Review of mathematical models for production planning under uncertainty due to lack of homogeneity: proposal of a conceptual model

[EN] Lack of homogeneity in the product (LHP) appears in some production processes that confer heterogeneity in the characteristics of the products obtained. Supply chains with this issue have to classify the product in different homogeneous subsets, whose quantity is uncertain during the production planning process. This paper proposes a generic framework for reviewing in a unified way the literature about production planning models dealing with LHP uncertainty. This analysis allows the identification of similarities among sectors to transfer solutions between them and gaps existing in the literature for further research. The results of the review show: (1) sectors affected by LHP inherent uncertainty, (2) the inherent LHP uncertainty types modelled, and (3) the approaches for modelling LHP uncertainty most widely employed. Finally, we suggest a conceptual model reflecting the aspects to be considered when modelling the production planning in sectors with LHP in an uncertain environment.This research was initiated within the framework of the project funded by the Ministerio de Economía y Competitividad [Ref. DPI2011-23597] entitled ‘Methods and models for operations planning and order management in supply chains characterised by uncertainty in production due to the lack of product uniformity’ (PLANGES-FHP) already finished. After, the project leading to this application has received funding from the European Union’s research and innovation programme under the H2020 Marie Skłodowska-Curie Actions with the grant agreement No 691249, Project entitled ’Enhancing and implementing Knowledge based ICT solutions within high Riskand Uncertain Conditions for Agriculture Production Systems’ (RUC-APS).Mundi, I.; Alemany Díaz, MDM.; Poler, R.; Fuertes-Miquel, VS. (2019). 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Advanced methods and models in uncertainty for the order promising process in supply chain characterized by the lack of homogeneity in product

