Multiperiod production planning carrying over set-up time

Set-ups eat production capacity time and continue troubling production planning, especially on bottlenecks. The shortening of production planning periods to days, shifts or even less has increased the relative length of set-up times against the periods. Yet, many production planning models either ignore set-up times or, paradoxically, split longer multiperiod batches by adding set-ups at breaks between planning periods. The MILP-based capacitated lot-sizing models that include set-up carry-overs, i.e. allow a carry-over of a set-up of a product to the next period in case a product can be produced in subsequent periods, have incorporated fixed set-up fees without consideration of capacity consumed by set-up time. Inspired by production planning in process industries where set-up times still remain substantial, we incorporated set-up time with associated cost in two modifications of carry-over models. Comparison with an earlier benchmark model without set-up carry-over shows that substantial savings can be derived from the fundamentally different production plans enforced by carry-overs. Moreover, we show that heuristic inclusion of carry-overs by removal of set-ups from non-carry-over solutions is inefficient.     

Minimising general setup costs in a two-stage production system

This paper addresses a problem arising in the coordination between two consecutive stages of a production system. Production is organised in batches of identical jobs. Each job is characterised by two distinct attributes, and all jobs sharing the same attributes are processed together as a single batch. Due to the structural and organisational characteristics of the production system, the two stages have to process the same batch sequence. When two consecutive batches with different attributes are processed, at least one stage must pay a setup, in order to reconfigure its own devices. Each stage incurs a setup cost that is a general non-decreasing function of the number of its own setups, and the problem consists of finding a batch sequence minimising the total setup costs of the production system. We present an original solution approach for the considered problem that is shown to be very effective using an extensive experimental campaign.     

Minimizing and balancing setups in a serial production system

This paper addresses a problem arising in the coordination between two consecutive manufacturing departments of a production system, in which parts are processed in batches, and each batch is characterized by two distinct attributes. Due to limited interstage buffering between the two stages, the two departments have to follow the same batch sequence. In the first department, a setup occurs every time the first attribute of the new batch is different from the previous one. In the downstream department, there is a setup when the second attribute of the new batch changes. The problem consists of finding a common batch sequence optimizing some global utility index. Here we propose a metaheuristic approach to a bi-criteria version of the problem considering two indices, namely the total number of setups paid for by the two departments and the maximum number of setups paid for by either department.     

Coordinating batching decisions in manufacturing networks

Family-based dispatching heuristics aim for improving job flow times by reducing time spent on set-ups. They realise set-up efficiencies by batching similar types of jobs. By their intuitiveness and the simplicity of their decision logic, they may contribute to an easy to implement and viable strategy in many practical settings. Similar to common dispatching rules most existing family-based dispatching heuristics are myopic, i.e. their decision scope is restricted to a single manufacturing stage. Hence, they neglect opportunities for improving shop performance by coordinating batching decisions with other manufacturing stages. Case examples from industry underpin the need for exploring these opportunities. We do so by studying a simple two-stage flow shop, entailing a serial and a batch stage. To facilitate shop coordination we propose extensions to existing family-based dispatching heuristics. Extended heuristics seek to further increase set-up efficiencies by allowing for upstream job re-sequencing, and pro-active set-ups, i.e. set-ups that may be initiated prior to the arrival of a job. Outcomes of an extensive simulation study indicate significant performance gains for extended heuristics vs. existing heuristics. Performance gains are largest for moderate and high set-up to run-time ratios.     

Increasing production rate in U-type assembly lines with sequence-dependent set-up times

U-shaped assembly lines are commonly used in just-in-time production systems as they have some advantages over straight lines. Although maximizing production rates on these lines by assigning tasks to stations is common practice in industrial environments, studies on the stated assembly line balancing problem are limited. This article deals with maximizing the production rate on U-shaped assembly lines under sequence-dependent set-up times. Sequence-dependent set-up times mean that after a task is performed, a set-up time, the duration of which depends on adjacent tasks, is required to start the next task operation. These set-ups are considered by dividing them into two groups, named forward and backward set-ups, to make the problem more practical. Two heuristics based on simulated annealing and genetic algorithms are improved beside the mathematical model. Experimental results show that solving the stated problem using the mathematical model is nearly impossible, while heuristics may obtain solutions that have acceptable deviations from the lower bounds.     

