Nima Kazemi

An inventory model with backorders with fuzzy parameters and decision variables

The paper considers an inventory model with backorders in a fuzzy situation by employing two types of fuzzy numbers, which are trapezoidal and triangular. A full-fuzzy model is developed where the input parameters and the decision variables are fuzzified. The optimal policy for the developed model is determined using the Kuhn-Tucker conditions after the defuzzification of the cost function with the graded mean integration (GMI) method. Numerical examples and a sensitivity analysis study are provided to highlight the differences between crisp and the fuzzy cases.

Incorporating human learning into a fuzzy EOQ inventory model with backorders

This paper considers fuzzy lot-sizing problem with human learning effect.A new fuzzy EOQ model with backorders and learning in fuzziness is developed.The proposed model has a good performance in terms of efficiency.The result suggests ordering with more frequency when human learning in fuzziness is considered. Even though publications on fuzzy inventory problems are constantly increasing, modelling the decision makers characteristics and their effect on his/her decisions and consequently on the planning outcome has not attracted much attention in the literature. In order to fill this research gap and model reality more accurately, this paper develops a new fuzzy EOQ inventory model with backorders that considers human learning over the planning horizon. The paper is an extension of an existing EOQ inventory model with backorders in which both demand and lead times are fuzzified. Here, the assumption of constant fuzziness is relaxed by incorporating the concept of learning in fuzziness into the model considering that the degree of fuzziness reduces over the planning horizon. The proposed fuzzy EOQ inventory model with backorders and learning in fuzziness has a good performance in efficiency. Finally, it is worth mentioning that learning in fuzziness decreases the total inventory cost.

A fuzzified version of the economic production quantity (EPQ) model with backorders and rework for a single-stage system

This paper extends a recent work that investigated a single-stage production-inventory model with reworks and planned backorders by fuzzifying its input parameters. The graded mean integration representation (GMIR) method, a useful and effective defuzzification method, is employed to develop a fuzzified total inventory cost function of model of interest. Triangular and trapezoidal fuzzy numbers are used to examine the developed fuzzy model. Later, the optimal policy, including the batch size, the backordering level and total cost, is determined using the classical approach. Furthermore, the derived optimal policies are tested using arbitrary fuzzy numbers. [Received 4 July 2011; Revised 4 November 2011; Revised 3 February 2012; Revised 16 July 2012; Accepted 27 October 2012]

Development of a fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters

This paper develops an inventory model for items with imperfect quality in a fuzzy environment by assuming that learning occurs in setting the fuzzy parameters. This implies that inventory planners collect information about the inventory system and build up knowledge from previous shipments, and thus learning process occurs in estimating the fuzzy parameters. So, it is hypothesized that the fuzziness associated with all fuzzy inventory parameters is reduced with the help of the knowledge acquired by the inventory planners. In doing so, the study developed a total profit function with fuzzy parameter, where triangular fuzzy number is used to quantify the fuzziness of the parameters. Next, the learning curve is incorporated into the fuzzy model to account for the learning in fuzziness. Subsequently, the optimal policy, including the batch size and the total profit are derived using the classical approach. Finally, numerical examples and a comparison among the fuzzy learning, fuzzy and crisp cases are provided to highlight the importance of using learning in fuzzy model.

A fuzzy EOQ model with backorders and forgetting effect on fuzzy parameters

This paper considers a fuzzy lot-sizing problem with forgetting effect.A new fuzzy EOQ model with backorders and forgetting is developed.The result suggests decreasing the maximum inventory and the total inventory cost. The study of learning effect on inventory models with imprecise parameters is a research topic that has recently emerged. The research papers have published so far studied this aspect from a theoretical point of view and thus the literature lacks the investigation of this topic from a practical standpoint. To close this research gap, we conducted a semi-structured interview with a number of industry experts to gain insights into the prevalence of learning and forgetting in real applications. Based on the insights gained from the interviews, we have developed a recently published model by countering the assumption of full transfer of learning. The model developed herein proposes a situation where the knowledge gained by the operator in setting imprecise parameters deteriorates over the planning cycles due to intermittent planning process. A numerical study suggests that accounting for the effect of knowledge depreciation/forgetting on imprecise parameters leads to reduction in maximum inventory, which consequently reduces the total cost of the system.

