linear search algorithm is introduced to find the optimal throughput rate and batch size at the same time. Numerical examples are examined to see how the batching algorithm works.     

Scheduling a batch processing machine with non-identical job sizes

The problem of scheduling batch processors is important in some industries and, at a more fundamental level, captures an element of complexity common to many practical scheduling problems. We describe a branch and bound procedure applicable to a batch processor model with arbitrary job processing times, job weights and job sizes. The scheduling objective is to minimize total weighted completion time. We find that the procedure returns optimal solutions to problems of up to 25 jobs in reasonable CPU time, and can be adapted for use as a heuristic for larger problems.     

Single machine batch scheduling with sequential job processing

The problem of scheduling n jobs on a single machine in batches to minimize some regular cost functions is studied. Jobs within each batch are processed sequentially so that the processing time of a batch is equal to the sum of the processing times of the jobs contained in it. Jobs in the same batch are completed at the same time when the last job of the batch has finished its processing. A constant set-up time precedes the processing of each batch. The number of jobs in each batch is bounded by some value b. If b < n, then the problem is called bounded. Otherwise, it is unbounded. For both the bounded and unbounded problems, dynamic programming algorithms are presented for minimizing the maximum lateness, the number of late jobs, the total tardiness, the total weighted completion time, and the total weighted tardiness when all due dates are equal, which are polynomial if there is a fixed number of distinct due dates or processing times. More efficient algorithms are derived for some special cases of both the bounded and unbounded problems in which all due dates and/or processing times are equal. Several special cases of the bounded problem are shown to be NP-hard. Thus, a comprehensive classification of the computational complexities of the special cases is provided.     

Minimising makespan heuristics for scheduling a single batch machine processing machine with non-identical job sizes

In this paper, the problem of minimising maximum completion time on a single batch processing machine is studied. A batch processing is performed on a machine which can simultaneously process several jobs as a batch. The processing time of a batch is determined by the longest processing time of jobs in the batch. The batch processing machine problem is encountered in many manufacturing systems such as burn-in operations in the semiconductor industry and heat treatment operations in the metalworking industries. Heuristics are developed by iterative decomposition of a mixed integer programming model, modified from the successive knapsack problem by Ghazvini and Dupont (1998 Ghazvini, F.J. and Dupont, L. 1998. Minimising mean flow times criteria on a single batch processing machine with non-identical jobs sizes. International Journal of Production Economics, 55: 273–280. [Crossref], [Web of Science ®] , [Google Scholar], Minimising mean flow times criteria on a single batch processing machine with non-identical jobs sizes. International Journal of Production Economics 55: 273–280) and the waste of batch clustering algorithm by Chen, Du, and Huang (2011 Chen, H., Du, B. and Huang, G.Q. 2011. Scheduling a batch processing machine with non-identical job sizes: a clustering perspective. International Journal of Production Research, 49(19): 5755–5778. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Scheduling a batch processing machine with non-identical job sizes: a clustering perspective. International Journal of Production Research 49 (19): 5755–5778). Experimental results show that the suggested heuristics produce high-quality solutions comparable to those of previous heuristics in a reasonable computation time.     

Scheduling a batch processing machine with non-identical job sizes: a clustering perspective

Batch processing machines that process a group of jobs simultaneously are often encountered in semiconductor manufacturing and metal heat treatment. This paper considered the problem of scheduling a batch processing machine from a clustering perspective. We first demonstrated that minimising makespan on a single batching machine with non-identical job sizes can be regarded as a special clustering problem, providing a novel insight into scheduling with batching. The definition of WRB (waste ratio of batch) was then presented, and the objective function of minimising makespan was transformed into minimising weighted WRB so as to define the distance measure between batches in a more understandable way. The equivalence of the two objective functions was also proved. In addition, a clustering algorithm CACB (constrained agglomerative clustering of batches) was proposed based on the definition of WRB. To test the effectiveness of the proposed algorithm, the results obtained from CACB were compared with those from the previous methods, including BFLPT (best-fit longest processing time) heuristic and GA (genetic algorithm). CACB outperforms BFLPT and GA especially for large-scale problems.     

