A Novel Method for Optimal Solution of Fuzzy Chance Constraint Single-Period Inventory Model

A method is proposed for solving single-period inventory fuzzy probabilistic model (SPIFPM) with fuzzy demand and fuzzy storage space under a chance constraint. Our objective is to maximize the total profit for both overstock and understock situations, where the demand D~j for each product j in the objective function is considered as a fuzzy random variable (FRV) and with the available storage space area W~, which is also a FRV under normal distribution and exponential distribution. Initially we used the weighted sum method to consider both overstock and understock situations. Then the fuzziness of the model is removed by ranking function method and the randomness of the model is removed by chance constrained programming problem, which is a deterministic nonlinear programming problem (NLPP) model. Finally this NLPP is solved by using LINGO software. To validate and to demonstrate the results of the proposed model, numerical examples are given

Development of Fuzzy Inventory Model under Decreasing Demand and increasing Deterioration Rate

This research study proposed an inventory model with both the time varying variable deterioration and demand rate under the fuzzy environment. Fuzzy set theory is generally consider with imprecision and uncertainty nature of quantitative coefficients. In this system, we assumed the linearly increasing and decreasing function of time  for deterioration and demand respectively. In this research work, we discuss a fuzzy inventory model solving by signed distance method where demand follow time varying.&nbsp

Detailed Inventory Record Inaccuracy Analysis

This dissertation performs a methodical analysis to understand the behavior of inventory record inaccuracy (IRI) when it is influenced by demand, supply and lead time uncertainty in both online and offline retail environment separately. Additionally, this study identifies the susceptibility of the inventory systems towards IRI due to conventional perfect data visibility assumptions. Two different alternatives for such methods are presented and analyzed; the IRI resistance and the error control methods. The discussed methods effectively countered various aspects of IRI; the IRI resistance method performs better on stock-out and lost sales, whereas error control method keeps lower inventory. Furthermore, this research also investigates the value of using a secondary source of information (automated data capturing) along with traditional inventory record keeping methods to control the effects of IRI. To understand the combined behavior of the pooled data sources an infinite horizon discounted Markov decision process (MDP) is generated and optimized. Moreover, the traditional cost based reward structure is abandoned to put more emphasis on the effects of IRI. Instead a new measure is developed as inventory performance by combining four key performance metrics; lost sales, amount of correction, fill rate and amount of inventory counted. These key metrics are united under a unitless platform using fuzzy logic and combined through additive methods. The inventory model is then analyzed to understand the optimal policy structure, which is proven to be of a control limit type

A Fuzzy Inventory System with Deteriorating Items under Supplier Credits Linked to Ordering Quantity

[[abstract]]The inventory problem associated with trade credit is a popular topic in which interest income and interest payments are important issues. Most studies related to trade credit assume that the interest rate is both fixed and predetermined. However, in the real market, many factors such as financial policy, monetary policy and inflation, may affect the interest rate. Moreover, within the environment of merchandise storage, some distinctive factors arise which ultimately affect the quality of products such as temperature, humidity, and storage equipment. Thus, the rate of interest charges, the rate of interest earned, and the deterioration rate in a real inventory problem may be fuzzy. In this paper, we deal with these three imprecise parameters in inventory modeling by utilizing the fuzzy set theory. We develop the fuzzy inventory model based on Chang et al.'s [1] model by fuzzifying the rate of interest charges, the rate of interest earned, and the deterioration rate into the triangular fuzzy number. Subsequently, we discuss how to determine the optimal ordering policy so that the total relevant inventory cost, in the fuzzy sense, is minimal. Furthermore, we show that Chang et al.'s [1] model (the crisp model) is a special case of our model (the fuzzy model). Finally, numerical examples are provided to illustrate these results.[[notice]]補正完畢[[journaltype]]國內[[incitationindex]]SCI[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]TW

A Fuzzy Economic Order Quantity (EOQ) Model with Consideration of Quality Items, Inspection Errors and Sales Return

In this paper, we develop an economic order quantity model with imperfect quality, inspection errors and sales returns, where upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a lessen price, prior to receiving the next shipment. The screening process to remove the defective items may involve two types of errors. In this article we extend the Khan et al. (2011) model by considering demand and defective rate in fuzzy sense and also sales return in our model. The objective is to determine the optimal order lot size to maximize the total profit. We use the signed distance, a ranking method for fuzzy numbers, to find the approximate of total profit per unit time in the fuzzy sense. The impact of fuzziness of fraction of defectives and demand rate on optimal solution is showed by numerical example

