A production scheduling problem with uncertain sequence-dependent set-up times and random yield

A scheduling problem in a real production line with uncertain sequence-dependent set-up times and a random yield is considered. The production line can produce multiple product types as production lots, each of which is composed of a number of products of the same product type. To changeover product types, a sequence-dependent set-up operation should be performed, and only the lower and upper bounds are known for the sequence-dependent set-up times. Moreover, the processing time to produce the required number of product for each production lot is uncertain due to the random yield. For the objective of minimising the average tardy probability of given production lots, a systematic approximation scheme to estimate tardy probabilities of lots in any given production sequence is developed by taking not only the uncertainties but also the computational efficiency into account. As practical solution approaches, a simulated annealing and a discrete particle swarm optimisation algorithms using the approximation scheme are developed, and their performance are evaluated by computational experiments. Since there has been no research on the scheduling problems with uncertain sequence-dependent set-up times and random yield, the authors expect this research will make an excellent contribution to develop practical scheduling methodologies in uncertain scheduling environments.     

A hybrid Benders approach for coordinated capacitated lot-sizing of multiple product families with set-up times

We examine a coordinated capacitated lot-sizing problem for multiple product families, where demand is deterministic and time-varying. The problem considers set-up and holding costs, where capacity constraints limit the number of individual item and family set-up times and the amount of production in each period. Using a strong reformulation and relaxing the demand constraints, we improve both the upper and lower bounds using a combination of Benders decomposition and an evolutionary algorithm, followed by subgradient optimisation. Through computational experiments, we show that our method consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature.     

Non-exhaustive family based dispatching heuristics–exploiting variances of processing and set-up times

Group technology exploits similarities in product and process design to effectively meet the diversity of customer demand. In this paper we consider one of the implementations of this concept–heuristics for family based dispatching. Intrinsic to family based dispatching is the grouping of similar types of products for joint processing. Hence, the number of set-ups may be reduced. Consequently, lead time performance of the shop can be improved. Unfortunately, variances of processing and set-up times–as found in practice–have received little attention in heuristics’ construction and testing. To address this issue we propose several new, non-exhaustive heuristics. Whereas existing exhaustive heuristics set batch contents equal to all products available for a family, non-exhaustive heuristics allow for switching families, even when the current family queue is not empty. An extensive simulation study shows how this flexibility in batch composition improves shop performance, especially in case of high variances of processing and set-up times.     

Sequence Dependent Machine Set-Up Times and Similarity of Parts: A Mathematical Model

This paper attempts to develop a mathematical relation between machine set-up times and similarity of parts. First, the task for setting up a machine was broken down into a distinct number of elements whose state was expressed as a binary vector called set-up task elimination vector. By introducing a corresponding rime vector, it was shown that sequence dependent set-up time is the product of the two vectors. Next, a quantitative relation between set-up tasks and the design characteristics of parts was defined as a binary interaction matrix while the similarity of parts was defined as a binary vector. It turned out that the set-up tasks elimination vector is the Boolean product of the interaction matrix and the similarity vector. Using this information, a machine set-up model was developed in terms of similarity of parts. The computation of machine set-up times and a sequencing heuristic using the model were illustrated.     

Pull-type manufacturing systems with multiple product types

A multiple-product facility consisting of a manufacturing process and a finished product warehouse for several types of products is considered. An (R, r) continuous-review inventory control policy is applied to each type of product in the warehouse. The demand arrival process of each type is assumed to be Poisson. The processing times and the set-up times are arbitrarily distributed. We have developed an iterative procedure to approximately compute the average inventory level of each product in the warehouse under different priority schemes     

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.     

SINGLE-STAGE, MULTI-PRODUCT PRODUCTION/INVENTORY SYSTEMS WITH BACKORDERS

A production/inventory system consisting of a single-stage facility producing multiple product types and a warehouse is considered. The demand process is assumed to be Poisson and the excess demand is backordered. Products have a priority structure and the processor is shared according to a switching rule. (R, r) continuous-review inventory control policies are used to start and stop production of each product. Production of a product continues until its target level is reached. Then, a switch-over takes place to the highest priority product among the ones that need the processor's attention. A set-up takes place every time a switch-over occurs. Both processing and set-up times are assumed to have arbitrary distributions. The number of switch-overs among the high priority products is restricted in case low priority products need attention. The objective is to obtain performance measures such as the average inventory and backorder levels as well as die probability of having a backorder upon arrival for each product. We develop an approximation procedure which emphasizes the characterization of the delay each product type experiences in receiving the processor's attention, once they place a request for it. The approximating arguments are based on independence assumptions.     

