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

Application of Optimization in Production, Logistics, Inventory, Supply Chain Management and Block Chain

The evolution of industrial development since the 18th century is now experiencing the fourth industrial revolution. The effect of the development has propagated into almost every sector of the industry. From inventory to the circular economy, the effectiveness of technology has been fruitful for industry. The recent trends in research, with new ideas and methodologies, are included in this book. Several new ideas and business strategies are developed in the area of the supply chain management, logistics, optimization, and forecasting for the improvement of the economy of the society and the environment. The proposed technologies and ideas are either novel or help modify several other new ideas. Different real life problems with different dimensions are discussed in the book so that readers may connect with the recent issues in society and industry. The collection of the articles provides a glimpse into the new research trends in technology, business, and the environment

Volume flexible multi items inventory system with imprecise environment

This paper addresses a multi items volume flexible system for time dependent decaying items with the concept of machine breakdown and imprecise environment. In this study, partially backlogged shortages have been discussed. All the costs are fuzzified with signed distance method. Numerical examples are given to illustrate the theoretical results and sensitivity analysis is given to validate the results for various parameters

Sustainable Inventory Management Model for High-Volume Material with Limited Storage Space under Stochastic Demand and Supply

Inventory management and control has become an important management function, which is vital in ensuring the efficiency and profitability of a company’s operations. Hence, several research studies attempted to develop models to be used to minimise the quantities of excess inventory, in order to reduce their associated costs without compromising both operational efficiency and customers’ needs. The Economic Order Quantity (EOQ) model is one of the most used of these models; however, this model has a number of limiting assumptions, which led to the development of a number of extensions for this model to increase its applicability to the modern-day business environment. Therefore, in this research study, a sustainable inventory management model is developed based on the EOQ concept to optimise the ordering and storage of large-volume inventory, which deteriorates over time, with limited storage space, such as steel, under stochastic demand, supply and backorders. Two control systems were developed and tested in this research study in order to select the most robust system: an open-loop system, based on direct control through which five different time series for each stochastic variable were generated, before an attempt to optimise the average profit was conducted; and a closed-loop system, which uses a neural network, depicting the different business and economic conditions associated with the steel manufacturing industry, to generate the optimal control parameters for each week across the entire planning horizon. A sensitivity analysis proved that the closed-loop neural network control system was more accurate in depicting real-life business conditions, and more robust in optimising the inventory management process for a large-volume, deteriorating item. Moreover, due to its advantages over other techniques, a meta-heuristic Particle Swarm Optimisation (PSO) algorithm was used to solve this model. This model is implemented throughout the research in the case of a steel manufacturing factory under different operational and extreme economic scenarios. As a result of the case study, the developed model proved its robustness and accuracy in managing the inventory of such a unique industry

An enhanced approximation mathematical model inventorying items in a multi-echelon system under a continuous review policy with probabilistic demand and lead-time

An inventory system attempts to balance between overstock and understock to reduce the total cost and achieve customer demand in a timely manner. The inventory system is like a hidden entity in a supply chain, where a large complete network synchronizes a series of interrelated processes for a manufacturer, in order to transform raw materials into final products and distribute them to customers. The optimality of inventory and allocation policies in a supply chain for a cement industry is still unknown for many types of multi-echelon inventory systems. In multi-echelon networks, complexity exists when the inventory issues appear in multiple tiers and whose performances are significantly affected by the demand and lead-time. Hence, the objective of this research is to develop an enhanced approximation mathematical model in a multi-echelon inventory system under a continuous review policy subject to probabilistic demand and lead-time. The probability distribution function of demand during lead-time is established by developing a new Simulation Model of Demand During Lead-Time (SMDDL) using simulation procedures. The model is able to forecast future demand and demand during lead-time. The obtained demand during lead-time is used to develop a Serial Multi-echelon Inventory (SMEI) model by deriving the inventory cost function to compute performance measures of the cement inventory system. Based on the performance measures, a modified distribution multi-echelon inventory (DMEI) model with the First Come First Serve (FCFS) rule (DMEI-FCFS) is derived to determine the best expected waiting time and expected number of retailers in the system based on a mean arrival rate and a mean service rate. This research established five new distribution functions for the demand during lead-time. The distribution functions improve the performance measures, which contribute in reducing the expected waiting time in the system. Overall, the approximation model provides accurate time span to overcome shortage of cement inventory, which in turn fulfil customer satisfaction

