A data-driven iterative refinement approach for estimating clearing functions from simulation models of production systems

Clearing functions that describe the expected output of a production resource as a function of its expected workload have yielded promising production planning models. However, there is as yet no fully satisfactory approach to estimating clearing functions from data. We identify several issues that arise in estimating clearing functions such as sampling issues, systematic underestimation and model misspecification. We address the model misspecification problem by introducing a generalised functional form, and the sampling issues via iterative refinement of initial parameter estimates. The iterative refinement approach yields improved performance for planning models at higher levels of utilisation, and the generalised functional form results in significantly better production plans both alone and when combined with the iterative refinement approach. The IR approach also obtains solutions of similar quality to the much more computationally demanding simulation optimisation approaches used in previous work.     

An exploratory study of disaggregated clearing functions for production systems with multiple products

Clearing functions (CFs) have shown considerable promise for representing production capacity in production planning models due to their ability to capture the non-linear relationships between throughput, order releases and lead times. Most CFs developed to date use the total work in progress of all products, in units of processing time, as the state variable. In this paper, we investigate CFs for multi-product systems where the overall throughput of the system is affected by the product mix. We show that the aggregate work in process (WIP) variable used in the previous CF literature may lead to inaccurate estimates of expected throughput for individual products. To address this issue, we explore the use of multi-dimensional CFs (MDCFs) that use an extended definition of resource state based on the disaggregated WIP levels for individual products. Several new functional forms for MDCFs are postulated for single machine multi-product systems and their ability to represent system behaviour is assessed using simulation experiments. Results reveal that MDCFs are better able to predict system performance in the presence of mix-dependent capacity losses. We also discuss the extension of the MDCF approach to multi-stage production systems.     

Work-in-process clearing in supply chain operations planning

In this study we provide insights into the effectiveness of the clearing function concept in a hierarchical planning context. The clearing function is a mathematical representation of the relation between the Work-In-Process (WIP) and the throughput of a production process. We use it in a deterministic order release planning model to anticipate the dynamics of the operational level, which is subject to uncertainties. A multi-period single-item order release and scheduling problem is considered in which the delivery schedule of the orders is determined through the planned lead times, and the capacity loading decisions are separated from the order release decisions in a way so as to plan for on-time deliveries. Early or late delivery of the orders, which are released and delivered in batches, has not been considered explicitly in previous studies on clearing functions, and it significantly affects the inventory costs. Both linear and non-linear clearing functions are tested using a simulation approach. The results indicate that modeling the clearing of WIP by a shop should be based on the short-term operational dynamics of the shop rather than on the long-term average shop behavior, since it improves the consistency between the operational planning and scheduling levels of the hierarchy. The presented methods and results provide valuable information on modeling production characteristics in aggregate production planning and scheduling models.     

Information processing-related infrastructural antecedents of manufacturing flexibility – a real options perspective

The relationship between manufacturing flexibility and environmental uncertainty has been widely studied; however, research involving manufacturing flexibility and associated infrastructural antecedents is sparse. In this paper, using the real options perspective, we develop a research model to explicate management support’s influence on an organisation’s manufacturing flexibility. We use a second-order, multi-dimensional construct and survey data collected from US manufacturers to test our hypotheses. The study provides evidence to suggest that management support through teamwork, information systems effectiveness, and integrated supply chain effectiveness enhances an organisation’s manufacturing flexibility.     

A hybrid scheduling approach for automated flowshops with material handling and time constraints

Flowshop scheduling problems have been extensively studied by several authors using different approaches. A typical flowshop process consists of successive manufacturing stages arranged in a single production line where different jobs have to be processed following a predefined production recipe. In this work, the scheduling of a complex flowshop process involving automated wet-etch station from semiconductor manufacturing systems requires a proper synchronisation of processing and transport operations, due to stringent storage policies and fixed transfer times between stages. Robust hybrid solution strategies based on mixed integer linear programming formulations and heuristic-based approaches, such as aggregation and decomposition methods, are proposed and illustrated on industrial-scale problems. The results show significant improvements in solution quality coupled with a reduced computational effort compared to other existing methodologies.     