The effect of risk aversion on product family design under uncertain consumer segments

A product family refers to a group of products that have been derived from a common product platform and which are specifically designed to satisfy a variety of market segments. In this paper, we consider a firm utilising product family design in order to respond to the requirements of two consumer segments, each characterised by different quality valuations. Although the total number of consumers in the market is known, the proportions each segment share are random, with known mean and variance. We show how the uncertainty of the market segmentation affects the firm's decision whether to use common rather than unique components. Motivated by a problem faced by a major automotive manufacturer, we study the consequence of low and high uncertainty, various product quality levels and the difference of marginal valuation on the best configuration.     

Minimising makespan in flowshop group scheduling with sequence-dependent family set-up times using inserted idle times

This paper focuses on the permutation flowshop group scheduling problem to minimise makespan, which is typically found in flowline manufacturing cells. In contrast to classical flowshop scheduling, it is characterised by a scheduling task at two levels: on the one hand, jobs within part families and on the other hand, a number of part families have to be sequenced. Integrating sequence-dependent set-up times for every changeover of families, this problem can represent practical cases. By modelling each family as a job with time lags, some specific problem characteristics of the group scheduling problem are pointed out. It is shown that generating job sequences by minimising the sum of inserted machine idle times instead of makespan on the first level of scheduling and the use of the schedule heads on the second level can lead to significant improvements for some test problems. These findings are used for the improvement of existing constructive heuristic algorithms, whose effectiveness is assessed for several test instances with sequence-dependent family set-up times.     

Heuristics and sequence-dependent set-up jobs in flow line cells

A key operational issue in cellular manufacturing systems is the scheduling of jobs within a family at each cell. Sequence-dependent set-up times during changeovers from one job to another afford scope for the exploitation of similarities at this stage to minimize the time spent on set-ups. This paper proposes heuristics for scheduling jobs within a part family by identifying subfamilies and sequencing them to improve the use of machines within a cell and to reduce the tardiness as well as the number of tardy jobs. The proposed heuristic, when evaluated by comparison with existing benchmark heuristics, yielded encouraging results.     

Sequence dependent set-up times and job sequencing

On many machine tools the set-up times are sequence dependent; that is, the time to set-up for the new part is dependent upon the part for -which the machine is currently set-up. In scheduling lots on the machine, the set-up time is often a significant component of the total time required to complete each lot. Set-up times are frequently not available to the production scheduler, and when they are, they frequently are only averages which conceal the sequence dependency of the set-up times. In this paper, we first develop a procedure that classifies set-up operations and predicts the set-up times and we then develop a method for sequencing the jobs so as to minimize the total set-up time. An example using real world data is used to illustrate these procedures     

A modified framework for modelling set-up carryover in the capacitated lotsizing problem

In this note, a modified framework to model set-up carryovers in the capacitated lotsizing problem is presented. The proposed framework allows product dependent set-up times and costs to be incorporated. This is an extension of an earlier published work on modelling set-up carryovers for the constant set-up time scenario. An example to illustrate the modified framework is also provided.     

Iterated greedy algorithms to minimize the total family flow time for job-shop scheduling with job families and sequence-dependent set-ups

This study addresses a variant of job-shop scheduling in which jobs are grouped into job families, but they are processed individually. The problem can be found in various industrial systems, especially in reprocessing shops of remanufacturing systems. If the reprocessing shop is a job-shop type and has the component-matching requirements, it can be regarded as a job shop with job families since the components of a product constitute a job family. In particular, sequence-dependent set-ups in which set-up time depends on the job just completed and the next job to be processed are also considered. The objective is to minimize the total family flow time, i.e. the maximum among the completion times of the jobs within a job family. A mixed-integer programming model is developed and two iterated greedy algorithms with different local search methods are proposed. Computational experiments were conducted on modified benchmark instances and the results are reported.     

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.     

