EPQ Inventory Model Research Articles

EPQ Inventory Model with Backorders and Energy Implications

With the scarcity of energy supply in the world and especially in the European region, energy price is soaring rapidly. Therefore, finding solutions to save energy is a top priority for manufacturers. This study introduces an EPQ inventory model that takes into account the correlation between production processes and energy consumption, while also allowing for backorders. The energy consumption during both production and non-production periods of the machine is computed. The energy consumption in EPQ policies is contingent upon the production rate and the machine's states (off or standby) during non-production phases. Utilizing the proposed resolution algorithm, the model under examination seeks to minimize the average total system cost while considering the production rate, cycle time, the initial production time of the cycle, and the optimal machine state during non-production periods. To demonstrate the formulated model, a numerical analysis is conducted, with a particular focus on the impact of allowing backorders.

A cleaner EPQ inventory model involving synchronous and asynchronous rework process with green technology investment

The amount of carbon emission in the atmosphere continues to grow, and production, storage and transportation are major contributors that are repeatedly unnoticed when it comes to solving the problem. A carbon levy and cap EPQ model has been explored in this study for a controlled carbon emission in view of cleaner production under imperfect production processes where a fraction of the products is faulty. The model incorporates emissions from transportation, production, and storage activities, which are meant to be decreased by green investment. The manufacturer employs a rework approach to rectify the faulty products. Flexible rework allows the manufacturer to choose the rework rate, which can differ from the manufacturing rate, as well as the process of rework, which can be asynchronous or synchronous. A linear rework cost function of the rework rate is assumed. We sought to obtain the lowest cost with respect to optimal lot size, and backorder under the effect of controlling carbon emissions by applying the exponential form of green investment. Keeping these in mind, several mathematical models derived for various rework rate and rework process assumptions with the objective emphases on gaining a trade-off between cost and emissions, thereby finding the optimal production-distribution inventory strategy and an appropriate sustainable plan for handling both synchronous and asynchronous rework process. We show a constrained non-linear programme (NLP) and derive a calculus optimization technique to solve it. An iterative solution technique is used to arrive at the optimal decisions, which are shown analytically and numerically. The results validate the impacts of controlled carbon emissions on the production strategies. The findings mainly suggest that increasing the carbon levy reduces emissions. The firm has more options to decrease emissions caused by industrial activity with the help of green technologies. Although green technology has a higher upfront cost, the producer will reap the advantages of lower emissions.

An EPQ Inventory Model with Green Techology and Multi Variable Demand under the Shortages and Volume Flexibility

A hectic life makes fitness difficult, especially if you consume chemicals. Knowing this fact, we have analyzed an economic production inventory model for deteriorating items. The manufacturing model is developed with green technology in order to produce eco-friendly products. The volume flexibility is taken into account. Multivariable demand rate has been taken into consideration which is dependent on selling price, green degree and green preferences of the customer. In response to the growing green preferences of customers, manufacturers should increase their investment in green technology. It is allowed to have shortages and all backlogs are fully backlogged. A closed-form solution has been provided for the optimal values of the green degree and replenishment cycle. In addition to analyzing the volatility of the system numerically and sensitivity-wise, the model can also provide some managerial insights in favor of the manufacturer to maintain customer satisfaction and increase profit.

Optimisation of a sustainable fuzzy EPQ inventory model using sextic equation

Optimisation of a sustainable fuzzy EPQ inventory model using sextic equation

Optimization of a sustainable fuzzy EPQ inventory model using sextic equation

Optimization of a sustainable fuzzy EPQ inventory model using sextic equation

An Application of Possibilistic Moments of Nonlinear Type of Fuzzy Numbers in Supply Chain Management

The supply chain (SC) network is prone to disturbance due to various uncertainties associated with their subsystems. The COVID-19 outbreak has exposed the global vulnerability of the supply chain network. The current pandemic has severely affected almost every SC network because its members are situated at the international level. One of the reasons for SC network failure is the deterministic assumptions of different parameters. A realistic SC network model requires the use of the uncertain value of the parameters, which can be further captured by fuzzy numbers. This paper discusses the possibilistic moment of several nonlinear types of fuzzy numbers that are important for SC network modeling. We give closed-form possibilistic moments’ expression for various types of fuzzy numbers that are very similar to the moment’s properties in probability theory and stochastic process. We then illustrate the application of proposed fuzzy numbers by solving an inventory model. This paper also provides results related to the EPQ inventory model in a fuzzy possibilistic setup.