Replenishment Policy for Pareto Type Deteriorating Items With Quadratic Demand under Partial Backlogging And Delay in Payments

The present model develops a replenishment policy in which the demand rate is quadratic polynomial-time function. Deterioration rate is a Pareto type function. Shortages are partial backlogging and delay in payments are allowed. Holding cost is a linear function of time. The backlogging rate varies with the waiting duration for the next replenishment. The present paper determines the optimal policy for the individual by minimizing the total cost. The optimization procedure has been explained by a numerical example and a detailed sensitivity analysis of the optimal solution has been carried out to display the effect of various parameters

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

Fuzzy Continuous Review Inventory Model using ABC Multi-Criteria Classification Approach: A Single Case Study

Abstract. Inventory is considered as the most expensive, yet important,to any companies. It representsapproximately 50% of the total investment. Inventory cost has become one of the majorcontributorsto inefficiency, therefore it should be managed effectively. This study aims to propose an alternative inventory model,  by using ABC multi-criteria classification approach to minimize total cost. By combining FANP (Fuzzy Analytical Network Process) and TOPSIS (Technique of Order Preferences by Similarity to the Ideal Solution), the ABC multi-criteria classification approach identified 12 items of 69 inventory items as “outstanding important class†that contributed to 80% total inventory cost. This finding  is then used as the basis to determine the proposed continuous review inventory model.This study found that by using fuzzy trapezoidal cost, the inventory  turnover ratio can be increased, and inventory cost can be decreased by 78% for each item in “class A†inventory.Keywords:ABC multi-criteria classification, FANP-TOPSIS, continuous review inventory model lead-time demand distribution, trapezoidal fuzzy numberÂ

Fuzzy Modeling Approach to On-Hand Stock Levels Estimation in (R, S) Inventory Systems with Lost Sales

[EN] Purpose: One challenge in inventory control models is to know the stock available at the beginning of the cycle to satisfy future demands, i.e. to know the on-hand stock levels at order delivery. For inventory managers, this knowledge is necessary to both determine service levels and establish the control parameters of the inventory policy. However, the calculation of on-hand stock levels when unfilled demand is lost is mathematically complex since on-hand stock cannot be negative by definition. The purpose of this paper is to propose a new approach to estimate on-hand stock levels when the inventory is periodically reviewed and unfilled demand is lost, through the use of fuzzy techniques. Design/methodology/approach: This paper applies fuzzy set techniques for the calculation of the on-hand stock levels at order delivery in the lost sales context, based on the uncertainty that real demand introduces. To this end, we propose a new approach based on modeling the on-hand stock as an imprecise Markov chain using possibility functions, which reduces significantly the computational effort required to obtain the on-hand stock levels. Findings: To illustrate the performance of the proposed method, two experiments are carried out. The first experiment shows that the proposed fuzzy method correctly calculates on-hand stock levels with insignificant deviation with respect the exact vector. Additionally, the results illustrate that the fuzzy method simplifies the calculation and highly reduces the computational efforts. The second experiment shows the performance of the fuzzy method when it is used to estimate service levels by means of the fill rate. The results show that the proposed method accurately estimates the fill rate with average deviations lower than 0.00015. Practical implications: Knowing the on-hand stock vector is important for inventory managers to establish the control parameters of the system, i.e. to determine the minimum base stock level, S, that guarantees the achievement of a target service level. The difficulty of this estimation is that to obtain the on-hand stock vector in a lost sales context requires a huge computational effort and it is difficult to implement in companies' information systems. However, the proposed fuzzy method leads to a very accurate calculation of the on-hand stock vector significantly reducing the computational costs, which makes this method easily implementable in practical environments. Originality/value: Fuzzy set techniques have been widely used in inventory models to introduce the uncertainty of demand, costs or shortage. However, to the best of our knowledge, this is the first paper which deals directly with fuzzy estimation of on-hand levels.This work was supported by Generalitat Valenciana under the project with reference GV/2017/032.Guijarro, E.; Babiloni, E.; Canós-Darós, MJ.; Canós-Darós, L.; Estelles Miguel, S. (2020). Fuzzy Modeling Approach to On-Hand Stock Levels Estimation in (R, S) Inventory Systems with Lost Sales. Journal of Industrial Engineering and Management. 13(2):464-474. https://doi.org/10.3926/jiem.3071S46447413