Batch sizing with controllable production rates in a multi-stage production system

In this paper, a comprehensive model is presented for cell formation and layout design in cellular manufacturing systems (CMS). The proposed model incorporates an extensive coverage of important operational features and especially layout design aspects to determine optimal cell configuration and Intra and Inter-cell layout in CMS. Hence, proposed integrated approach attempts to design intra and inter-cell layout and material handling flow path structure simultaneously. We examine the great potential benefits of providing these features consist of routing flexibility, operation sequence, machine capacity, considering number of cells as a decision variable, un-equal dimension of machines, free machines and cells orientation, and considering pickup and drop off station for each cell. In order to show the effects and important of integrated design in the CMS, two approaches, sequentially and integrated, have been investigated and demonstrate the integrated approach improve the quality of obtained solution. The proposed model is a mixed integer non-linear programme. Linearisation procedures are proposed to transfer it into a linearised mixed integer programming formulation. Computational results are presented with the linearised formulation. We presented several enhancements in terms of valid inequalities and extensions to the proposed model in order to improve its computational performance. Finally, concluding remarks are provided.     

Capacitated lot-sizing problem with production carry-over and set-up splitting: mathematical models

This work proposes mathematical models (MMs) for the capacitated lot-sizing problem with production carry-over and set-up splitting, which can handle two scenarios, namely (1) situation/scenario where the set-up costs and holding costs are product dependent and time independent, and with no backorders or lost sales, and (2) situation where the set-up costs and holding costs are product dependent and time dependent, and with no backorders or lost sales. Previously, in an existing study the authors had developed a MM for the same problem and situation where the set-up costs and holding costs are product dependent and time independent, i.e. our Scenario 1. We compare our proposed models with the model in the existing study that appears to be incorrect.     

On the stability and bullwhip effect of a production and inventory control system

This paper focuses on the discrete-time automatic pipeline, inventory and order-based production control system (APIOBPCS), a well-established production and inventory control model. The feedback mechanism within the replenishment rule enables the model to mitigate the bullwhip effect, but introduces a stability problem. In this research, a comprehensive stability analysis is conducted for arbitrary lead times using difference equation theory. On the basis of stability, a state space approach is advocated to analyse the impact of replenishment parameters, demand processes, and lead times on the robustness of the bullwhip effect. The stability results demonstrate that the production control system can easily be destabilised without incorporating the work-in-progress (WIP) feedback loop. Furthermore, it reveals that the stability problem for long lead times can be simplified with the stability condition independent of the lead time. The results obtained in this study provide useful guidelines for the selection of replenishment parameters to guarantee stability and mitigate the bullwhip effect.     

Lot-sizing for a single-stage single-product production system with rework of perishable production defectives

We consider a single-stage single-product production system. Produced units may be non-defective, reworkable defective, or non-reworkable defective. The system switches between production and rework. After producing a fixed number (N) of units, all reworkable defective units are reworked. Reworkable defectives are perishable or can become technologically obsolete. We assume that the rework time and the rework cost increase linearly with the time that a unit is held in stock. Therefore, N should not be too large. On the other hand, N should not be too small either, since there are set-up times and costs associated with switching between production and rework. For a given N, we derive an explicit expression for the average profit (sales revenue minus costs). Using this expression, the optimal value for N can be determined numerically. Moreover, it is easy to perform a sensitivity analysis, as we illustrate. RID="*" ID="*"The research of Dr. Ruud H. Teunter has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research presented in this paper is part of the research on re-use in the context of the EU sponsored TMR project REVersed LOGistics (ERB 4061 PL 97-5650) in which take part the Otto-von-Guericke Universitaet Magdeburg (D), the Erasmus University Rotterdam (NL), the Eindhoven University of Technology (NL), INSEAD (F), the Aristoteles University of Thessaloniki (GR), and the University of Piraeus (GR). We thank the anonymous referees for their many helpful comments. Correspondence to: R. H. Teunter     

A Markovian approach for multi-level multi-product multi-period capacitated lot-sizing problem with uncertainty in levels

This paper considers a multi-level, multi-item, multi-period capacitated lot-sizing problem with sequence-dependent family set-up times, set-up carry over and uncertainty in levels due to uncertainty in inspection, rework and scrap. In this study, we, first, determined total processing time for each product of each family. Then, expected number of times associated with visiting each level of each product as well as amount of raw materials are calculated. We developed a mixed integer linear programming model with a numerical example and sensitivity analysis.     