Tesis por compendioThe Lack of Homogeneity in the Product (LHP) appears in productive processes with raw materials, which directly stem from nature and/or production processes with operations that confer heterogeneity to the characteristics of the outputs obtained, even when the inputs used are homogeneous. LHP appears in different sectors such as ceramic tile, horticulture, marble, snacks, among others. LHP becomes a managerial problem when customers require to be served with homogeneous product. Supply chains responsible to provide homogeneous product face the need to include classification activities in their productive processes to obtain sub-lots of homogeneous product. Due to the inherent LHP uncertainty, these homogeneous sub-lots will not be known until the product have been produced and classified. An improper management of the LHP can have a very negative impact on the customers' satisfaction due to inconsistencies in the answer to their requirements and also on the Supply Chain's efficiency. The Order Promising Process (OPP) appears as a key element for properly managing the LHP in order to ensure the matching of uncertain homogeneous supply with customer order proposals. The OPP refers to the set of business activities that are triggered to provide a response to the orders from customers. These activities are related to the acceptance/rejection decision, and to set delivery dates. For supply chains affected by the LHP, the OPP must consider the homogeneity as another requirement in the answer to the orders. Besides, due to the LHP inherent uncertainty, discrepancies between the real and planned homogeneous quantities might provoke that previously committed orders cannot be served. The Shortage Planning (SP) process intends to find alternatives in order to minimise the negative impact on customers and the supply chain. Considering LHP in the OPP brings a set of new challenging features to be addressed. The conventional approach of assuming homogeneity in the product for the master production schedule (MPS) and the quantities Available-To-Promise (ATP) derived from it is no longer adequate. Instead, both the MPS and ATP should be handled in terms of homogeneous sub-lots. Since the exact quantity of homogeneous product from the planned lots in the MPS is not exactly known until the classification activities have been performed, the ATP also inherits this uncertainty, bringing a new level of complexity. Non-homogeneous product cannot be accumulated in order to fulfil future incoming orders. Even more, if the product handled is perishable, the homogeneity management becomes considerably more complex. This is because the state of the product is dynamic with time and related variables to it, like quality, price, etc., could change with time. This situation could bring unexpected wasting costs apart from the shortages already mentioned. The perishability factor is itself another source of uncertainty associated to the LHP. This dissertation proposes a conceptual framework and different mathematical programming models and tools, in both deterministic and uncertainty environments, in order to support the OPP and SP under LHP's effect. The aim is to provide a reliable commitment with customer orders looking for a high service level not just in the due date and quantity but also in the homogeneity requirements. The modelling of the characteristics inherent to LHP under deterministic context constitutes itself one of the main contribution of this dissertation. Another novelty consists in the inclusion of uncertainty in the definition of homogeneous sub-lots, their quantities and their dynamic state and value. The uncertainty modelling approach proposed is mainly based on the application of fuzzy set theory and possibility theory. The proposed mathematical models and tools have been validated in real cases of SC, specifically in the ceramic tile sector for non perishables, and in the fruit sector for perishables. The results show a ...La Falta de Homogeneidad en el Producto (LHP, por sus siglas del inglés ``Lack of Homogeneity in the Product'') aparece en procesos productivos con materias primas que derivan directamente de la naturaleza y/o procesos de producción con operaciones que confieren heterogeneidad a las características de los productos obtenidos, incluso cuando los insumos utilizados son homogéneos. La LHP aparece en diferentes sectores como la cerámica, horticultura, mármol, snacks, entre otros. Se convierte en un problema gerencial cuando los clientes requieren homogeneidad en el producto y las cadenas de suministro enfrentan la necesidad de incluir actividades de clasificación en sus procesos productivos para obtener sub-lotes de producto homogéneo. Debido a la incertidumbre inherente a la LHP, los sub-lotes homogéneos y su cantidad no serán conocidos hasta que el producto haya sido producido y clasificado. Una gestión inadecuada de la LHP puede tener un impacto muy negativo en la satisfacción de los clientes debido a inconsistencias en la respuesta a sus requerimientos y también en la eficacia de la Cadena de Suministro. El Proceso de Comprometer de Pedido (OPP, por sus siglas del inglés ``Order Promising Process'') aparece como un elemento clave para gestionar adecuadamente la LHP, con el fin de asegurar la coincidencia entre el suministro incierto de producto homogéneo y las propuestas de pedido del cliente. El OPP se refiere al conjunto de actividades empresariales realizadas para proporcionar una respuesta a las órdenes de los clientes. Estas actividades están relacionadas con las decisiones de aceptación/rechazo, y establecimiento de fechas de entrega para las órdenes del cliente. En las cadenas de suministro afectadas por la LHP, el OPP debe considerar la homogeneidad como otro requisito adicional en la respuesta a los pedidos. Además, debido a la incertidumbre intrínseca de la LHP, las discrepancias entre las cantidades homogéneas reales y planificadas podrían provocar que las órdenes comprometidas anteriormente no puedan ser completadas