Work performance dependent screening process under preservation technology in an imperfect production system

ABSTRACT This study presents an EPQ inventory model which provides some imperfect quality products. Initially, due to the existence of all fresh sources, the system remains in good condition, i.e., in-control state. But, after a certain time of production, this system must produce some defective items with the perfect ones, i.e., the system goes into an out-of-control state. Here, the transition time from one state to another state has been considered as a random variable. Besides that, a generalized screening process has been proposed which is based on the work performance of a worker that also depends on time, this is the key contribution of this study. Also, we have considered a preservation investment cost in the manufacturing system to control the defective rate. A generalized stochastic demand function has been proposed. Finally, numerical implications, managerial implications, and conclusions are made for the justification of my proposed model.

WITHDRAWN: Solving a multi product single machine EPQ inventory model with GP mode: By using python

Solving a multi product single buyer EPQ model with various fuzzy numbers and different defuzzifications are treated in this paper. The decision variables are Length of cycle and Number of shipments. The main development of this paper is to find maximize the profit for relevant total cost and investigates the Length of cycle and Number of shipments are derived by using a GP mode. At the end of this paper, numerical examples and with some relevant graphs are given to illustrate the useful of this model.

An EPQ Inventory Model for Decaying Items with Time Varying Demand under the Trade Credit Policy

This study develops a production inventory model with time dependent demand under the effect of permissible delay. Production rate is demand dependent. The concept of non-instantaneous deterioration is taken into consideration as in some realistic cases deterioration of the product starts after some time. Numerous possible cases on the bases of the positions of trade-credit period and starting point of deterioration have been enlightened. Numerical examples are given to illustrate the proposed model in all cases. The sensitivity analysis is also performed and convexity of the average total cost function for each case is revealed graphically.

A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand

This paper presents an inventory model for a three-echelon supply chain with multiple products and multiple members considering the demand as an increasing function of the marketing effort. In the proposed inventory model, a collaborative approach is studied and an analytical method is applied to obtain the optimal production lot size and the optimal marketing effort in order to achieve the maximum profits. Some numerical examples are illustrated to justify the model. Moreover, a sensitivity analysis is well done in order to analysis the effect of the changes of key parameters of inventory model on the the maximum benefits of all members of the chain.

Technical note: Solving inventory models by algebraic method

We consider the open question raised by Chang et al. (2005) to solve the EOQ and EPQ inventory models without referring to calculus. Lau et al. (2016) and Chiu et al. (2017) both extended this open question by deriving criterion for the existence and uniqueness of the interior minimum solution but they used analytical techniques that are related to calculus. Moreover, their derivations are incomplete and contained questionable results. In this note, we only used algebraic approach for their extended open question.

Learning and screening errors in an EPQ inventory model for supply chains with stochastic lead time demands

This paper investigates the role of variable lead time, learning in production and screening errors in a vendor–buyer supply chain with defective items. The vendor–buyer supply chain is modelled for supplying a single item considering that the lots from vendor may contain some defective items. It is assumed that demand during lead time follows a normal distribution. Moreover, the production time at vendor’s facility is assumed to follow learning whereas buyer’s screening for defective items is prone to errors as well. Numerical examples are presented to illustrate the impact of different variables in the model. The analysis shows that delay in transportation lead time forces the buyer to carry more inventories to avoid shortages. Further, Type I error has a major impact on this cost. It was found that learning in production keeps on reducing the total cost of the supply chain up to a threshold.