A fuzzy periodic review integrated inventory model involving stochastic demand, imperfect production process and inspection errors

In this study, we investigate an integrated production-inventory system consisting of a single-vendor and single-buyer. The buyer manages its inventory level periodically at a certain period of time. We consider a fuzzy annual demand, imperfect production, inspection errors, partial backordering, and adjustable production rate in the proposed model. Additionally, it is assumed that the protection interval demand follows a normal distribution. The model contributes to the current literature by allowing the inclusion of fuzzy annual demand, adjustable production rate and imperfect production and inspection processes. Our objective is to optimize the number of deliveries from vendor to buyer, the buyer’s review period, and the vendor’s production rate, so that the joint expected total annual cost incurred has the minimum value. Furthermore, an iterative procedure is proposed to find the optimal solutions of the model. We also provide a numerical example and conduct a simple sensitivity analysis to illustrate the model’s behaviour and feasibility. The results from the sensitivity analysis show that the defective rate, type I inspection error, fuzzy annual demand, fixed production cost, variable production cost and setup cost give impacts to both the review period and production rate. Finally, it is concluded that the proposed model can be applied by managers or practitiones for managing inventories across the supply chain involving a vendor and a buyer

Efficient near-optimal procedures for some inventory models with backorders-lost sales mixture and controllable lead time, under continuous or periodic review

This paper considers a number of inventory models with backorders-lost sales mixture, stockout costs, and controllable lead time. The lead time is a linear function of the lot size and includes a constant term that is made of several components. These lot-size-independent components are assumed to be controllable. Both single- and double-echelon inventory systems, under periodic or continuous review, are considered. To authors knowledge, these models have never been previously studied in literature. The purpose of this paper is to analyse and optimize these novel inventory models. The optimization is carried out by means of heuristics that work on an ad hoc approximation of the cost functions. This peculiarity permits to exploit closed-form expressions that make the optimization procedure simpler and more readily applicable in practice than standard approaches. Finally, numerical experiments investigate the efficiency of the proposed heuristics and the sensitivity of the developed models

Supply Chain

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications

Inventory management under uncertainty : a military application

Inventory management under uncertainty is a widely researched field and many different types of inventory models have been used to address inventory problems in practice [1, 10, 11, 26, 50, 35]. However, there is a lack of published studies focusing on inventory planning in environments, such as the military, that are characterised by uncertainty as a result of extreme events. A critical area in military decision support is inventory management. Planning for stock levels in particular can be a daunting task, due to the uncertainty associated with the future. The military is typically an environment where improbable events can have massive impacts on operations; and the availability of the correct amount of stock can enhance the responsiveness, efficiency, and preparedness of the military, and ultimately save human lives. On the other hand, excessive stock - especially ammunition - can result in huge monetary losses through damages, stock degradation, and stock obsolescence. Excessive ammunition also poses a risk to public safety, and can ultimately challenge a country's ability to control the use of force. It is therefore very important to provide proper attention to determining the required stock levels during military inventory management. This dissertation aims, therefore, to develop a reliable decision support tool that can assist with inventory management in the military. To achieve this, a mixed multi-objective mathematical model is used that attempts to minimise cost, shortages, and stock while incorporating demand uncertainty by means of probability distributions and fuzzy numbers. The model considers three different scenarios, and determines the minimum required stock level and the best order quantity for three different stock categories, for a single ammunition item. The model is converted into its crisp, non-fuzzy, and deterministic counterpart first by transforming the fuzzy constraints into their crisp versions and then deriving the deterministic model of the crisp recourse stochastic model. The corresponding crisp, deterministic model is then solved using exact branch-and-bound embedded in the LINGO 10.0 optimisation software package and the reliability of the solutions in different scenarios is tested by means of discrete event simulation. The reliability of the model is then compared with the reliabilities of the well known (r;Q) and (s; S) inventory models in the literature. The comparison indicates that the mixed model proposed in this dissertation is more reliable in extreme scenarios than the (r;Q) and (s; S) inventory models in the literature. A sensitivity analysis is then performed and results indicate that the model yields reliable solutions with a reliability that varies between 74.54% and 100%, depending on the scenario investigated. The lower reliability is during the high demand scenario, this is caused by the ability of the inventory model to prioritise different scenarios based on their estimated possibility to ensure that stock levels are not unneccessary escalated for highly improbable events. It can be concluded that the proposed mixed multi-objective mathematical model that aims to minimise inventory cost, surplus stock, and shortages is a reliable inventory decision support model for the uncertain military environment.Dissertation (MEng)--University of Pretoria, 2011.Industrial and Systems Engineeringunrestricte

