Optimal Sublot Research Articles

Integrating scheduling with optimal sublot for parallel machine with job splitting and dependent setup times

This paper addresses a novel problem of the parallel capacitated machines with job splitting and dependent setup times (PCMS), Pmc|split, pj, sjp|Cmax. A mixed integer programming (MIP) model is developed to find an optimal schedule with minimum makespan. Since the problem is NP-hard, metaheuristics are required to find a near optimal solution for larger, more practical problems. Therefore, this paper presents the first applications of two effective metaheuristics, Particle Swarm Optimization (PSO) and Differential Evolution (DE) with a solution representation scheme for solving the problem. To evaluate the metaheuristics’ performances, the lower bound is also firstly developed. Experimental results reveal that, in the small-size problems, there are no distinctive differences between the two algorithms’ performances, since both algorithms are able to find the optimal solutions. However, for medium to large size problems, the DE outperforms the PSO by providing significantly superior results of makespan for 22 out of 27 instances.

Energy-efficient scheduling of flexible flow shop of composite recycling

Composite recycling technologies have been developed to tackle the increasing use of composites in industry and as a result of restrictions placed on landfill disposal. Mechanical, thermal and chemical approaches are the existing main recycling techniques to recover the fibres. Some optimisation work for reducing energy consumed by above processes has also been developed. However, the resource efficiency of recycling composites at the workshop level has never been considered before. Considering the current trend of designing and optimising a system in parallel and the future needs of the composite recycling business, a flexible flow shop for carbon fibre reinforced composite recycling is modelled. Optimisation approaches based on non-dominated sorting genetic algorithm II (NSGA-II) have been developed to reduce the time and energy consumed for processing composite wastes by searching for the optimal sub-lot splitting and resource scheduling plans. Case studies on different composite recycling scenarios have been conducted to prove the feasibility of the model and the developed algorithm.

Lot streaming in the presence of learning in sublot-attached setup times and processing times

Lot streaming is the process of splitting a production lot into sublots, and then processing the sublots on different machines in an overlapping manner. In this paper, we study the use of lot streaming for processing a lot in a two-machine flow shop when a sublot-attached setup time is incurred before the processing of each sublot. The objective is to determine number of sublots and sublot sizes and minimize makespan. We also consider the case when the effect of learning is observed in processing times, sublot-attached setup times, or, both. We present closed-form expressions for optimal sublot sizes and efficient search schemes to determine optimal number of sublots.

Optimal control of an imperfect repetitive synchronised production environment

We develop optimal sublot policies to minimise total expected costs in a failure-prone two-stage, high-volume repetitive production process which manufactures batches of the same item over a long period of time. The first stage starts in control but may fail at an exponentially distributed random time, producing only good units before failure and only defective units afterward. Failure is detected upon encountering defective units in the second stage, at which time the first stage process may be restored to good condition. To enhance quality, a production lot in Stage 1 is subdivided into sublots which are transferred as soon as possible to Stage 2 for inspection and processing. We determine exact closed-form continuous solutions as well as an efficient algorithm for finding optimal integer sublots. We provide managerial insights as to what control mechanism would be adopted depending on the state of the production process parameters. [Received 14 May 2015; Revised 16 February 2016; Accepted 1 March 2016]

Lot Streaming and Preventive Maintenance in a Multiple Product Permutation Flow Shop with Intermingling

A mathematical model forlot streaming problem with preventive maintenance was proposed. A mixed-integer linear model for multiple-product lot streaming problems was also developed. Mixed-integer programming formulation was presented which will enable the user to identify optimal sublot sizes and sequences simultaneously. Two situations were considered:1) all machines were available, and 2) all machines needed preventive maintenance tasks. For both situations a new mixed-integer formulation was developed. To demonstrate the practicality of the proposed model, numerical example was used. It showed that the percentage of make span reduction due to lot streaming in permutation flow shop is 54% when compared to consistent sublots with intermingling case.

Comparison of Improved Sheep Flock Heredity Algorithm and Artificial Bee Colony Algorithm for lot Streaming in m-Machine Flow Shop Scheduling

Lot streaming is a technique used to split the processing of lots into several sublots (transfer batches) to allow the overlapping of operations in a multistage manufacturing systems thereby shortening the production time (makespan). The objective of this paper is to minimize the makespan and total flow time of n-job, m-machine lot-streaming problem in a flow shop with variable size sublots and also to determine the optimal sublot size. In recent times researchers are concentrating and applying intelligent heuristics to solve Flow shop problems with lot streaming. In this research, Improved Sheep Flock Heredity algorithm (ISFHA) and Artificial Bee Colony (ABC) algorithms are used to solve the problem. The results obtained by the proposed algorithms are also compared with the performance of other worked out traditional heuristics. The computational results show that the identified algorithms are more efficient, effective and better than the algorithms already tested for this problem.