Campaign planning for multi-stage batch processes in the chemical industry

Inspired by a case study from industry, the production of special chemical products is considered. In this industrial environment, multi-purpose equipment is operated in batch mode to carry out the diverse processing tasks. Often, extensive set-up and cleaning of the equipment are required when production switches between different types of products. Hence, processes are scheduled in campaign mode, i.e. a number of batches of the same type are processed in sequence. The production of chem ical products usually involves various stages with significant cumulative lead times. Typically, these production stages are assigned to different plants. A hierarchical modelling approach is presented which co-ordinates the various plant operations within the entire supply network. In the first stage, the length of the campaigns, their timing, the corresponding material flows, and equipment requirements have to be determined. At this stage, an aggregation scheme based on feasibility constraints is employed in order to reflect the limited availability of the various types of production equipment. The second stage consists of an assignment model, which allocates the available equipment units between the production campaigns determined in the first stage of the solution procedure. In the third stage, resource conflicts are resolved, which may occur if clean-out operations and minimal campaign lengths have to be considered. The proposed hierarchical approach allows a more compact model formulation compared to ot her approaches known from the literature. As a result, a very efficient and flexible solution approach is obtained. In particular, commercially available standard solvers can be used to solve a wide range of campaign planning problems arising in the chemical industry.     

Part type selection,machine loading and part type volume determination problems in FMS planning

The solution to subproblems of FMS planning problems require an integrated approach. The mathematical programming approaches, which are often followed, are not suitable for large problems. In this paper, we have proposed a three stage approach to solving part type selection, machine loading and part type volume determination problems. In contrast to the usual approach of maximizing the part types in each batch (or minimizing the number of batches), we have attempted to maximize the routeing flexibility of the batches. A heuristic has been proposed for the part type selection problem and simple mathematical programs for the other two problems. The illustrative examples show that by improving the routeing flexibility of the batches the overall system performance has improved.     

A batch splitting method for a job shop scheduling problem in an MRP environment

The job shop scheduling problem has been a major target for many researchers. Unfortunately though, most of the previous research was based on assumptions that are different from the real manufacturing environment. Among those distorted assumptions, two assumptions about set-up time and job composition can greatly influence the performance of a schedule. First, most of the past studies ignored the impact of the before-arrival set-up time. If we know the sequence of operations in advance, we can obtain an improved schedule by preparing the setup before a job arrives. Secondly, most of the past studies assumed that a job consists of only a single part, that is a batch of size one. However, if we assume that a job consists of a batch size greater than one, as in many real manufacturing environments, then we can obtain an improved schedule because we can fill up the idle times of machines with jobs which have smaller processing times by splitting the original batches. However, the number of job orders may then increase due to the split, and the size of the scheduling problem would become too large to be solved in a practical time limit. Consequently, there may be an optimum batch size considering trade-off between better solution and tractability. The current study is the result of an attempt to find an acceptable solution when the production requirement from a MRP system for a planning period exceeds the capacity of a production system. We try to get an improved schedule by splitting the original batch into smaller batches, and consider setting up a machine before the actual arrival of jobs to that machine. Thereby we can meet the due date requirement without resorting to rescheduling of the master production schedule. For the given batch, we disaggregate it according to the algorithm we are proposing. A so-called 'modified shifting bottleneck procedure' is then applied to solve the job shop scheduling problem with a before-arrival family set-up time considering release date, transportation time and due date. The study also shows that we can adapt to unexpected dynamic events more elegantly by allowing the splitting of batches.     

Computer-aided set-up planning for machining centres configuration

One of the key issues in defining the optimal configuration of a machining centre is the problem of determining the minimal number of set-ups for the part types to be machined. This paper proposes a method to define near-optimal set-up plans for prismatic workpieces when multiple parts can be mounted on the same pallet. Set-ups are determined taking into account the accessibility of the machining directions of the workpiece and the technological constraints among the required operations. The technological constraints are divided into three types: constraints that force the operations to share the same set-up, precedence constraints that cannot be violated in the sequence of set-ups, and constraints that translate technological preferences and that might be sacrificed to optimize the set-up plan. The technological constraints are analysed with a graph-based approach. The method proposes a solution for three-, four- and five-axis machines. The set-up plan for three axes is the starting point to determine the solutions for four- and five-axis machines: the set-up plan for four and five axes results from the combination of set-ups of the three-axis machine. Alternative solutions with the minimal number of set-ups are determined. Each solution specifies the orientation of the workpiece on the pallet fixture in each set-up, the operations to be executed in each set-up and the precedence relations among set-ups. Starting from the results of the set-up planning, the configuration of the pallet can be defined and taking into account the pallet configuration, the optimal machining centre for specific manufacturing needs is selected.     

Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops

This study considers the batching and scheduling problem in two-stage hybrid flow shops in which each job with a distinct due-date is processed through two serial production stages, each of which has identical machines in parallel. Under the fundamental trade-off that large batch sizes with less frequent changeovers may reduce setup costs and hence increase machine utilisation, while small batch sizes may reduce job flow times and hence improve scheduling performance, the problem is to determine the number of batches, the batch compositions, the allocation of batches to the parallel machines at each stage, and the sequence of the batches allocated to each machine for the objective of minimising the total job tardiness. A mixed integer programming model is developed for the reduced problem in which the number of batches is given, and then, three iterative algorithms are proposed in which batching and scheduling are done repeatedly until a good solution is obtained. To show the performance of the algorithms, computational experiments were done on a number of test instances, and the results are reported. In particular, we show that the number of batches decreases as the ratio of the batch setup time to the job processing time increases.     

Product batching and batch sequencing for NC punch presses

This paper proposes a two-stage practical product batching and batch sequencing algorithm for NC punch presses used in the production of precision sheet metal electronics components. The first stage of the algorithm batches a given set of products in order to maximize the number of products in a batch as well as the tool magazine utilization. In this stage, tool magazine constraints such as number of available slots, size of slots, tool configurations and tool locations are taken into consideration. The resulting batches are passed to the second stage of the algorithm which sequences these batches. The sequencing is done by using the ‘ nearest neighbour’ heuristic for the ‘ travelling salesman problem’ Comparison of the new method with the procedure previously used by a manufacturer of such components demonstrated a significant reduction in setup times.     

Maximising profit for multiple-product,single-period,single-machine manufacturing under sequential set-up constraints that depend on lot size

The classical problem of order acceptance/rejection in make-to-order environments, when aiming to maximise profit with machine set-ups is extended in this paper to multiple set-ups depending on manufacturing batch size. In this case, if the manufacturing batch is larger than certain product-dependent bounds, not only is the initial set-up required but also periodic reset-ups are in order, generating sub-batches of the same order, such as tool resharpening and machine recalibration. A network formulation provides the basis for identifying effective algorithms to obtain a solution to the problem. A binary programming model (BPM) and a dynamic programming formulation (DPF) are proposed to solve the problem to optimality. In addition, two heuristics are developed to obtain lower bounds on maximum profit: each attempt to maximise customer satisfaction under production time restrictions, and to provide an extension to the classical knapsack problem. Numerical experimentation shows that computational time is not an issue when BPM and heuristics are applied, but the cost of commercial solvers for BPM algorithms might be problematic. However, if the aim is to code the DPF in-house, the curse of dimensionality in dynamic programming must be addressed, although dynamic programming does yield a full sensitivity analysis, which is useful for decision-making.     

The Economic Lot Sizes in Multistage Production Systems

This article develops a model for a single-product multistage production-inventory system with static deterministic demand, where the product moves between the stages in a serial fashion. In this model, it is assumed that the unfilled demand of the finished product is backlogged. Overproduction (with limitation) is allowed at the different stages so that each stage t may produce ki batches once every ki cycles. The decision variables for each stage i are the number of batches per run k_i the batch size Q_i, and the shortage quantity of the finished product Q_s. These are determined by minimizing the total cost per unit time which includes the inventory holding cost, the shortage cost, and the setup cost. The problem is also considered for the case with storage constraints at the different stages.     

Advanced scatter search approach and its application in a sequencing problem of mixed-model assembly lines in a case company

Mixed-model assembly line sequencing is significant in reducing the production time and overall cost of production. To improve production efficiency, a mathematical model aiming simultaneously to minimize overtime, idle time and total set-up costs is developed. To obtain high-quality and stable solutions, an advanced scatter search approach is proposed. In the proposed algorithm, a new diversification generation method based on a genetic algorithm is presented to generate a set of potentially diverse and high-quality initial solutions. Many methods, including reference set update, subset generation, solution combination and improvement methods, are designed to maintain the diversification of populations and to obtain high-quality ideal solutions. The proposed model and algorithm are applied and validated in a case company. The results indicate that the proposed advanced scatter search approach is significant for mixed-model assembly line sequencing in this company.     