Minimizing total tardiness on a batch processing machine with incompatible job families

Motivated by an application in semiconductor manufacturing, we study the problem of minimizing total tardiness on a batch processing machine with incompatibl8e job families, where all jobs of the same family have identical processing times and jobs of different families cannot be processed together. We present a dynamic programming algorithm which has polynomial time complexity when the number of job families and the batch machine capacity are fixed. We also examine various heuristic solution procedures which can provide near optimal solutions in a reasonable amount of computation time.     

Minimising makespan on a batch processing machine using heuristics improved by an enumeration scheme

Batch processing machines can process several job simultaneously and are encountered in many manufacturing environments. Jobs in a batch are processed together and have the same start and end processing time. Since jobs are non-identical in job sizes and job processing times, they should be reasonably scheduled to improve the machine utilisation and processing efficiency. Two well-known heuristics, first fit longest processing time and best fit longest processing time (BFLPT), are improved in this study by considering identical job sizes and then BFLPT is further improved by an enumeration scheme proposed. Computational experiments are conducted to evaluate the performance of the improvement and the results are compared with the existing heuristics.     

Optimal production control policy in unreliable batch processing manufacturing systems with transportation delay

This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimise the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton–Jacobi–Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation-based approach. Thus, a combined discrete–continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis.     

Minimising makespan on a single batch processing machine with dynamic job arrivals and non-identical job sizes

Batch scheduling is a prevalent policy in many industries such as burn-in operations in semiconductor manufacturing and heat treatment operations in metalworking. In this paper, we consider the problem of minimising makespan on a single batch processing machine in the presence of dynamic job arrivals and non-identical job sizes. The problem under study is NP-hard. Consequently, we develop a number of efficient construction heuristics. The performance of the proposed heuristics is evaluated by comparing their results to two lower bounds, and other solution approaches published in the literature, namely the first-fit longest processing time-earliest release time (FFLPT-ERT) heuristic, hybrid genetic algorithm (HGA), joint genetic algorithm and dynamic programming (GA+DP) approach and ant colony optimisation (ACO) algorithm. The computational experiments demonstrate the superiority of the proposed heuristics with respect to solution quality, especially for the problems with small size jobs. Moreover, the computational costs of the proposed heuristics are very low.     

Consignment stock theory with a fixed batch manufacturing process

This paper deals with stock control in a supply chain. The focus is on consignment stock (CS), an innovative collaborative relationship, which can create a win–win situation between the vendor and the buyer. Recently some analytical formulations have been proposed to optimise CS, and the present paper extends these models by considering a new critical factor: a fixed batch production process at the vendor's plant. This kind of production is typical if there are batch processing machines that can hold and simultaneously process a finite number of items, such as kilns for long heat treatment. Specifically, we consider a deterministic single-vendor single-buyer system. The buyer consumes a single product at a constant rate and is replenished by the vendor who produces in batches and incurs set-up costs. Each batch is dispatched to the buyer in a number of shipments, some of which may take place while production is still running. To minimise total operating costs (that is, manufacturing, replenishment and holding), two alternative production and shipment policies are proposed and analytically formulated as integer optimisation models. A step by step heuristic procedure to obtain the optimal solution is finally presented and demonstrated through numerical examples.     

A method combining rules with genetic algorithm for minimizing makespan on a batch processing machine with preventive maintenance

This paper considers the problem of minimising makespan on a single batch processing machine with flexible periodic preventive maintenance. This problem combines two sub-problems, scheduling on a batch processing machine with jobs’ release dates considered and arranging the preventive maintenance activities on a batch processing machine. The preventive maintenance activities are flexible but the maximum continuous working time of the machine, which is allowed, is determined. A mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed, in which the grouping of jobs with incompatible job families, the starting time of batches and the preventive maintenance activities are optimised simultaneously. A method combining rules with the genetic algorithm is proposed to solve this model, in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities. The computational results indicate the method is effective under practical problem sizes. In addition, the influences of jobs’ parameters on the performance of the method are analyzed, such as the number of jobs, the number of job families, jobs’ processing time and jobs’ release time.     

