Quantitative models for printing production planning in a lean manufacturing approach under uncertainty

Modelos cuantitativos para la planificación de la producción de impresión bajo enfoque de fabricación ajustada bajo incertidumbre

Tania Rojas¹, Josefa Mula², Raquel Sanchis³

Recibido: 02/11/2023 | Aceptado: 27/06/2024

Abstract

Demand uncertainty is inherent to production planning processes in a manufacturing environment due to intermittent customer order acceptance, among others. Hence the need to provide approaches and tools capable of facing these challenges regarding uncertainties. This paper aims to present a comparative analysis of several quantitative modelling approaches for production planning in a lean manufacturing (LM) approach under uncertainty. It should be noted that we wish to focus approaches on the printing industry. The search methodology consisted of selecting articles that centre on LM and uncertainty, and the printing industry, or another industry with similar characteristics from a quantitative perspective. The main findings are related to the identification of the applied modelling approaches and lean tools. After analysing the selected articles, the use of six modelling approaches was identified by highlighting stochastic programming (SP) and mixed integer linear programming (MILP). The identified models aim to minimise costs, optimise production and satisfy customer demand in an uncertain environment. Using LM tools improves stability and resource efficiency and should include more of them. The reviewed models offer several approaches to deal with uncertainty in production systems, which can be very useful for the printing industry and other sectors.

Keywords: Lean manufacturing, production planning, quantitative modelling, uncertainty, printing.

Resumen

La incertidumbre de la demanda es inherente a los procesos de planificación de la producción en un entorno de fabricación, debido, entre otras cosas, a la aceptación intermitente de pedidos por parte de los clientes. En este sentido, es necesario proporcionar enfoques y herramientas capaces de hacer frente a estos retos relacionados con la incertidumbre. El objetivo de este artículo es presentar un análisis comparativo de varios enfoques de modelización cuantitativa para la planificación de la producción en un enfoque de fabricación ajustada (LM) bajo incertidumbre. Cabe señalar que se desea centrar los enfoques en la industria de la impresión. La metodología de búsqueda consistió en seleccionar artículos centrados en LM e incertidumbre y en la industria gráfica u otra de características similares desde una perspectiva cuantitativa. Los principales resultados están relacionados con la identificación de los enfoques de modelización y las herramientas Lean aplicadas. Tras el análisis de los artículos seleccionados, se ha identificado el uso de seis enfoques de modelización, destacando la programación estocástica (SP) y la programación lineal entera mixta (MILP); asimismo, los modelos identificados tienen como objetivo minimizar los costes, optimizar la producción y satisfacer la demanda de los clientes en un entorno incierto. El uso de herramientas de LM mejora la estabilidad y la eficiencia de los recursos, por lo que debería incluirse un mayor número de ellas. Los modelos revisados ofrecen varios enfoques para hacer frente a la incertidumbre en los sistemas de producción, que pueden ser muy útiles para la industria gráfica y otros sectores.

Palabras clave: Fabricación ajustada, planificación de la producción, modelado cuantitativo, incertidumbre, impresión.

1. Introduction

Lean manufacturing (LM) has evolved considerably since its origins in major industrial sectors like automotive (Holweg, 2007), textile (Hodge et al. 2011), footwear (Reyes et al. 2024), technology (Lu, Yang, and Wang, 2011), among others, along with service industries in developed countries (Maware, Okwu, and Adetunji, 2022). As there are very few literature and research works that relate the principles of LM tools to the printing industry, it can be stated that its application to this industry type is scarce (Rojas et al. 2022). This may be because it is a labour-intensive production process, and production times are uncertain for depending on the working environment, and fatigue and skills of staff (Chan and Tay, 2018). Ainul et al. (2017) and Rai (2013) mention that the application of LM tools in printing industries has been deficient. The production planning process in printing industries is generally developed by fat-tailed distribution, which consists of combining small and large jobs according to the production schedule that, in turn, considers the combination of jobs and their respective arrival times. In their research, Gomero et al. (2020) contemplate how delays in product deliveries in a printing industry are due to long set-up times, poor machine availability, no standardisation of procedures and poor production scheduling. To solve these problems, they propose a two-dimensional production management model: workplace organisation (5S technique, human resources, visual management) and process organisation (SMED, Johnson method, focused improvement). It also takes a matrix failure mode and effects analysis (FMEA) to generate improvement that focuses on potential failures, which lowers the percentage of delay from 20% to 6%.