Comparison between rule- and optimization-based workload control concepts: a simulation optimization approach

An important goal of Production Planning and Control systems is to achieve short and predictable flow times, especially where high flexibility in meeting customer demand is required, while maintaining high output and due-date performance. One approach to this problem is the workload control (WLC) concept. Within WLC research two directions have been developed, largely separately, over time: Rule based and optimisation-based models. If a company intends to introduce an order release concept based on WLC it first has to decide which of these two approaches should be applied. Therefore, this paper compares two of the most widely used and considered best performing periodic order release models out of both streams: the LUMS (rule based) and the clearing function model (optimisation based). The parameters of both approaches are set using simulation optimisation. The performance is compared using a simulation study of a hypothetical job shop in a rolling horizon setting. The results show that the optimisation model outperforms the rule-based mechanism in all instances with stochastic demand (exponential inter-arrival times), but is outperformed in aggregate cost of backorders and inventory holding and balancing measures by the LUMS approach for scenarios with high utilisation and seasonal demand.     

Convex optimisation for aggregate production planning

This paper presents a new solution approach to the problem of aggregate production planning (APP). As identified by many researchers, the APP cost function is convex and piecewise. Thus, the convex optimisation approach can be applied to the APP problem. Solving the APP problem using convex optimisation is attractive since it leads to an improved solution over the classical solution methods and it can be applied to a wider range of functions. The classical Linear Decision Rule model of APP is solved using convex optimisation and the resulting solution is compared to three solution approaches which have been historically used to solve this model. The results suggest that convex optimisation may be an effective approach for solving certain types of planning models.     

Economic tolerance design for quality

This paper provides a few general mathematical models for determining product tolerances which minimize the combined manufacturing costs and quality loss. The models contain quality cost with a quadratic loss function and represent manufacturing costs with geometrical decay functions. The models are also formulated with multiple variables which represent the set of characteristics in a part. Applications of these models include minimizing the total cost with effective tolerance allocation in product design.     

A Constraint Programming model for food processing industry: a case for an ice cream processing facility

This paper presents a Constraint Programming (CP) scheduling model for an ice cream processing facility. CP is a mathematical optimisation tool for solving problems either for optimality (for small-size problems) or good quality solutions (for large-size problems). For practical scheduling problems, a single CP solution model can be used to optimise daily production or production horizon extending for months. The proposed model minimises a makespan objective and consists of various processing interval and sequence variables and a number of production constraints for a case from a food processing industry. Its performance was compared to a Mixed Integer Linear Programming (MILP) model from the literature for optimality, speed, and competence using the partial capacity of the production facility of the case study. Furthermore, the model was tested using different product demand sizes for the full capacity of the facility. The results demonstrate both the effectiveness, flexibility, and speed of the CP models, especially for large-scale models. As an alternative to MILP, CP models can provide a reasonable balance between optimality and computation speed for large problems.     

A heuristic algorithm for master production scheduling problem with controllable processing times and scenario-based demands

Master production scheduling (MPS) is widely used by manufacturing industries in order to handle the production scheduling decisions in the production planning hierarchy. The classical approach to MPS assumes infinite capacity, fixed (i.e. non-controllable) processing times and a single pre-determined scenario for the demand forecasts. However, the deterministic optimisation approaches are sometimes not suitable for addressing the real-world problems with high uncertainty and flexibility. Accordingly, in this paper, we propose a new practical model for designing an optimal MPS for the environments in which processing times may be controllable by allocating resources such as facilities, energy or manpower. Due to the NP-hardness of our model, an efficient heuristic algorithm using local search technique and theory of constraints is developed and analysed. The computational results especially for large-sized test problems show that the average optimality gap of proposed algorithm is four times lower than that of exact solution using GAMS while it consumes also significantly smaller run times. Also, the analysis of computational results confirms that considering the controllable processing times may improve the solution space and help to more efficiently utilise the available resources. According to the model structure and performance of the algorithm, it may be proposed for solving large and complex real-world problems particularly the machining and steel industries.     