An economic order quantity model considering different holding costs for imperfect quality items subject to fuzziness and learning

This paper extends an economic order quantity (EOQ) model for items with imperfect quality based on two different holding costs and learning considerations. This is one of the few attempts aiming at combining the EOQ model, learning theory, and fuzzy technique in solving an EOQ problem. In present research, a fuzzy model is developed in which both parameters and decision variables are fuzzified and represented by triangular fuzzy numbers (TFNs). The total profit per unit time is obtained using fuzzy arithmetic operations, and then defuzzified by the graded mean integration value (GMIV) method. Using Karush-Kuhn-Tucker (KKT) conditions, the optimal lot size is obtained from the defuzzified total profit per unit time function. A numerical example for investigating the behavior of the model in a fuzzy situation is presented, and directions for future study are proposed. Besides, the results of the developed fully fuzzy model are compared with some previous ones in the literature.

A fuzzy lot-sizing problem with two-stage composite human learning

Due to the repetitive nature of inventory planning over the planning horizon, the operator in charge has to perform planning tasks repetitively, and consequently s/he becomes more familiar with the tasks over time. Familiarity with the tasks suggests that learning takes place in inventory planning. Even though the operator’s learning over time might improve his/her efficiency, prior research on fuzzy lot-sizing problems mostly overlooked the effect of human learning in their models and its impact on the operator’s performance. To close the research gap in this area, this paper models the operators learning in a fuzzy economic order quantity model with backorders. The paper models a situation where the operator applies the acquired knowledge over the cycles in setting the fuzzy parameters at the beginning of every planning cycle, where his/her learning ability includes the cognitive and motor capabilities of a human being. Subsequently, a mathematical model which takes account of a two-stage human learning over the planning cycles is developed, which is then analytically investigated using sample data-sets. The results indicate that both operator’s capabilities, cognitive and motor, affect the efficiency of the fuzzy lot-sizing inventory model, but the influence of the cognitive capability is more profound, which in turn suggests the importance of training programmes for the workforces. The results of the sensitivity analysis also draw some managerial insights for the case that some model parameters vary over the planning horizon.

Fuzzy inventory models

Display Omitted We give an overview of the fuzzy inventory models literature gathering 210 papers from 1987 onward.The current state of the literature is categorized into 13 areas under five main groups.We provide details to describe the applied methodologies.The research is concluded with future research directions. Over the years since the advancement of inventory management and fuzzy set theories, a vast number of studies have been published to integrate these concepts. Nonetheless, no comprehensive and systematic literature review can be found that analyzed the studies in this research stream. It motivated us to conduct this survey as a systematic and comprehensive review in the field of fuzzy inventory management to identify major achievements attained so far and shed light on future directions. First, the earlier review papers are presented to reveal the necessity of this study, and then methodology applied in collecting sample papers is described, followed by an in-depth analysis of the papers. Totally, a sample of 210 papers is identified and classified according to the common characteristics of the models. Several aspects of the models are assessed that led to identification of some areas overlooked by researchers so far.

Economic order quantity models for items with imperfect quality and emission considerations

ABSTRACTIncorporation of quality and environmental concerns in production and inventory models has received considerable attention in the inventory management literature; however, researchers studied these topics mostly independently. Thus, it is required to jointly incorporate those two relevant aspects in a single research to support decisions, compare the results and obtain new insights for complexities in practice. This paper takes a step in this line of thought and revisits some economic order quantity (EOQ) models with imperfect quality from a sustainable point of view. The objective is to investigate the impact of emission costs on the replenishment order sizes and the total profit of a buyer (retailer) in an imperfect supply process, where the buyer receives the batches containing a percentage of imperfect quality items. First, an EOQ model with imperfect quality items and emission costs, which are the result of warehousing and waste disposal activities, is formulated. Next, the model is extended ...

Applying fuzzy multi-objective linear programming to a project management decision with nonlinear fuzzy membership functions

This paper investigates a multi-objective project management problem where the goals of the decision maker are fuzzy. Prior research on this topic has considered linear membership functions to model uncertain project goals. Linear membership functions, however, are not much flexible to model uncertain information of projects in many situations, and therefore, fuzzy models with linear membership functions are not suitable to be applied in many practical situations. Hence, the purpose of this paper is to apply nonlinear membership functions in order to develop a better representation of fuzzy project planning in practice. This approach supports managers in examining different solution strategies and in planning projects more realistically. In doing so, a fuzzy mathematical project planning model with exponential fuzzy goals is developed first which takes account of (a) the time between events, (b) the crashing time for activities, and (c) the available budget. Following, a weighted max–min model is applied for solving the multi-objective project management problem. The performance of the developed solution procedure is compared with the literature that applied linear membership functions to this problem, and it is shown that the model developed in this paper outperforms the existing solution.