Becerra et al. (2019) understand that in order to reduce production times in the printing sector, a model can be adapted that integrates LM tools, i.e., Kanban, SMED and value stream mapping (VSM), into a make-to-order (MTO) production system, in addition to the application of process simulation using the Arena® software. The uncontrollable input variables are arrival time and service station time. The controllable input variables are number of workers, work schedule and break time. The controllable output variables are systems times and the number of processed products.

Due to lack of information about models related to LM tools in the graphics industry, some studies have been explored in other industries with similar production process models. Agnetis et al. (2019) focus on patient scheduling in an Italian hospital by combining lean thinking with mathematical optimisation to shorten patient waiting times. For the initial phase, they use plan-do-check-act (PDCA) for the quantitative analysis of data collection. In the study conducted in a pipeline company, Azadeh et al., (2017) validate the impact of resilience engineering integrated with LM principles, and propose an algorithm based on a radial basis function (RBF), a multilayer perceptron (MLP) and an adaptive neurofuzzy inference system (ANFIS) to handle fuzzy data.

It is important to highlight that validated quantitative LM approaches are needed (Pearce and Pons, 2019). Rojas et al. (2024) provide an exhaustive literature review on quantitative modelling LM approaches under uncertainty. Here the aim of this article is to analyse and compare research related to quantitative modelling as a reference for production planning in an LM environment under uncertainty. The main contributions of the article are to: (i) identify existing works related to the quantitative modelling of LM production systems under uncertainty; (ii) analyse and compare the identified models so that they can serve as a reference for proposing new models.

1.The remainder of the paper is structured as follows. Section 2 describes the printing industry. Section 3 presents the comparative analysis of the reviewed articles. Section 4 discusses the main results of this study. Finally, Section 5 describes the conclusions and future research directions on the addressed topic.

2. Printing industry

In general, the printing industry has been stagnated due to digital economy evolution, and also to artificial intelligence, e-books and multimedia. It has also been affected by COVID-19 consequences since 2020, which marks the need for cost reduction (Chivatxaranukul, 2019). However, an opportunity has arisen for this sector to generate packaging products as a complement to growing food home delivery and parcel delivery processes.

When making books, magazines or commercial materials, there are several factors that intervene to configure a printing process, such as machine condition, paper condition and materials, which could represent more than 50% of the total process time with medium printing batches. With small printing batches, the percentage of preparation time is more representative and, therefore, the success of implementing or using single minute exchange of die (SMED) depends on some factors like operators’ motivation and mentality, among others (Chivatxaranukul, 2019). In addition, factors that affect productivity in a printing industry are related to changeover times, information flow, machine condition, quality, production rate and workers (Indrawati et al., 2018).

The wide variety of products, quantities and formats that can be produced by MTO companies, like the printing industry, among others, means that production planning has become increasingly complex because orders are intermittently received with ever-decreasing production volumes. In addition, MTO systems lead to longer changeover or preparation times from one product to another, which results in either more waste (Ainul et al., 2017) or longer delivery times to customers that, in turn, lead to last-minute changes (Indrawati et al., 2018).

3. Comparative analysis

In order to search for models, the Scopus and Web of Science databases (Bartol et al. 2014) were used to select the articles related to the quantitative models that can be applied to the characteristics of the printing or graphic industry by also considering uncertainty and LM tools. The used keywords query involved the following: (TITLE ("lean") AND TITLE ("quantit*" OR "model*ing" OR "uncertain*") AND ALL ("printing" OR "graphic")). This searching query provided 24 articles, of which the eight most relevant ones to the printing industry were selected. At this point, it is important to highlight the scarceness of research into LM under uncertainty in the printing industry, which is the main objective of this work.