Thermal conditions affecting heat transfer in FDM/FFE: a contribution towards the numerical modelling of the process

The performance of parts produced by Free Form Extrusion (FFE), an increasingly popular additive manufacturing technique, depends mainly on their dimensional accuracy, surface quality and mechanical performance. These attributes are strongly influenced by the evolution of the filament temperature and deformation during deposition and solidification. Consequently, the availability of adequate process modelling software would offer a powerful tool to support efficient process set-up and optimisation. This work examines the contribution to the overall heat transfer of various thermal phenomena developing during the manufacturing sequence, including convection and radiation with the environment, conduction with support and between adjacent filaments, radiation between adjacent filaments and convection with entrapped air. The magnitude of the mechanical deformation is also studied. Once this exercise is completed, it is possible to select the material properties, process variables and thermal phenomena that should be taken in for effective numerical modelling of FFE.     

Tensors-structured numerical methods in scientific computing: Survey on recent advances

In the present paper, we give a survey of the recent results and outline future prospects of the tensor-structured numerical methods in applications to multidimensional problems in scientific computing. The guiding principle of the tensor methods is an approximation of multivariate functions and operators relying on a certain separation of variables. Along with the traditional canonical and Tucker models, we focus on the recent quantics-TT tensor approximation method that allows to represent N-d tensors with log-volume complexity, O(d log N). We outline how these methods can be applied in the framework of tensor truncated iteration for the solution of the high-dimensional elliptic/parabolic equations and parametric PDEs. Numerical examples demonstrate that the tensor-structured methods have proved their value in application to various computational problems arising in quantum chemistry and in the multi-dimensional/parametric FEM/BEM modeling—the tool apparently works and gives the promise for future use in challenging high-dimensional applications.     

DEA cross-efficiency aggregation method based upon Shannon entropy

Existing approaches for DEA cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. The most widely used approach is to aggregate the efficiencies in each row or column in the cross-efficiency matrix with equal weights into an average cross-efficiency score for each Decision Making Unit (DMU) and view it as the overall performance measurement of the DMU. This paper focuses on the aggregation process of the efficiencies in the cross-efficiency matrix and proposes the use of Shannon entropy for cross-efficiency aggregation. In the study, we propose an entropy model to generate a set of weights for aggregating and determining the ultimate cross-efficiency instead of the traditional average cross-efficiency. We prove that the set of weight is a unique global optimal solution which can reflect the goodness of this method. Finally, two examples of a flexible manufacturing system and 27 industrial robots are illustrated to examine the validity of the proposed method.     

Minimisation of non-machining times in operating automatic tool changers of machine tools under dynamic operating conditions

In many optimisation studies, it is assumed that problem related data does not change once the generated solution plan or schedule is currently in use. However, majority of real-life manufacturing problems are time-varying in their nature due to unpredictable events such as changes in lot sizes, fluctuating capacities of manufacturing constraints, changes in costs or profits. A problem, which contains at least one of these feature is referred as dynamic optimisation problem (DOP) in the related literature. The present study introduces a practical industrial application of a DOP, emerging particularly in flexible manufacturing systems (FMSs), where numerically controlled machine tools with automatic tool changers are employed. It is already known in FMSs that minimisation of non-machining times is vital for an efficient use of scarce resources. Therefore, fast response to possible changes in production is crucial in order to attain flexibility. In this context, first, a benchmarking environment is created by making use of already published problems and by introducing dynamic events. Next, effective strategies, including simulated annealing (SA) algorithm along with SA with multiple starts are developed for the introduced problem. Numerical results show that the developed SA with multiple starts is a promising approach for the introduced problem.     