Selection of a pull production control system in multi-stage production processes

In this paper, we conduct an analytical comparison of three pull production control systems: Kanban, CONWIP and Base-stock in multi-stage production processes. First, we compare the three control systems in a multi-stage serial production process. Then, we compare them in multi-stage assembly production processes, and present guidelines that allow us to select the best system. As a result, we show which structural parameters decide the superiority of one control scheme to the others, and how they are related. A key for superiority is a configuration of parameters, such as processing times and number of cards employed in the system. We show that there is no general superiority amongst the analysed concepts. Finally, we verify the effect of variability on the system performance, and generalise the analytical results of deterministic cases by conducting numerical experiments.     

Robust production planning and control for multi-stage systems with flexible final assembly lines

Production planning of final assembly systems is a challenging task, as the often fluctuating order volumes require flexible solutions. Besides, the calculated plans need to be robust against the process-level disturbances and stochastic nature of some parameters like manual processing times or machine availability. In the paper, a simulation-based optimisation method is proposed that utilises lower level shop floor data to calculate robust production plans for final assembly lines of a flexible, multi-stage production system. In order to minimise the idle times when executing the plans, the capacity control that specifies the proper operator–task assignments is also determined. The analysed multi-stage system is operated with a pull strategy, which means that the production at the final assembly lines generates demands for the preceding stages providing the assembled components. In order to guarantee the feasibility of the plans calculated for the final assembly lines, a decomposition approach is proposed to optimise the production plan of preceding stages. By this way, the robust production can be ensured resulting in reduced losses and overall production costs even though the system is exposed to changes and disturbances.     

A bi-objective robust inspection planning model in a multi-stage serial production system

In this paper, we present a bi-objective mixed-integer linear programming (BOMILP) model for planning an inspection process used to detect nonconforming products and malfunctioning processors in a multi-stage serial production system. The model involves two inter-related decisions: (1) which quality characteristics need what kind of inspections (i.e. which-what decision) and (2) when the inspection of these characteristics should be performed (i.e. when decision). These decisions require a trade-off between the cost of manufacturing (i.e. production, inspection and scrap costs) and the customer satisfaction. Due to inevitable variations in manufacturing systems, a global robust BOMILP (RBOMILP) is developed to tackle the inherent uncertainty of the concerned parameters (i.e. production and inspection times, errors type I and II, misadjustment and dispersion of the process). In order to optimally solve the presented RBOMILP model, a meta-heuristic algorithm, namely differential evolution (DE) algorithm, is combined with the Taguchi and Monte Carlo methods. The proposed model and solution algorithm are validated through a real industrial case from a leading automotive industry in France.     

An integrated sizing and planning problem in designing diverse vegetable farming systems

To support the short food supply chain development in cities, we propose a diverse vegetable farm design model to maximise the farm revenue in response to clients' daily demands in local fresh fruits and vegetables. The model supports decision in creating or adapting farms within or around cities with viable business models. To the best of our knowledge, our model is a first attempt to integrate strategic and tactical decisions on multi-techniques, multi-products and multi-clients production systems. Integrating strategic and tactical decisions, we obtain new solutions that could not be obtained by separating the two decision levels, due to product short-time perishability constraints: on-plot and cold-room storage, loss functions and price reduction. We define a specific formulation of the production methods in the model to consider both cultivation and harvest tasks that compete for limited and expensive labour resource. This paper presents the mixed integer linear programme we develop, as well as graphical and computational results. We have been able to find relevant solutions on a real farm case study that demonstrates the interest of using short time-paces for the strategic sizing of a farm growing fresh perishable products.     