The comparison of these potential models with their main application characteristics, modelling approach, problem type, application context, manufacturing strategy, uncertainty factors, objective function, and decision variables, LM tool and software tool appears in Table 1. These eight models belong to: Björk and Carlsson (2007); Karabuk (2008); Mirzapour, Malekly and Aryanezhad (2011); Wu (2011); Tayyab, Sarkar, and Ullah (2018); Kant, Pattanaik, and Pandey (2020); Gürsoy (2021); Ghahremani and Ghaderi (2022).

Björk and Carlsson (2007) present two mixed-integer linear programming (MILP) models with a fixed time horizon; one combines production and inventory decisions with fixed lead times, and the other does so with flexible lead times in relation to the context of an application producer in a tissue supply chain. Models are solved with a MILP solver and a genetic algorithm. These models seek to minimise the total cost of production and inventory holding, and late delivery penalty costs, based on the operation of a single product production line per planning period. The authors consider demand to be a factor of uncertainty, and the decision variables they take into account are related to quantity of product backordered, product in stock, product inventory status and generated product. It also considers binary variables in the problem: (i) whether products are produced during a time period; (ii) whether a product needs to be set up in production during a time period or not. It is worth mentioning that they do not relate the application of any LM tools. The authors propose the LP software to solve the genetic algorithm.

The model approach with stochastic programming (SP) and MH algorithms is applied by Karabuk (2008) and Wu (2011), and both in the textile sector. Karabuk (2008) explicitly includes uncertainty to solve yarn production planning problems in the form of discrete scenarios, which resulted in a large-scale mixed integer model that was difficult to solve with existing solvers. So it was necessary to create a pre-processing algorithm to improve computational requirements by demonstrating the advantages of an SP approach over a deterministic model. It aims to minimise the total rack change cost, the total expected rack change and the stock holding cost by applying CPLEX, version 8.1 (Karabuk, 2008). The decision variables used by Karabuk (2008) are related to: (i) rover changeovers, (ii) frame changeovers; (iii) inventory amount, focused on production machinery.

Wu (2011) addresses the problems of production loading between different factories in distinct countries with demand and import quota uncertainties to minimise the total production cost by using AIMMS 3.8 (with the CPLX 11.1 Solver). The SP model is developed in two stages: (i) when accurate market information is not available; (ii) when stochasticity materialises, which allows the firm to quickly react to changes in market information to minimise the total production cost. This stochastic resource model provides a more flexible, responsive and cost-effective production load system. During its development, it considers seven decision variables related to production quantity, machine capacity, workforce level and, initially available quotas: (i) production quantities of product by skilled/unskilled workers; (ii) planned labour time to hire workers; (iii) planned labour time to fire workers; (iv) used regular/additional machine capacities; (v) workers’ used labour time; (vi) skilled/unskilled workers’ used overtime; (vii) the initially allocated quota quantity of a product. Neither of the authors applied LM tools while developing their models.

Another approach is presented by Mirzapour, Malekly and Aryanezhad (2011). They apply a modelling approach with robust multi-objective mixed integer non-linear programming (MOMINLP) to solve problems related to multilocation, multiperiod and multiproduct aggregate production planning under uncertainty in a supply chain context. The aims are to: minimise total supply chain losses, including production cost, labour cost, hiring cost, firing cost, training cost, raw material inventory holding cost, end product inventory holding cost, transportation cost, raw material purchasing cost and shortage cost, from which the total sales are deducted; minimise stockouts between customer sites as much as possible by resorting to Lingo 8.0. While developing the model, seven variables are considered: (i) number of produced products; (ii) number of level workers at the site; (iii) inventory level of the raw material; (iv) inventory level of the end product; (v) number of units of raw material, (vi) number of units of end product; (vii) shortage of product at the demand point. The authors consider the proposed model feasible after applying it in an industrial case study, where the results provide a promising approach to efficient production planning in a supply chain. Some of the features of the proposed model are as follows: (i) considering the majority of supply chain cost parameters, such as transportation cost, inventory holding cost, shortage cost, production cost and human related cost; (ii) contemplating some aspects, such as employment, dismissal and workers productivity; (iii) considering the working levels and possibility of staff training and upgrading; (iv) contemplating the lead time between suppliers and sites, and between sites and customers’ zones; (v) cost parameters and demand fluctuations are subject to uncertainty.

