The Fuzzy Economic Order Quantity Problem with a Finite Production Rate and Backorders

The track of developing Economic Order Quantity (EOQ) models with uncertainties described as fuzzy numbers has been very lucrative. In this paper, a fuzzy Economic Production Quantity (EPQ) model is developed to address a specific problem in a theoretical setting. Not only is the production time finite, but also backorders are allowed. The uncertainties, in the industrial context, come from the fact that the production availability is uncertain as well as the demand. These uncertainties will be handled with fuzzy numbers and the analytical solution to the optimization problem will be obtained. A theoretical example from the process industry is also given to illustrate the new model

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

An inventory system with time-dependent demand and partial backordering under return on inventory investment maximization

Producción CientíficaIn this article, we study an inventory system for items that have a power demand pattern and where shortages are allowed. We suppose that only a fixed proportion of demand during the stock-out period is backordered. The decision variables are the inventory cycle and the ratio between the initial stock and the total quantity demanded throughout the inventory cycle. The objective is to maximize the Return on Inventory Investment (ROII) defined as the ratio of the profit per unit time over the average inventory cost. After analyzing the objective function, the optimal global solutions for all the possible cases of the inventory problem are determined. These optimal policies that maximize the ROII are, in general, different from those that minimize the total inventory cost per unit time. Finally, a numerical sensitivity analysis of the optimal inventory policy with respect to the system input parameters and some useful managerial insights derived from the results are presented.Ministerio de Ciencia, Innovación y Universidades - Fondo Europeo de Desarrollo Regional (project MTM2017-84150-P

A lot-sizing model for a multi-state system with deteriorating items, variable production rate, and imperfect quality

Conventional production systems assume that during the manufacturing processes, machines operate without breakdown over an infinite planning horizon and manufacture only products of good quality. Imperfect production processes as a result of machine degradation are common in manufacturing. This paper deals with a problem that concerns the modelling and evaluation of the performance of a multi-state production system that is subject to degradation and its effect on lot sizing. Here, we consider that the cycle starts with a particular production rate until a point when the inventory reaches a certain level after which the failure mode is activated due to the deterioration of certain components, leading to a reduction in the production rate in order to ensure the continuity of supply until the maximum inventory level is reached. Production then stops to restore the machine and the cycle starts again. We have assumed that the rate at which inventory deteriorates is exponential and that demand is constant. A numerical example is used to illustrate the model application, followed by sensitivity analysis. This paper contributes to lot sizing in the area of machine reliability by considering a production system in a degraded state with a non-increasing production rate for deteriorating items with imperfect quality and partial backlogging.http://www.ijmems.inhj2023Industrial and Systems Engineerin

Multi products single machine economic production quantity model with multiple batch size

In this paper, a multi products single machine economic order quantity model with discrete delivery is developed. A unique cycle length is considered for all produced items with an assumption that all products are manufactured on a single machine with a limited capacity. The proposed model considers different items such as production, setup, holding, and transportation costs. The resulted model is formulated as a mixed integer nonlinear programming model. Harmony search algorithm, extended cutting plane and particle swarm optimization methods are used to solve the proposed model. Two numerical examples are used to analyze and to evaluate the performance of the proposed model

Fuzzy production planning models for an unreliable production system with fuzzy production rate and stochastic/fuzzy demand rate

In this article, we consider a single-unit unreliable production system which produces a single item. During a production run, the production process may shift from the in-control state to the out-of-control state at any random time when it produces some defective items. The defective item production rate is assumed to be imprecise and is characterized by a trapezoidal fuzzy number. The production rate is proportional to the demand rate where the proportionality constant is taken to be a fuzzy number. Two production planning models are developed on the basis of fuzzy and stochastic demand patterns. The expected cost per unit time in the fuzzy sense is derived in each model and defuzzified by using the graded mean integration representation method. Numerical examples are provided to illustrate the optimal results of the proposed fuzzy models