Integration of Lot Sizing and Flow Shop Scheduling with Lot Streaming

We will develop a mathematical model for the integration of lot sizing and flow shop scheduling with lot streaming. We will develop a mixed-integer linear model for multiple products lot sizing and lot streaming problems. Mixed-integer programming formulation is presented which will enable the user to find optimal production quantities, optimal inventory levels, optimal sublot sizes, and optimal sequence simultaneously. We will use numerical example to show practicality of the proposed model. We test eight different lot streaming problems: (1) consistent sublots with intermingling, (2) consistent sublots and no intermingling between sublots of the products (without intermingling), (3) equal sublots with intermingling, (4) equal sublots without intermingling, (5) no-wait consistent sublots with intermingling, (6) no-wait equal sublots with intermingling, (7) no-wait consistent sublots without intermingling, and (8) no-wait equal sublots without intermingling. We showed that the best makespan can be achieved through the consistent sublots with intermingling case.

Comparison of Firefly algorithm and Artificial Immune System algorithm for lot streaming in -machine flow shop scheduling

Abstract Lot streaming is a technique used to split the processing of lots into several sublots (transfer batches) to allow the overlapping of operations in a multistage manufacturing systems thereby shortening the production time (makespan). The objective of this paper is to minimize the makespan and total flow time of n-job, m-machine lot streaming problem in a flow shop with equal and variable size sublots and also to determine the optimal sublot size. In recent times researchers are concentrating and applying intelligent heuristics to solve flow shop problems with lot streaming. In this research, Firefly Algorithm (FA) and Artificial Immune System (AIS) algorithms are used to solve the problem. The results obtained by the proposed algorithms are also compared with the performance of other worked out traditional heuristics. The computational results shows that the identified algorithms are more efficient, effective and better than the algorithms already tested for this problem.

A local-best harmony search algorithm with dynamic sub-harmony memories for lot-streaming flow shop scheduling problem

In this paper, a local-best harmony search (HS) algorithm with dynamic sub-harmony memories (HM), namely DLHS algorithm, is proposed to minimize the total weighted earliness and tardiness penalties for a lot-streaming flow shop scheduling problem with equal-size sub-lots. First of all, to make the HS algorithm suitable for solving the problem considered, a rank-of-value (ROV) rule is applied to convert the continuous harmony vectors to discrete job sequences, and a net benefit of movement (NBM) heuristic is utilized to yield the optimal sub-lot allocations for the obtained job sequences. Secondly, an efficient initialization scheme based on the NEH variants is presented to construct an initial HM with certain quality and diversity. Thirdly, during the evolution process, the HM is dynamically divided into many small-sized sub-HMs which evolve independently so as to balance the fast convergence and large diversity. Fourthly, a new improvisation scheme is developed to well inherit good structures from the local-best harmony vector in the sub-HM. Meanwhile, a chaotic sequence to produce decision variables for harmony vectors and a mutation scheme are utilized to enhance the diversity of the HM. In addition, a simple but effective local search approach is presented and embedded in the DLHS algorithm to enhance the local searching ability. Computational experiments and comparisons show that the proposed DLHS algorithm generates better or competitive results than the existing hybrid genetic algorithm (HGA) and hybrid discrete particle swarm optimization (HDPSO) for the lot-streaming flow shop scheduling problem with total weighted earliness and tardiness criterion.

Lot-splitting for inspection in a synchronised two-stage manufacturing process with finite production rates and random out-of-control shifts in the first stage

We consider a non-repetitive manufacturing environment where the first stage will successively process different types of items that require different set up modes. Optimal sublot sizes are determined by studying the trade-off between the cost and time spent in restoration and rework. In addition, we discuss the resulting economical batch sizes, number of sublots, and processing rates. Finally, we provide recommendations on how to design the material handling flow system to implement our suggested inspection policies. Some of the managerial implications we found is that quality improves significantly when Stage 2 is more responsive (has faster processing times) than Stage 1 and when large batch sizes are divided into more sublots. Depending on the relative magnitude of poor quality and rework costs, we show that there is a threshold for the batch size under which sublot formation becomes inefficient. ]Received 17 July 2007; Revised 30 September 2007; Accepted 12 October 2007]

Lot streaming in a multiple product permutation flow shop with intermingling

In this paper we study the multi-product lot streaming problem in a permutation flow shop. The problem involves splitting given order quantities of different products into sublots and determining their optimal sequence. Each sublot has to be processed successively on all machines. The sublots of the particular products are allowed to intermingle, that is sublots of different jobs may be interleaved. A mixed integer programming formulation is presented which enables us to find optimal sublot sizes as well as the optimal sequence simultaneously. With this formulation, small- and medium-sized instances can be solved in a reasonable time. The model is further extended to deal with different settings and objectives. As no lot streaming instances are available in the literature, LSGen, a problem generator, is presented, facilitating valid and reproducible instances. First results concerning the average benefit of lot streaming with multiple products are presented, and are based on a computational study with 160 small- and medium-sized instances.

An application of genetic algorithms to lot-streaming flow shop scheduling

A Hybrid Genetic Algorithm (HGA) approach is proposed for a lot-streaming flow shop scheduling problem, in which a job (lot) is split into a number of smaller sublots so that successive operations can be overlapped. The objective is the minimization of the mean weighted absolute deviation of job completion times from due dates. This performance criterion has been shown to be non-regular and requires a search among schedules with intermittent idle times to find an optimal solution. For a given job sequence, a Linear Programming (LP) formulation is presented to obtain optimal sublot completion times. Objective function values of LP solutions are used to guide the HGA's search toward the best sequence. The performance of the HGA approach is compared with that of a pairwise interchange method.