Tayyab, Sarkar and Ullah (2018) propose a modelling approach with fuzzy multi-objective non-linear programming (FMONLP) to consider the economic quantity of production with uncertain demand, as well as fuzzy objective programming to solve problems related to lot size to minimise costs (configuration, order processing, rework, inventory maintenance) and carbon emissions. The proposed model is solved with a metaheuristic approach. The results are analysed to illustrate the robustness and its practical applicability for the model’s formulation. The following assumptions are taken into account: (i) a single type of item is produced during a multistage manufacturing process consisting of n number of stages; (ii) highly uncertain product demand; (iii) production rates above the demand rate to avoid shortages in the system; (iv) uncertain defective ratio in each stage of the multistage production system; (v) energy costs, labour costs and inspection costs are considered in each production stage to be components of the production cost; (vi) the cost and time of the material transfer between stages are negligible. Model optimisation is implemented using MATLAB R2015a with system specifications of 4 GB RAM at 1.80 GHz processor speed. An experimental study is performed to verify the model’s practical implication. The results are evaluated with an uncertainty control analysis and a sensitivity analysis of the important parameters. Seven waste types are taken into account in the LM tools considered in the analysis and development of the model. Lot sizing is also considered.

Kant et al. (2020) present a modelling approach of the elitist genetic algorithms (EGA) meta-heuristic to solve problems related to the reconfiguration of machines destined to the lean assembly line of multiple products by considering demand uncertainty to eliminate errors on the assembly line. To solve the model, they use the MATLAB ® version R2015b software with robust multi-objective mixed integer non-linear programming. The development of the model is divided into two stages: pre-production and production. In the pre-production stage, families of components and machine cells are formed using developed heuristics that comply with the features built into the reconfigurable cellular manufacturing system (CMS); in the production stage, an elitist genetic algorithm is applied twice in sequence for two optimisation problems formulated for each demand time period. For that purpose, two mathematical formulations in the form of combinatorial optimisation problems are developed to identify the best reconfiguration of machines by optimally selecting the modules in the cells to minimise: (i) the total error with takt time and then the optimal product assembly sequence; (ii) the total reconfiguration time and efforts. An elitist genetic algorithm (GA) is used as a meta-heuristic to search for optimal solutions in both minimisation tasks. Uncertainty during the demand time periods is also considered. To develop the proposed model, binary decision variables are taken into account if: (i) an operation is required for a component; (ii) an operation is performed on an auxiliary module; (iii) an auxiliary module belongs to a machine; (iv) a module is configured on a machine; (v) a product is scheduled after a product. This article suggests that, instead of taking the binary component-operation incidence, the actual sequence of operations can be considered to minimise the transport of material within cells during cell formation. It is also suggested that the hybrid CMS model may be suitable for manufacturing modular platform-based products.