debido a la escasez de producto. El proceso de planificación de la escasez (SP, por sus siglas del inglés "Shortage Planning") se encarga de encontrar alternativas para minimizar este impacto negativo en los clientes y la cadena de suministro. Considerar la LHP dentro del OPP implica un conjunto nuevo de características desafiantes que deben ser abordadas. El enfoque convencional de asumir la homogeneidad en el producto para el programa maestro de producción (MPS, por sus siglas del inglés "Master Production Schedule") y las cantidades disponibles a comprometer (ATP, por sus siglas del inglés "Available-To-Promise") derivadas de él, no es adecuado. En cambio, tanto el MPS como el ATP deben manejarse en términos de sub-lotes homogéneos. Dado que la cantidad exacta de producto homogéneo de los lotes previstos en el MPS no se sabe exactamente hasta que se han realizado las actividades de clasificación, el ATP también hereda esta incertidumbre, trayendo un nuevo nivel de complejidad. El producto no homogéneo no se puede acumular para satisfacer futuras órdenes entrantes. Más aún, si el producto manipulado es perecedero, el manejo de la homogeneidad se vuelve mucho más complejo. Esto se debe a que el estado del producto es dinámico en el tiempo, y variables relacionadas como calidad, precio, etc., podrían también cambiar con el tiempo. Esta situación puede provocar costos inesperados de desperdicio aparte de la escasez ya mencionada. El factor de perecedero es en sí mismo otra fuente de incertidumbre asociada a la LHP. Esta disertación propone un marco conceptual y diferentes modelos y herramientas de programación matemática, tanto en entornos deterministas como de incertidumbre, para apoyar al OPP y SP considerando el efecto de LHP. El objetivo es proporcionar un compromiso fiable con los pedidos de los clientes en busca de un alto nivel de servicio no sLa Falta d'Homogeneïtat en el Producte (LHP, per les seues sigles de l'anglés ''Lack of Homogeneity in the Product'') apareix en processos productius amb matèries primes que deriven directament de la natura i/o processos de producció amb operacions que conferixen heterogeneïtat a les característiques dels productes obtinguts, fins i tot quan les entrades utilitzades són homogènies . La LHP apareix en diferents sectors com la ceràmica, horticultura, marbre, snacks, entre altres. Es convertix en un problema gerencial quan els clients requereixen homogeneïtat en el producte i les cadenes de subministrament enfronten la necessitat d'incloure activitats de classificació en els seus processos productius per a obtindre sublots de producte homogeni. A causa de la incertesa inherent a la LHP, els sublots homogenis i la seua quantitat no seran coneguts fins que el producte haja sigut produït i classificat. Una gestió inadequada de la LHP pot tindre un impacte molt negatiu en la satisfacció dels clients degut a inconsistències en la resposta als seus requeriments i també en l'eficàcia de la Cadena de Subministrament. El Procés de Comprometre Comandes (OPP, per les seues sigles de l'anglés ''Order Promising Process'') apareix com un element clau per a gestionar adequadament la LHP, a fi d'assegurar la coincidència entre el subministrament incert de producte homogeni i les propostes de comanda del client. L'OPP es refereix al conjunt d'activitats empresarials realitzades per a proporcionar una resposta a les ordres dels clients. Aquestes activitats estan relacionades amb les decisions d'acceptació/rebuig, i establiment de dates de lliurament per a les ordres del client. En les cadenes de subministrament afectades per la LHP, l'OPP ha de considerar l'homogeneïtat com un altre requisit addicional en la resposta a les comandes. A més, a causa de la incertesa intrínseca de la LHP, les discrepàncies entre les quantitats homogènies reals i planificades podrien provocar que les ordres compromeses anteriorment no puguen ser completades a causa de l'escassetat de producte. El procés de planificació de l'escassetat (SP, per les seues sigles de l'anglés "Shortage Planning") s'encarrega de trobar alternatives per a minimitzar aquest impacte negatiu en els clients i en la cadena de subministrament. Considerar la LHP dins de l'OPP implica un conjunt nou de característiques desafiants que han de ser abordades. L'enfocament convencional d'assumir l'homogeneïtat en el producte per al programa mestre de producció (MPS, per les seues sigles de l'anglés "Master Production Schedule") i les quantitats disponibles a comprometre (ATP, per les seues sigles de l'anglés "Available-To-Promise") derivades d'ell, no és adequat. En canvi, tant el MPS com l'ATP han de manejar-se en termes de sublots homogenis. Atés que la quantitat exacta de producte homogeni dels lots previstos en el MPS no se sap exactament fins que s'han realitzat les activitats de classificació, l'ATP també hereta aquesta incertesa, portant un nou nivell de complexitat. El producte no homogeni no es pot acumular per a satisfer futures ordees entrants. Més encara, si el producte manipulat és perible, el maneig de l'homogeneïtat es torna molt més complex. Açò es deu al fet que l'estat del producte és dinàmic en el temps, i variables relacionades com qualitat, preu, etc., podrien també canviar amb el temps. Aquesta situació pot provocar costos inesperats de rebuig a banda de l'escassetat ja esmentada. El factor de perible és en si mateix un altra font d'incertesa associada a la LHP. Aquesta dissertació proposa un marc conceptual i diferents models i eines de programació matemàtica, tant en entorns deterministes com d'incertesa, per a recolzar a l'OPP i SP considerant l'efecte de LHP. L'objectiu és proporcionar un compromís fiable amb les comandes dels clients a la recerca d'un alt nivell de servei no sols en la data i la quantitat esperades, sGrillo Espinoza, H. (2017). Advanced methods and models in uncertainty for the order promising process in supply chain characterized by the lack of homogeneity in product [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/91110TESISCompendi