Rolling Kanban: a new visual tool to schedule family batch manufacturing processes with kanban

Rolling Kanban is the name of a kanban management methodology for batch processes manufacturing environment. Proposed in the early 2000s by FESTO Consulting, for two decades we have lost knowledge both from operative and scientific point of view. Basically, Rolling Kanban means a visual planning methodology based on the production of product-families and variants where: (i) set-up times are reduced between the products of the same family, and (ii) relevant times (dozens of minutes if not even hours) must be considered for changeover between products of different families. In addition, the cyclic production sequence between different product families cannot be maintained. Considering that very few technical information and documents are available about this approach, the main objective of this paper is to retrieve and present, for the first time to the scientific community, the Rolling Kanban methodology. Besides, a real industrial implementation concerning a manufacturer of domestic fittings is discussed as a case study. More specifically, two novel versions of the original Rolling Kanban technique are fully presented to effectively overcome certain limits and criticalities found during its operative use, such as the difficulty to realise a pull production, considering increased set-up time for changeover between products of different families.     

Family-based dispatching with parallel machines

Family-based dispatching heuristics seek to lower set-up frequencies by grouping similar types of jobs for joint processing. Hence, job flow times may be improved as less time is spent on set-ups. So far, family-based dispatching with parallel machines received little attention in literature. We address the perceived gap by proposing extensions to existing family-based dispatching heuristics. Main extensions concern improved rules for family priority settings and for coordinating the number of machines in use by a single family. Extended heuristics are tested by an extensive simulation study. Significant performance gains for extended heuristics vs. existing heuristics are found. Performance gains are largest for high set-up to run-time ratios.     

Closed loop supply chain network design and optimisation using fuzzy mixed integer linear programming model

Owing to the revolution in sustainable and green manufacturing the production planning and network design of closed loop supply chain concept has got the attention of researchers and managers. In this paper, a multi-product, multi-facility capacitated closed-loop supply chain framework is proposed in an uncertain environment including reuse, refurbish, recycle and disposal of parts. The uncertainty related to demand, fraction of parts recovered for different product recovery processes, product acquisition cost, purchasing cost, transportation cost, processing, and set-up cost is handled with fuzzy numbers. A fuzzy mixed integer linear programming model is proposed to decide optimally the location and allocation of parts at each facility and number of parts to be purchased from external suppliers in order to maximise the profit of organisation. The proposed solution methodology is able to generate a balanced solution between the feasibility degree and degree of satisfaction of the decision maker. The proposed model has been tested with an illustrative example.     

Scheduling parallel machines to minimize weighted flowtime with family set-up times

We describe and evaluate several branch-and-bound algorithms for an identical parallel machine scheduling problem with family set-up times and an objective of minimizing total weighted flowtime. The algorithms differ by choice of lower bound method. Computational results suggest conditions favourable to a particular algorithm as well as the range of problem sizes that can be optimally solved in reasonable CPU time.     

A mathematical programming model for reconfiguration of flexible manufacturing cells

In flexible manufacturing cells, changes in demand size, product mix, part variety, existing routings and set-up/operation times may require reconfiguration of the cells. In this study, an approach is developed to decide when and how such a reconfiguration should be carried out for existing cells. This study considers reconfiguration in terms of changing part routings, adding a new machine type in a cell, duplicating an existing machine type, removing an existing machine from a cell and transferring a machine to another cell. The study also shows the total number of tools of each type on each machine located in each cell after reconfiguration. To make the optimal reconfiguration decisions, a mathematical programming model to minimize the total reconfiguration cost is developed. The developed model considers the lower and upper bounds on machine utilizations and the time limits on machine cycle times to decide when to reconfigure the system.     

An ant colony optimisation algorithm for balancing two-sided U-type assembly lines with sequence-dependent set-up times

Some practical arrangements in assembly lines necessitate set-up times between consecutive tasks. To create more realistic models of operations, set-up times must be considered. In this study, a sequence-dependent set-up times approach for two-sided u-type assembly line (TUAL) structures is proposed for the first time. Previous studies on TUAL have not included set-up times in their analyses. Furthermore, an algorithm based on the Ant Colony Optimization (ACO) algorithm, which is using a heuristic priority rule based procedure has been proposed in order to solve this new approach. In this paper, we look at the sequence-dependent set-up times between consecutive tasks and consecutive cycles, called the “forward set-up time” and the “backward set-up time”, respectively. Additionally, we examine the “crossover set-up time”, which arises from a new sequence of tasks in a crossover station. In order to model more realistic assembly line configurations, it is necessary to include sequence-dependent set-up times when computing all of the operational times such as task starting times and finishing times as well as the total workstation time. In this study, the proposed approach aims to minimize the number of mated-stations as the primary objective and to minimize the number of total workstations as a secondary objective. In order to evaluate the efficiency of the proposed algorithm, a computational study is performed. As can be seen from the experimental results the proposed approach finds promising results for all literature-test problems.