Production planning mechanisms in demand-driven wood remanufacturing industry

L'objectif principal de cette thèse est d'étudier le problème de planification de la production dans le contexte d'une demande incertaine, d’un niveau de service variable et d’approvisionnements incontrôlables dans une usine de seconde transformation du bois. Les activités de planification et de contrôle de production sont des tâches intrinsèquement complexes et difficiles pour les entreprises de seconde transformation du bois. La complexité vient de certaines caractéristiques intrinsèques de cette industrie, comme la co-production, les procédés alternatifs divergents, les systèmes de production sur commande (make-to-order), des temps de setup variables et une offre incontrôlable. La première partie de cette thèse propose une plate-forme d'optimisation/simulation permettant de prendre des décisions concernant le choix d'une politique de planification de la production, pour traiter rapidement les demandes incertaines, tout en tenant compte des caractéristiques complexes de l'industrie de la seconde transformation du bois. À cet effet, une stratégie de re-planification périodique basée sur un horizon roulant est utilisée et validée par un modèle de simulation utilisant des données réelles provenant d'un partenaire industriel. Dans la deuxième partie de cette thèse, une méthode de gestion des stocks de sécurité dynamique est proposée afin de mieux gérer le niveau de service, qui est contraint par une capacité de production limitée et à la complexité de la gestion des temps de mise en course. Nous avons ainsi développé une approche de re-planification périodique à deux phases, dans laquelle des capacités non-utilisées (dans la première phase) sont attribuées (dans la seconde phase) afin de produire certains produits jugés importants, augmentant ainsi la capacité du système à atteindre le niveau de stock de sécurité. Enfin, dans la troisième partie de la thèse, nous étudions l’impact d’un approvisionnement incontrôlable sur la planification de la production. Différents scénarios d'approvisionnement servent à identifier les seuils critiques dans les variations de l’offre. Le cadre proposé permet aux gestionnaires de comprendre l'impact de politiques d'approvisionnement proposées pour faire face aux incertitudes. Les résultats obtenus à travers les études de cas considérés montrent que les nouvelles approches proposées dans cette thèse constituent des outils pratiques et efficaces pour la planification de production du bois.The main objective of this thesis is to investigate the production planning problem in the context of uncertain demand, variable service level, and uncontrollable supply in a wood remanufacturing mill. Production planning and control activities are complex and represent difficult tasks for wood remanufacturers. The complexity comes from inherent characteristics of the industry such as divergent co-production, alternative processes, make-to-order, short customer lead times, variable setup time, and uncontrollable supply. The first part of this thesis proposes an optimization/simulation platform to make decisions about the selection of a production planning policy to deal swiftly with uncertain demands, under the complex characteristics of the wood remanufacturing industry. For this purpose, a periodic re-planning strategy based on a rolling horizon was used and validated through a simulation model using real data from an industrial partner. The computational results highlighted the significance of using the re-planning model as a practical tool for production planning under unstable demands. In the second part, a dynamic safety stock method was proposed to better manage service level, which was threatened by issues related to limited production capacity and the complexity of setup time. We developed a two-phase periodic re-planning approach whereby idle capacities were allocated to produce more important products thus increasing the realization of safety stock level. Numerical results indicated that the solution of the two-phase method was superior to the initial method in terms of backorder level as well as inventory level. Finally, we studied the impact of uncontrollable supply on demand-driven wood remanufacturing production planning through an optimization and simulation framework. Different supply scenarios were used to identify the safety threshold of supply changes. The proposed framework provided managers with a novel advanced planning approach that allowed understanding the impact of supply policies to deal with uncertainties. In general, the wood products industry offers a rich environment for dealing with uncertainties for which the literature fails to provide efficient solutions. Regarding the results that were obtained through the case studies, we believe that approaches proposed in this thesis can be considered as novel and practical tools for wood remanufacturing production planning