Using Interactive Multiobjective Optimization in Continuous Casting of Steel

We discuss some pros and cons of using different types of multiobjective optimization methods for demanding real-life problems like continuous casting of steel. In particular, we compare evolutionary approaches that are used for approximating the set of Pareto-optimal solutions to interactive methods where a decision maker actively takes part and can direct the solution process to such Pareto-optimal solutions that are interesting to her/him. Among the latter type of methods, we describe an interactive classification-based multiobjective optimization method: NIMBUS. NIMBUS converts the original objective functions together with preference information coming from the decision maker into scalar-valued optimization problems. These problems can be solved using any appropriate underlying solvers, like evolutionary algorithms. We also introduce an implementation of NIMBUS, called IND-NIMBUS, for solving demanding multiobjective optimization problems defined with different modelling and simulation tools. We apply NIMBUS and IND-NIMBUS in an optimal control problem related to the secondary cooling process in the continuous casting of steel. As an underlying solver we use a real-coded genetic algorithm. The aim in our problem is to find a control resulting with steel of the best possible quality, that is, minimizing the defects in the final product. Since the constraints describing technological and metallurgical requirements are so conflicting that they form an empty feasible set, we formulate the problem as a multiobjective optimization problem where constraint violations are minimized.     

Scheduling with multi-attribute set-up times on unrelated parallel machines

This paper studies a problem in the knitting process of the textile industry. In such a production system, each job has a number of attributes and each attribute has one or more levels. Because there is at least one different attribute level between two adjacent jobs, it is necessary to make a set-up adjustment whenever there is a switch to a different job. The problem can be formulated as a scheduling problem with multi-attribute set-up times on unrelated parallel machines. The objective of the problem is to assign jobs to different machines to minimise the makespan. A constructive heuristic is developed to obtain a qualified solution. To improve the solution further, a meta-heuristic that uses a genetic algorithm with a new crossover operator and three local searches are proposed. The computational experiments show that the proposed constructive heuristic outperforms two existed heuristics and the current scheduling method used by the case textile plant.     

Multi-objective production scheduling with controllable processing times and sequence-dependent setups for deteriorating items

The production scheduling problem is to find simultaneously the lot sizes and their sequence over a finite set of planning periods. This paper studies a single-stage production scheduling problem subject to controllable process times and sequence-dependent setups for deteriorating items. The paper formulates the problem by minimising two objectives of total costs and total variations in production volumes simultaneously. The problem is modelled and analysed as a mixed integer nonlinear program. Since it is proved that the problem is NP-hard, a problem-specific heuristic is proposed to generate a set of Pareto-optimal solutions. The heuristic is investigated analytically and experimentally. Computational experiences of running the heuristic and non-dominated sorting genetic algorithm-I over a set of randomly generated test problems are reported. The heuristic possesses at least 56.5% (in the worst case) and at most 94.7% (in the best case) of total global Pareto-optimal solutions in ordinary-size instances.     

Migration NSGA: method to improve a non-elitist searching of Pareto front,with application in magnetics

The paper describes a migration strategy to improve classical non-dominated sorting genetic algorithm (NSGA) to find optimal solution of a multi-objective problem. Migration NSGA has been tested to assess its performance using analytical functions for which the Pareto front is known in analytical form, as well as two case studies in electromagnetics, for which the Pareto front is not known a priori. This strategy improves the approximation of the Pareto-optimal solutions of a multi-objective problem by introducing new individuals in the population miming the effect of migrations.     

A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

The capacitated lot-sizing problem with set-up carryover and set-up splitting (CLSP-SCSS) is formulated as a mixed integer linear program. We define set-up carryover as the production of a product that is continued over from one period to another without incurring an extra set-up. Set-up splitting occurs when the set-up for a product is started at the end of a period and completed at the beginning of the next period. We allow product dependent set-ups. Initial experimentation highlights the importance of including set-up splitting in the CLSP model. In 12 out of the 18 problem instances tested, our model yielded better solutions or removed infeasibility when compared with a CLSP model without set-up splitting.     

Iterative approach to operation selection and sequencing in process planning

This paper considers the problem of selecting and sequencing operations in process planning for the objective of minimizing the sum of operation processing costs and machine, set-up and tool change costs. The main constraint is the precedence relations among operations. To represent the precedence relations and alternative operations, a tree-structured precedence graph is suggested. Based on the graph, the entire problem is decomposed into two subproblems: operation selection and operation sequencing. Then, three iterative algorithms are suggested that solve the two subproblems iteratively until optimal and near-optimal solutions are obtained. The algorithms are illustrated using an example part, and to show the performances of the algorithms, computational experiments were done on randomly generated test problems. The results show that the algorithms suggested work well for the test problems.