Gürsoy (2021) also takes an MILP modelling approach, but applied to the supply chain context to contemplate quality and time. The proposed model aims to minimise the supply chain’s total cost and to meet customer satisfaction. The model is based on a mixed integer mathematical model that spans many stages and time periods and considers raw material quality, including the inventory balance constraints and time constraints for JIT delivery. It is shown that, despite higher purchasing costs, manufacturers prefer high-quality raw materials to ensure JIT delivery. It is worth mentioning that JIT aims to reduce waste and costs in the supply chain. The supply chain under study comprises four stages that involve multiple suppliers, manufacturers, distribution centres and retailers. In this chain, raw materials of three quality levels are supplied, where manufacturers process raw materials according to their quality. This results in quality costs and additional processing times, and in such a way that increased purchasing costs in relation to raw material quality must be balanced against decreased quality costs. The supply chain operates with limited capacities in all the stages, and demands are deterministic. It engages JIT as an LM tool and solves the proposed model by the GAMS distribution 21.6 programme. The decision variables related to the item's supply chain correspond to the: (i) quality of the transported raw material; (ii) product transported from the manufacturer; (iii) product transported from the distribution centre; (iv) quality of the reprocessed raw material; (v) distribution centre’s inventory level; (vi) retailer’s inventory level; (vii) retailer’s backorder level; (viii) product’s delivery lead time from the distribution centre. According to the proposed model, the author determines that the preference for high-quality raw materials allows for lower costs and JIT delivery in the supply chain network. The possibility of integrating heuristic methods to reduce calculation times in the event of having large data volumes is considered, as is exploring the inclusion of multiple objectives in the model by contemplating aspects like carbon emissions and transport efficiency.

One of the last selected models is that developed by Ghahremani and Ghaderi (2022), who apply robust-fuzzy optimisation (RFO) and found that when LM tools are used under supply chain network conditions, the sustainability performance indicator (SPI) rises and the waste of production units decreases. They also mention that the increased uncertainty effect brings about higher demand and reduces capacity in the supply chain network.

The model covers retailers, distribution centres, production sites, suppliers and customers. The main objective is to demonstrate how a fuzzy robust optimisation technique can address uncertainties related to factors like transportation costs, facility capacity and demand. This approach improves reliability to meet customer demand. It focuses on three key objectives: (i) minimising the total cost of the LSC network design (economic aspect); (ii) reducing waste in production units (environmental aspect); (iii) maximising the overall SPI (social aspect). The study explores exact and metaheuristic methods to identify the Pareto front by demonstrating that when lean management tools are employed in the supply chain network, SPI increases, waste decreases, but network design costs go up. The involved decision variables are: (i) if the supplier and production cost is obtained from the minimum score from lean tools and quality specifications; (ii) if the production centre is selected; (iii) if the distribution centre is selected; (iv) if the retailer is selected; (v) the production centre obtains the minimum score from the lean tools and quality specifications for the produced product; (vi) the quantity of product that is shipped between the retailer and the customer during the time period; (vii) the quantity of product shipped between the distribution centre and the retailer during the time period; (viii) the quantity of product shipped between the production and distribution centres during the time period; (ix) the quantity of component supplied from the supplier during the time period; (x) if a vehicle is allocated to transfer products from the retailer to the customer during the time period; (xi) if a vehicle is allocated to transfer products from the distribution centre to the retailer during the time period; (xii) if a vehicle is allocated to transfer products from the production centre to the distribution centre during the time period; (xiii) if lean tools and practices are allocated to the programming for the production centre; (xiv) if lean tools and practices are allocated to the programming for suppliers; (xv) if lean tools and practices are allocated to the programming for the distribution centre; (xvi) if lean tools and practices are allocated to the programming for the retailer. It solves the proposed model using the CPLEX solver.

4. Discussion

Following the analysis of the reviewed models related to modelling uncertainty in LM systems, specifically in the printing industry or one with similar characteristics, it is relevant to understand how companies can address planning and operating challenges in an uncertain environment.

The analysis of eight production planning models, each tailored to address specific uncertainties, evidenced that uncertainty management is paramount in production planning. For instance, Björk and Carlsson (2007) grapple with demand uncertainties in paper production, while Karabuk (2008) and Wu (2011) confront similar challenges in the textile sector. Mirzapour, Malekly and Aryanezhad (2011) delve into multisite, multiperiod and multiproduct aggregate production planning by emphasising the unpredictability of demand in supply chains.

Some models consider the possibility of integrating LM tools, but not all of them explicitly use them. Applying LM in production environments can help to improve efficiency, reduce costs and minimise waste. Further exploring how these tools can be incorporated would be valuable. Uncertainty in demand, transportation costs, facility capacity and other factors is a common challenge in production planning. Several models employ stochastic programming approaches and GAs to deal with uncertainty. The choice of the appropriate method depends on the nature of the uncertainty and the objectives of the system.