Robust assignment of customer orders with uncertain configurations in a production network for aircraft manufacturing

Production of multi-variant products in a network requires the assignment of customer orders to locations and periods. This is a highly complex planning task, as requirements of procurement, production, distribution, and sales have to be considered. Providing customers with the flexibility of configuring their ordered products after order assignment further increases the complexity of the planning task by taking uncertainty into account. Therefore, a robust optimisation model, using scenarios representing potential customer-specific order configurations, is introduced. By providing enough flexibility to handle maximum work overload caused by the potential order configurations at locations, a robust assignment of orders can be guaranteed in order to avoid undesirable situations causing delays and additional costs. Therefore, the mid-term adjustments of the flexibility limits are enabled by the changeability of workforce supply by making use of external workers. An industrial application of the model in manufacturing of the Airbus A320 Family of aircrafts is presented. The costs for offering configuration flexibility to customers are quantified by the expected value of perfect information. The explicit consideration of configuration uncertainty through the use of scenarios is discussed based on the value of the stochastic solution in comparison to the results attained by simplistically using the expected value.     

A spread-sheet model for efficient production and scheduling of a manufacturing line/cell

In this paper we develop an efficient spread-sheet production planning/scheduling model for a resource-constraint production line or a manufacturing cell that produces several products but one at a time with significant changeover time and changeover cost. There are also management and physical constraints related to the operating hours, production capacity and amount of inventory allowed. The production line/cell supplies several products to customers who pull the products according to their own operating policy (working hours) that may be different from manufacture's operating hours. We also show several real-world applications and highlight the benefits and merits of the model.     

Congruence of manufacturing decision areas in a production system: a research framework

A well designed production system secures environmental and internal fit. Environmental fit in a production system refers to alignment of manufacturing decisions to the external settings such as product and market. Internal fit implies that manufacturing decisions are mutually supportive. This paper develops a framework to analyse congruence of manufacturing decision areas in a production system. The framework considers six broad manufacturing decision areas. Based on the literature review, 54 decision types and alternative decision choices for each decision type are identified. The subjective and/or objective constructs to measure decision type are presented which should be useful in designing construct and in data gathering to conduct empirical research. Using the proposed framework, many research questions concerning the settings of several decision types for a specific type of production system can be generated and empirically tested.     

Lot-sizing for a single-product recovery system with backordering

In this article, a single-product recovery system is studied. Used products are collected from customers and kept at the recoverable inventory warehouse for future recovery. The constant demand rate can be satisfied either by newly produced products or by recovered ones (serviceable inventory), which are regarded as perfectly as the new ones. Excess demand is completely backordered. Following an exact analytical approach, the optimal production and recovery policy is obtained. A numerical cost comparison of this model with the corresponding one without backordering is also performed. The results are general, as they were valid for finite and infinite production and recovery rates.     

Production system design to achieve energy savings in an automotive paint shop

Vehicle painting typically consumes the largest amount of energy in an automotive assembly plant. Effective reduction of energy usage in paint shops will lead to significant savings. Substantial effort has been devoted to reducing energy usage in paint shops through renovating the painting process and equipment. In this paper, we introduce a case study at an automotive paint shop to show that the energy consumption can be reduced significantly through production system design. Specifically, by selecting the appropriate repair capacity, the number of repainted jobs can be reduced, and less material and energy will be consumed. In addition, less atmospheric emissions would be generated during the painting process. Such a technique does not need to invent new chemicals, new painting processes or new control systems in painting booths and ovens. It provides an alternative way for energy and emission reduction to achieve energy-efficient and environmentally friendly manufacturing.     

Operator allocation planning for reconfigurable production line in one-of-a-kind production

In a one-of-a-kind production (OKP) company, the operation routing and processing time of an order are usually different from the others due to high customisation. As a result, an OKP company needs to dynamically adjust the production resources to keep the production lines reconfigurable. Through a proper assignment of operators in different sections of a production line, bottlenecks and operator re-allocation during production can be reduced effectively. In this paper, a mathematical model is introduced for optimal operator allocation planning on a reconfigurable production line in OKP. The optimisation objectives are to minimise the total number of the operators, total job earliness and tardiness, and the average work-in-process storage. A branch-and-bound algorithm with efficient pruning strategies is developed to solve this problem. The proposed model and the algorithm are empirically validated by using the data of a windows and doors manufacturing company. A software system based on the proposed approach has been implemented in the company.     