Simulation to reallocate supply to committed orders under shortage

[EN] This article aims to deal with the reallocating supply problem in both its real and planned contexts, to orders that result from the order promising process under shortage. To this end, we propose a system dynamics-based simulation model to facilitate modelling for order managers, and to provide a graphic support tool to understand the process and to make decisions. The basis of the simulation model's structure is a mixed-integer linear programming approach that intends to maximise profits by considering the possibility of making partial and delayed deliveries. To illustrate this, we consider a real-world problem from the ceramic sector that contemplates 35 orders. We obtained a solution by a mathematical programming model and a simulation model. The results show the simulation model's capacity to obtain near-optimum results, and to provide a simulated history of the system."This is an Author's Accepted Manuscript of an article published in Esteso, Ana, Josefa Mula, Francisco Campuzano-Bolarín, MME Alemany Diaz, and Angel Ortiz. 2018. Simulation to Reallocate Supply to Committed Orders under Shortage. International Journal of Production Research 57 (5). Informa UK Limited: 1552 70. doi:10.1080/00207543.2018.1493239, available online at: https://www.tandfonline.com/doi/full/10.1080/00207543.2018.1493239"Esteso, A.; Mula, J.; Campuzano-Bolarín, F.; Alemany Díaz, MDM.; Ortiz Bas, Á. (2019). Simulation to reallocate supply to committed orders under shortage. International Journal of Production Research. 57(5):1552-1570. https://doi.org/10.1080/00207543.2018.1493239S15521570575Alarcón, F., Alemany, M. M. E., Lario, F. C., & Oltra, R. F. (2011). La falta de homogeneidad del producto (FHP) en las empresas cerámicas y su impacto en la reasignación del inventario. Boletín de la Sociedad Española de Cerámica y Vidrio, 50(1), 49-58. doi:10.3989/cyv.072011Alemany, M. M. E., Alarcón, F., Oltra, R. F., & Lario, F. C. (2013). Reasignación óptima del inventario a pedidos en empresas cerámicas caracterizadas por la falta de homogeneidad en el producto (FHP). Boletín de la Sociedad Española de Cerámica y Vidrio, 52(1), 31-41. doi:10.3989/cyv.42013Alemany, M. M. E., Grillo, H., Ortiz, A., & Fuertes-Miquel, V. S. (2015). A fuzzy model for shortage planning under uncertainty due to lack of homogeneity in planned production lots. Applied Mathematical Modelling, 39(15), 4463-4481. doi:10.1016/j.apm.2014.12.057Alemany, M. M. E., Lario, F.-C., Ortiz, A., & Gómez, F. (2013). Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case. Applied Mathematical Modelling, 37(5), 3380-3398. doi:10.1016/j.apm.2012.07.022ALEMANY, M. M. E., A., A., BOZA, A., & FUERTES-MIQUEL, V. S. (2015). A MODEL-DRIVEN DECISION SUPPORT SYSTEM FOR REALLOCATION OF SUPPLY TO ORDERS UNDER UNCERTAINTY IN CERAMIC COMPANIES. Technological and Economic Development of Economy, 21(4), 596-625. doi:10.3846/20294913.2015.1055613Boza, A., Alemany, M. M. E., Alarcón, F., & Cuenca, L. (2013). A model-driven DSS architecture for delivery management in collaborative supply chains with lack of homogeneity in products. Production Planning & Control, 25(8), 650-661. doi:10.1080/09537287.2013.798085Campuzano-Bolarín, F., Mula, J., & Peidro, D. (2013). An extension to fuzzy estimations and system dynamics for improving supply chains. International Journal of Production Research, 51(10), 3156-3166. doi:10.1080/00207543.2012.760854Framinan, J. M., & Leisten, R. (2009). Available-to-promise (ATP) systems: a classification and framework for analysis. International Journal of Production Research, 48(11), 3079-3103. doi:10.1080/00207540902810544Georgiadis, P., & Michaloudis, C. (2012). Real-time production planning and control system for job-shop manufacturing: A system dynamics analysis. European Journal of Operational Research, 216(1), 94-104. doi:10.1016/j.ejor.2011.07.022Georgiadis, P., & Politou, A. (2013). Dynamic Drum-Buffer-Rope approach for production planning and control in capacitated flow-shop manufacturing systems. Computers & Industrial Engineering, 65(4), 689-703. doi:10.1016/j.cie.2013.04.013Grillo, H., Alemany, M. M. E., & Ortiz, A. (2016). A review of mathematical models for supporting the order promising process under Lack of Homogeneity in Product and other sources of uncertainty. Computers & Industrial Engineering, 91, 239-261. doi:10.1016/j.cie.2015.11.013Grillo, H., Alemany, M. M. E., Ortiz, A., & Mula, J. (2017). A Fuzzy Order Promising Model With Non-Uniform Finished Goods. International Journal of Fuzzy Systems, 20(1), 187-208. doi:10.1007/s40815-017-0317-yJeon, S. M., & Kim, G. (2016). A survey of simulation modeling techniques in production planning and control (PPC). Production Planning & Control, 27(5), 360-377. doi:10.1080/09537287.2015.1128010Mula, J., Campuzano-Bolarin, F., Díaz-Madroñero, M., & Carpio, K. M. (2013). A system dynamics model for the supply chain procurement transport problem: comparing spreadsheets, fuzzy programming and simulation approaches. International Journal of Production Research, 51(13), 4087-4104. doi:10.1080/00207543.2013.774487Olhager, J. (2003). Strategic positioning of the order penetration point. International Journal of Production Economics, 85(3), 319-329. doi:10.1016/s0925-5273(03)00119-1Tako, A. A., & Robinson, S. (2012). The application of discrete event simulation and system dynamics in the logistics and supply chain context. Decision Support Systems, 52(4), 802-815. doi:10.1016/j.dss.2011.11.01