Minimizing the mean weighted absolute deviation from due dates in lot-streaming flow shop scheduling

Lot-streaming is the process of splitting a job (lot) into a number of smaller sublots so that successive operations can be overlapped in a multi-stage production system. This paper presents a procedure for minimizing the mean weighted absolute deviation from due dates when jobs are scheduled in a lot-streaming flow shop. This performance criterion has been shown to be non-regular and requires a search among schedules with inserted idle times to find an optimal solution. For a given job sequence, we present linear programming formulations to obtain optimal sublot completion times for cases where buffers between successive machines have limited or infinite capacities, and sublots have equal-size or are consistent. A no-wait flow shop problem is also considered. Sixteen pairwise interchange methods are considered to generate the best sequences. These algorithms are obtained by combining four rules to generate initial sequences with four neighborhood search mechanisms. Computational experiments are conducted on 140 test problems. The results show that the best solutions are obtained by the heuristic algorithm with a non-adjacent pairwise interchange method and the smallest overall slack time rule to generate the initial sequence. Scope and purpose A flow shop scheduling problem involves scheduling jobs on multiple machines in series in order to optimize a given criterion. Lot-streaming scheduling allows the overlapping of operations between successive machines by splitting each job (lot) into a number of smaller sublots. The majority of research assumes that buffers between successive machines have infinite capacity, but this assumption may not be valid unless inventory costs are negligible. In the literature, the problem with infinite capacity buffers has been addressed mainly with the makespan performance measure. However, with the current interest in just-in-time production philosophy, earliness as well as tardiness should be considered. This paper presents linear programming formulations to find optimal starting and completion times for all the jobs in a given sequence considering various types of buffers and sublots. Heuristic algorithms that blend linear programming with several pairwise interchange strategies are proposed to find near-optimal solutions for multiple-job, multiple-machine lot-streaming flow shop scheduling problems.

An application of genetic algorithms to lot-streaming flow shop scheduling

A Hybrid Genetic Algorithm (HGA) approach is proposed for a lot-streaming flow shop scheduling problem, in which a job (lot) is split into a number of smaller sublots so that successive operations can be overlapped. The objective is the minimization of the mean weighted absolute deviation of job completion times from due dates. This performance criterion has been shown to be non-regular and requires a search among schedules with intermittent idle times to find an optimal solution. For a given job sequence, a Linear Programming (LP) formulation is presented to obtain optimal sublot completion times. Objective function values of LP solutions are used to guide the HGA's search toward the best sequence. The performance of the HGA approach is compared with that of a pairwise interchange method.

Lot streaming in open shops

We study lot streaming in shops in which the order the jobs are to be processed is immaterial. For a single job case, the properties of the optimal routing is determined. For the multi job case, two machine shops are analyzed. It is shown that lot streaming will improve makespan only if there is a job with large processing times. We show that there can be at most one such job and derive the optimal sublot sizes and their sequence.

Optimal streaming of a single job in a two-stage flow shop

Lot streaming is moving some portion of a process batch ahead to begin a downstream operation. The problem to be considered in this paper is the following: a single job consisting of U units is to be processed on two machines in the given order. Given a fixed number of possible transfer batches between the two machines, the problem is to find the timing and the size of the transfer batches (or, sublots) so as to optimize a given criterion. The schedules can be evaluated based on job completion, sublot completion, or item completion times. In the single job lot streaming problem, minimizing job completion time corresponds to minimizing the makespan, for which formulas for optimal sublot sizes are available. In this paper, the results for the sublot and item completion time models are presented.

Structural Properties of Lot Streaming in a Flow Shop

Lot streaming is the process of splitting a given lot or job to allow the overlapping of successive operations in multi-stage production systems, thereby reducing the makespan of the corresponding schedule. This paper considers the problem of finding sublot sizes to minimize the makespan for a single job in an m-machine flow shop. On each machine, the job is to be partitioned into a given number of sublots, and sublot sizes are the same on each machine. We introduce the concept of machine dominance, and propose an algorithm to reduce the problem so that only dominant machines are considered explicitly. After defining a network representation in which it is required to find the shortest critical path length, we identify the structure of critical paths for optimal sublot sizes. Knowledge of this structure considerably reduces the search for an optimal solution, which we illustrate by presenting algorithms for finding optimal sublot sizes.

Bayes Markovian Decision Models for a Multiperiod Reject Allowance Problem

Two versions of a multiperiod reject allowance problem are formulated as Markovian decision models. In the first, total output capacity is considered fixed; in the second, a maximum production rate is postulated. In both models it is assumed that output may be inspected at intermediate points within the production time span as well as at the conclusion of production. Also in both models the production process is characterized as a Bernoulli process with unknown parameter p, the probability of producing a defective. It is shown that optimal sublot size decision rules may be computed via linear programming methods.