An integrated approach to evaluating the production system in closed-loop supply chains

The increasing demands for environmental resource protection and sustainable development have been forcing enterprises to put sustainable supply chain management on their agendas in recent years. At the same time, intense global competition requires organisations to adopt practices that enable them to provide high-quality products and services. In this paper, we consider the problem of comprehensively evaluating the production system in closed-loop supply chains. We first propose an evaluation framework that consists of economic evaluation, product quality evaluation and ecological evaluation modules. Based on mathematical probability theory and the dynamic characteristics of reverse supply chain logistics, we then focus on the evolution dynamics in the quality evaluation dimension, where the concept of product quality, which builds on the reliability and the time-utility value of a product, is proposed. The basic production evaluation model is then extended to incorporate different sustainable procurement strategies, which take into consideration the trade-offs among cost, environment and quality. An outline and corresponding flow chart of corporate procurement strategy optimisation are provided which allow the proposed evaluation model to be implemented in computer-aided decision-making, further providing decision support for production system and supply chain management. Simulation and case studies are presented to promote a better understanding of the model approach and its managerial implications. Results also suggest that quality characteristics of components and sustainable procurement strategies are two important factors that determine the final production performance and should be paid special attention in closed-loop supply chain practice.     

Aggregate production planning in the automotive industry with special consideration of workforce flexibility

We present a new mixed integer linear programming approach for the problem of aggregate production planning of flowshop production lines in the automotive industry. Our model integrates production capacity planning and workforce flexibility planning. In contrast to traditional approaches, it considers discrete capacity adaptations which originate from technical characteristics of assembly lines as well as from work regulations and shift planning. In particular, our approach takes change costs into account and explicitly represents a working time account via a linear approximation. A solution framework containing different primal heuristics and preprocessing techniques is embedded into a decision support system. Finally, we present an illustrative case study and computational results on problem instances of practically relevant complexity.     

Using a multi-agent system to optimise resource utilisation in multi-site manufacturing facilities

Due to cost economies and better serving the global market, many enterprises expanded their manufacturing environment from a localised, single-site facility to more globalised, multi-site facilities. In order to take advantage of operating multi-site facilities, it is vital to make optimisation decisions of resource utilisation as if these facilities situated across different geographical locations are one integrated facility and take into account of the extended multi-site constraints and variables. This paper proposes a multi-agent system, using its characteristics of autonomy and intelligence, to integrate process planning and production scheduling across different facilities, so as to secure the most efficient and cost-effective plan and schedule to meet the demand. A currency-based agent iterative bidding mechanism is developed to facilitate the co-ordination of agents to achieve the goal. A genetic algorithm is employed to tune the currency values for agent bidding. In this paper, a case study is used for simulation in order to demonstrate the effectiveness and performance of the proposed agent system.     

Multi-dimensional clearing functions for aggregate capacity modelling in multi-stage production systems

Nonlinear clearing functions have been proposed in the literature as metamodels to represent the behaviour of production resources that can be embedded in optimisation models for production planning. However, most clearing functions tested to date use a single-state variable to represent aggregate system workload over all products, which performs poorly when product mix affects system throughput. Clearing functions using multiple-state variables have shown promise, but require significant computational effort to fit the functions and to solve the resulting optimisation models. This paper examines the impact of aggregation in state variables on solution time and quality in multi-item multi-stage production systems with differing degrees of manufacturing flexibility. We propose multi-dimensional clearing functions using alternative aggregations of state variables, and evaluate their performance in computational experiments. We find that at low utilisation, aggregation of state variables has little effect on system performance; multi-dimensional clearing functions outperform single-dimensional ones in general; and increasing manufacturing flexibility allows the use of aggregate clearing functions with little loss of solution quality.     

A reactive decision-making approach to reduce instability in a master production schedule

One of the primary factors that impact the master production scheduling performance is demand fluctuation, which leads to frequently updated decisions, thereby causing instability. Consequently, global cost deteriorates, and productivity decreases. A reactive approach based on parametric mixed-integer programming (MIP) is proposed that aims to provide a set of plans such that a compromise between production cost and production stability is ensured. Several stability measures and their corresponding MIP model are proposed. An experimental study is performed to highlight the effectiveness of the reactive approach with regard to the proposed performance measures. It is observed that an improvement in stability does not mean a significant increase in the total production cost. Furthermore, the procedure yields a set of plans that in practice would enable flexible management of production.