QUALITATIVE ANSWERING SURVEYS AND SOFT COMPUTING

In this work, we reflect on some questions about the measurement problem in economics and, especially, their relationship with the scientific method. Statistical sources frequently used by economists contain qualitative information obtained from verbal expressions of individuals by means of surveys, and we discuss the reasons why it would be more adequately analyzed with soft methods than with traditional ones. Some comments on the most commonly applied techniques in the analysis of these types of data with verbal answers are followed by our proposal to compute with words. In our view, an alternative use of the well known Income Evaluation Question seems especially suggestive for a computing with words approach, since it would facilitate an empirical estimation of the corresponding linguistic variable adjectives. A new treatment of the information contained in such surveys would avoid some questions incorporated in the so called Leyden approach that do not fit to the actual world.Computing with words, Leyden approach, qualitative answering surveys, fuzzy logic

A decision support tool for the order promising process with product homogeneity requirements in hybrid Make-To-Stock and Make-To-Order environments. Application to a ceramic tile company

[EN] Order promising in manufacturing systems that produce non-uniform units of the same finished good becomes a more complex process when customer orders need to be served with homogeneous units. To facilitate this task, we propose a mathematical model-based decision tool to support the order promising process according to product homogeneity requirements in hybrid Make-To-Stock (MTS) and Make-To-Order (MTO) contexts. In these manufacturing environments, the comparison of Available-To-Promise (ATP) and/or Capable-To-Promise (CTP) quantities with homogeneous ones ordered by customers is necessary during the order commitment. To properly deal with customers' product uniformity requirements, different ATP consumption rules are implemented by defining a novel objective function. CTP modelling in these systems also entails having to address new aspects, such as estimating future homogeneous quantities in additional lots to the master plan, accomplishing minimum lot sizes and saving in setups when programming new lots. By including CTP in the order promising model, a closer integration with the master production schedule is achieved. The resulting mathematical model was applied to a ceramic tile company in different supply scenarios and execution modes, and at several availability levels (ATP and ATP&CTP). The results validate model performance and provide insights into the impact of ATP consumption rules on the profits made from committed customer orders in different scenarios for the specific ceramic tile company.This work was supported by the Spanish Ministry of Economy and Competitiveness with Grant DPI2011-23597 and the Universitat Polito cnica de Valencia with Grant Ref. PAID-06-11/1840.Alemany Díaz, MDM.; Ortiz Bas, Á.; Fuertes-Miquel, VS. (2018). A decision support tool for the order promising process with product homogeneity requirements in hybrid Make-To-Stock and Make-To-Order environments. Application to a ceramic tile company. Computers & Industrial Engineering. 122:219-234. https://doi.org/10.1016/j.cie.2018.05.040S21923412