Workload planning in small lot printed circuit board assembly

The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.     

Decision support for design of reconfigurable rotary machining systems for family part production

To remain competitive in currently unpredictable markets, the enterprises must adapt their manufacturing systems to frequent market changes and high product variety. Reconfigurable manufacturing systems (RMSs) promise to offer a rapid and cost-effective response to production fluctuations under the condition that their configuration is attentively studied and optimised. This paper presents a decision support tool for designing reconfigurable machining systems to be used for family part production. The objective is to elaborate a cost-effective solution for production of several part families. This design issue is modelled as a combinatorial optimisation problem. An illustrative example and computational experiments are discussed to reveal the application of the proposed methodology. Insight gained would be useful to the decision-makers managing the configuration of manufacturing systems for diversified products.     

The impact of performance and practice factors on UK manufacturing companies' survival

This paper investigates the effects of manufacturing performance variables and practice factors at the firm level on UK manufacturing companies' survival performance in the last two decades. Statistic tests and econometric modelling have been employed on a longitudinal UK manufacturing database. The statistic tests generate different survival factors for individual sectors and the whole database. Model results support contentions that, in general, technology usage, total factor productivity, quality and cost reduction were important survival factors and, in addition, so were workforce flexibility, innovation and product development process in specific contexts. Furthermore, the results suggest that the probit and logit models can be reasonably robust predicting tools for analysing UK manufacturing companies' survival.     

Automatic control of industrial processes (an antonym-logic approach)

Conclusions Evaluation of functional ability and quality is usually conducted with methods based on mathematical statistics and probability theory (in functional fitness evaluation) and on the theory of mean values (in quality assessments).In this paper, the authors assume that control (evaluation) of a production process is a combination of monitoring of the state of production equipment and the state of product throughout the stages of its processing. On the basis of AL, making use of logical connections between these objects, mathematical models are constructed for industrial process control. These models represent different degrees of control stringency at different stages. The possibility of combining an assessment of the functional fitness of equipment with the comprehensive product quality assessment is provided by the flexibility of AL apparatus, which allows the construction of estimates for objects to be described in fuzzy terms.Translated from Izmeritel'naya Tekhnika, No. 9, pp. 8–10, September, 1991.     

An empirical examination of sourcing's role in developing manufacturing flexibilities

Past research on manufacturing flexibility has emphasized technology and its contributions to flexibility. This study examines the role of sourcing practices in achieving manufacturing flexibilities. Manufacturing flexibility is conceptualized as a multi-dimensional construct and a taxonomy of existing research is developed. An exploratory empirical examination of the sourcing practices-flexibility linkage using canonical correlation and regression analysis suggests significant relationships between sourcing practice and manufacturing flexibilities. The results support the need for treating manufacturing flexibility as a multi-dimensional construct. The results also suggest that a firm could deploy specific sourcing practices to target specific manufacturing flexibilities in pursuit of agilitybased competitive advantages.     

Conceptualising complementarities in manufacturing flexibility: a comprehensive view

In this paper, we develop an extended view of the manufacturing flexibility construct. Instead of a sequential view as emphasised with the competence-capability perspective, the model presented in this study suggests a holistic view of manufacturing flexibility comprised of six complementary dimensions. We contend that the complementary view of manufacturing flexibility (MFLX) consisting of six dimensions – product-mix flexibility (PMX), routing flexibility (RTG), equipment flexibility (EQP), volume flexibility (VOL), labour flexibility (LBR), and supply management flexibility (SPM) – provides a path to implementation of manufacturing flexibility. Manufacturing flexibility is hypothesised as a second order construct comprised of the six complementary dimensions. We test our proposed model using data collected from US manufacturing organisations. Structural equation modelling was used to analyse the data. The results of confirmatory factor analysis support our hypothesis of a second order multi-dimensional construct structure. This comprehensive conceptualisation of manufacturing flexibility should help researchers evaluate the effect of manufacturing flexibility on operational and financial performance.