The reviewed models reflect that companies must balance aspects to ensure efficient and sustainable operation, and all the authors consider cost minimisation. Additionally, Björk and Carlsson (2007), Tayyab, Sarkar and Ullah (2018), Tayyab, Sarkar and Ullah (2018), Ghahremani and Ghaderi (2022) focus on waste reduction; finally, Ghahremani and Ghaderi (2022) also contemplate maximising sustainable performance as an objective function. Each model employs different software and solution methods to address production planning problems. Choosing the appropriate software and solution strategy is crucial to obtain accurate and efficient results. Of those used to run the proposed models, we find MATLAB®, version R2015b, in relation to the problem type; (i) lot sizing and (ii) reconfiguration for the machines by selecting modules in cells and the product assembling sequence.

These models serve as the foundation for developing a new model to study the feasibility of applying LM approach in the printing industry. This new model will be proposed to facilitate the determination of the most suitable production plan while considering the uncertainty factors that may arise during the planning process. This approach addresses the need for a more efficient and effective production planning system in the printing industry.

Figure 1 classifies the main research domains and summarises the findings per domain.

5. Conclusion

After the analysis of various quantitative models for production planning in the manufacturing system, the following conclusions can be drawn: (i) six types of modelling approaches are applied: EGA, FMONLP, MILP, MINLP, RFO and SP; (ii) there are a few instances in which LM tools are considered in the application of these models. Only five reviewed articles reveal that these tools have been applied in different industries to address uncertainties in production processes. All these models seek to minimise costs, optimise production and satisfy customer demand in an uncertain environment. Of the most commonly used LM tools, we find JIT, Pareto, takt time, push and seven wastes, and particularly re-work. The use of these LM tools helps to improve the stability and efficiency of resource utilisation on production lines, which indicates an opportunity for developing a mathematical model that integrates more LM tools in the future.

Each model addresses production and planning for different sectors, such as textiles, supply chain, yarn production, component production, product assembly, and many more. In most models, uncertainty in demand, transportation costs, facility capacity and other relevant factors are considered. It is important to note that some models do not explicitly use LM tools, while others mention the possibility of applying them in future research. These models offer a variety of approaches to deal with uncertainty in production systems, which can be extremely useful for the printing industry and other sectors.

A forthcoming work is oriented to propose a model that can be adapted to the graphic industry, which takes into account the following: (i) both external and internal uncertainties; (ii) incorporation of LM tools to ensure the stability of processes and efficient resources utilisation; (iii) integration of fuzzy logic to handle ambiguous and subjective information, which is crucial for decision making in complex and uncertain environments; (iv) focusing on production planning that helps to ensure that final products are delivered on time; (v) other methods can be used for this type of problems, such as mathematical techniques related to artificial intelligence, fuzzy logic, neural networks, among others.

Funding

The research leading to these results received funding from Project "Industrial Production and Logistics Optimization in Industry 4.0" (i4OPT) (Ref. PROMETEO/2021/065) granted by the Valencian Regional Government; and from Grant PDC2022-133957-I00 (CADS4.0-II) funded by MCIN/AEI /10.13039/501100011033 and by European Union Next Generation EU/PRTR.

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¹ Industrial Engineering Department, Universidad Politécnica Salesiana, Chambers 227, 090114, Guayaquil, Ecuador. Email: trojas@ups.edu.ec. Universitat Politècnica de València, Research Centre on Production Management and Engineering (CIGIP), c/ Alarcón, 1, 03801, Alcoy, Alicante, Spain. Email: taropar@doctor.upv.es

² Universitat Politècnica de València, Research Centre on Production Management and Engineering (CIGIP), c/ Alarcón, 1, 03801, Alcoy, Alicante, Spain. Email: fmula@cigip.upv.es

³ Universitat Politècnica de València, Research Centre on Production Management and Engineering (CIGIP), c/ Alarcón, 1, 03801, Alcoy, Alicante, Spain. Email: rsanchis@cigip.upv.es