3D Printing Concrete Structures and Verifying Integrity of their G-Code Instructions: Border Wall a Case Study

Thanks to advances in Additive Manufacturing (AM) technology and continued research by academics and entrepreneurs alike, the ability to “3d print” permanent concrete structures such as homes or offices is now a reality. Generally, AM is the process that allows for a 3d model of an object to be converted into hardware instructions to generate that object layer by layer using a malleable medium such as a plastic. Specifically, large scale concrete AM can now generate a structure, such as a building, layer by layer more quickly and efficiently than traditional construction methods [6, 39]. This innovative, semi-autonomous process promises many improvements over traditional construction methods, but it also introduces new challenges to be overcome. The increased level of automation, the accelerated construction speed, and costly nature of defects are all important factors that emphasize the need for a thorough review of the final hardware instruction sets before production of the project ever begins. In this research, we propose and explore five methods to help verify model integrity of the print instructions: visual inspection of the design elements, using Fuzzy Logic to predict thermal stress, extrusion end point evaluation, pathing collision checks, and ray tracing for identification and analysis of overhangs. While these methods are not all inclusive, they will help to identify potential defects and high risk design elements in the pre-production phases of a project. Collectively these five verification methods proposed serve as a starting point for verifying model integrity. These verification methods derive detailed information from the instruction sets, execute various simulations and data analysis, and provide feedback to improve the overall model design and print process. Additionally the simulation process described herein can be built upon to produce other methods of verification. Earthquake or wind resistance tolerances could potentially be verified using existing model data and material data. Lastly these verification methods will be actively applied across a case study for a proposed wall along the southern border of the United States. This applications was selected specifically because Additive Manufacturing should clearly have substantial benefits over traditional hands on construction methods for this project. A concrete wall without any of the intrinsic complications of lived in buildings, may prove to be an outstanding killer application of 3d printing technology. Not only is the border wall used as a test case for the verification methods, but it also serves as a cost analysis to predict the cost benefits of 3d printing simple mostly automated projects. The author does not endorse any political stance by proposing this case study. The case study is purely a scientific endeavor to explore the feasibility of concrete structures outside the scope of traditional buildings. Additional applications of the research could include water levees, dams, and perhaps even bridges. The construction of large scale concrete infrastructure may prove to be an ideal problem domain for Additive Manufacturing

A GENETIC ALGORITHM APPROACH FOR DYNAMIC SUPPLIER SELECTION

Supplier selection has a great impact on supply chain management. This decision considers many factors such as price, order quantity, quality, and delivery performance. We address a dynamic supplier selection problem (DSSP) which a buyer should procure multiple product from multiple supplier in multiple periods. Furthermore, transportation cost has significant impact in the procurement decision. However, only a few researchers consider transportation cost in their model. This paper proposes a dynamic supplier selection problem considering truckload shipping. A mixed integer non-linear programming (MINLP) model is developed to solve dynamic supplier selection problem. The purpose of model is to assign the best supplier that will be allocated products and to determine the right time to order that can minimize total procurement cost. In addition, constraints such as suppliers’ capacity, truck capacity, inventory balance, service level, and buyer storage are taken into consideration in the model. Due to the complexity of the problem, the formulated problem is NP-hard in nature so a genetic algorithm (GA) is presented to solve dynamic supplier selection problem. Finally numerical example has been solved by the proposed GA and the classical method using Lingo 16. The results illustrate an understandable slight errors in total cost when GA is compared to commonly used classical method