Control policy simulation based on machine age in a failure prone one-machine,one-product manufacturing system

This paper deals with the production planning problem of a flexible manufacturing system (FMS). This problem is within the class of problems which are usually faced during the life cycle of FMS. There are basically two approaches used to solve this problem: analytical and simulation. The objective of this paper is to develop a methodology for determine the control policy for a given FMS by using the combination of both analytical and simulation approaches. The production rate control of a one-machine one-product system is presented to illustrate our approach. The contribution of the analytical part of the proposed model consists of generating a near-optimal controller based on the concept of an age-dependent hedging point policy. This sub-optimal policy is used as input of the simulation part and the improvement of operating conditions (control policies) achieved with a constant demand rate. The proposed model includes also a stochastic demand and lot sizes in production which consists of similar products batches with bulk arrivals. The robustness of the controller against both demand rates and production types has been validated.     

Optimizing production smoothing decisions via batch selection for mixed-model just-in-time manufacturing systems with arbitrary setup and processing times

This paper is concerned with the production smoothing problem that arises in the context of just-in-time manufacturing systems. The production smoothing problem can be solved by employing a two-phase solution methodology, where optimal batch sizes for the products and a sequence for these batches are specified in the first and second phases, respectively. In this paper, we focus on the problem of selecting optimal batch sizes for the products. We propose a dynamic programming (DP) algorithm for the exact solution of the problem. Our computational experiments demonstrate that the DP approach requires significant computational effort, rendering its use in a real environment impractical. We develop three meta-heuristics for the near-optimal solution of the problem, namely strategic oscillation, scatter search and path relinking. The efficiency and efficacy of the methods are tested via a computational study. The computational results show that the meta-heuristic methods considered in this paper provide near-optimal solutions for the problem within several minutes. In particular, the path relinking method can be used for the planning of mixed-model manufacturing systems in real time with its negligible computational requirement and high solution quality.     

Measuring machine and product mix flexibilities of a manufacturing system

This paper provides a brief discussion on flexibility concepts in manufacturing. It emphasizes that flexibility measurements in a manufacturing system should be studied under dynamically changing environments rather than static ones. The approaches for assessing two major flexibility types, machine flexibility and product mix flexibility response, are presented. The machine flexibility model is based on machine-operation efficiency. The product mix flexibility response model is based on the difference between products in terms of tooling requirements, the number of operations that a machine can perform and the efficiency of different machines.     

Process planning for small batch manufacturing of sheet metal parts

The paper describes process planning for order-based small batch sheet metal part manufacturing. In this domain, general purpose CNC machinery and standard tools are being used. An example of a process planning system is given and some areas of special interest are discussed in more detail. Process planning for sheet bending and tolerance reasoning are important and intricate tasks within process planning, whereas abstractions in design and nesting are important due to their relations with other manufacturing functions. In general, manufacturing functions tend to become increasingly intertwined and traditional boundaries become blurred. Sheet metal industries, customers and suppliers alike, can benefit from this.     

Capacity-driven acceptance of customer orders for a multi-stage batch manufacturing system: models and algorithms

An automotive parts manufacturer produces a wide variety of parts in a job shop environment. Many of the manufacturing operations have substantial setups. When a client phones in an order, the manufacturer must decide quickly whether or not it has the capacity required to accept the order. We develop a simplified formulation of the order acceptance problem. We formulate the discrete-time version as an integer program. The problem is NP-hard, but in 51 out of 51 test problems the LP relaxation is tight. For larger problems we test several heuristics. Three of the heuristics look promising: simulated annealing, a genetic algorithm, and a linear-programming-based heuristic.     

Failure analysis of a machine support for fique fibre processing

Replacement cast steel supports for a machine consisting of bars that straighten out fique fibres have presented recurrent fracture, beyond 10⁶ cycles of service and their failure surfaces show features typical of fatigue under alternating bending conditions. Differences between original supports and replacement supports related to geometry roughness, hardness, chemical composition and microstructure were identified. To obtain a longer service life selected modifications of the geometry and use of different material were proposed based on load state analysis, finite element analysis, and fatigue strength calculations.     

Identification of independent modules in fault trees which contain dependent basic events

The reliability performance of a system is frequently a function of component failures of which some are independent whilst others are interdependent. It is possible to represent the system failure logic in a fault tree diagram, however only the sections containing independent events can be assessed using the conventional fault tree analysis methodology. The analysis of the dependent sections will require a Markov analysis. Since the efficiency of the Markov analysis largely depends on the size of the established Markov model, the key is to extract from the fault tree the smallest sections which contain dependencies. This paper proposes a method aimed at establishing the smallest Markov model for the dependencies contained within the fault tree.