Note on “An Easy Method to Derive EOQ and EPQ Inventory Models with Backorders”

Note on “An Easy Method to Derive EOQ and EPQ Inventory Models with Backorders”

Determining Replenishment Lot Size and Shipment Policy for an EPQ Inventory Model with Delivery and Rework

The determination of production-shipment policies for a vendor-buyer system is dealt within this paper. The main objective is to derive the optimal replenishment lot size and shipment policy for an EPQ inventory model with multiple deliveries and rework. This inventory model contains two decision variables: the replenishment lot size and the number of deliveries. Previous researches solve this inventory model considering both variables to be continuous. However, the number of deliveries must be considered as a discrete variable. In this direction, this paper solves the inventory model considering two cases: Case 1: the replenishment lot size as a continuous variable and the number of shipments as a discrete variable and Case 2: the replenishment lot size and the number of shipments as discrete variables. The final results are two simple and easy-to-apply solution procedures to find the optimal values for the replenishment lot size and the number of deliveries for each case.

The EPQ model with deteriorating items under two levels of trade credit in a supply chain system

There are two kinds of two levels of trade credit policies addressed by Huang [15] and Teng [29], respectively. Liao [24] presents the EPQ model with deteriorating items under two-level trade credit policy from the viewpoint of Huang [15], while Chang, Teng and Chern [2] discuss the model from the viewpoint of Teng [29]. However, errors are found in the process of the modeling in Chang et al. [2]. The main purpose of this study is to improve the model of Chang et al. [2] and develop a more general EPQ inventory model. A theorem is also provided for practitioners to make right decisions.

Economic Production Inventory model with the associated costs of internet advertising to acquire customers residing worldwide

In recent times, we are witnessing the technological revolution which provides access to tremendous changes in all the fields including the industrial sectors. The notable benefit of the modern technology is quick accomplishment of complex tasks within a short span of time, which has motivated the manufacturers to imbibe novelty techniques in the production process to enhance the quality of the product so as to retain its market position amidst the competitors. As globalization has gained more concern, the manufacturers employ internet advertising strategy to elevate the product to international level and to propagate the attributes of the products to the customers residing worldwide. In this paper an EPQ inventory model is developed in which the associated costs of technology, acquisition of local and international customers via internet advertising costs are included, a numerical example is also presented to validate the model.

An EPQ Inventory Model with Allowable Shortages for Deteriorating Items under Trade Credit Policy

This paper attempts to obtain the replenishment policy of a manufacturer under EPQ inventory model with backorder. It is assumed here that the manufacturer delays paying for the received goods from the supplier and the items start deteriorating as soon as they are being produced. Based on these assumptions, the manufacturer’s inventory model is formulated, and cuckoo search algorithm is applied then to find the replenishment time, order quantity, and selling price with the objective of maximizing the manufacturer’s total net profit. Besides, the traditional inventory system is shown as a special case of the proposed model in this paper, and numerical examples are given to demonstrate better performance of trade credit. These examples are also used to compare the results of cuckoo search algorithm with genetic algorithm and investigate the effects of the model parameters on its variables and net profit.

The complete solution procedure for the EOQ and EPQ inventory models with linear and fixed backorder costs

The basic EOQ/EPQ inventory models with backorders have been developed from different perspectives by several researchers. However, the arguments to locate and guarantee the optimal solution are not complete. This paper presents a complete and analytic solution procedure to the EOQ/EPQ inventory models with linear and fixed backorder costs to locate and ensure the optimal solutions. First, the sufficient and necessary conditions for the existences of the optimal solution are developed. Second, in the case if these conditions are not satisfied, then also the optimal solutions are identified for this situation. The final results are two lemmas and four useful theorems to obtain the optimal solutions to both inventory problems.

A note on how to compute economic order quantities without derivatives by cost comparisons: some comments

This paper discusses some points of the algebraic optimisation method and the cost comparisons optimisation method. Moreover, mathematical expressions are derived for the backorders level for the EOQ and EPQ inventory models with planned backorders that were not provided by the cost comparisons method using the well known marginal cost analysis and simple geometric relations.

An easy method to derive EOQ and EPQ inventory models with backorders

Recently, a cost minimization method to determine the lot size for the EOQ/EPQ models with backorders was published. This method is based on the well-known arithmetic–geometric mean inequality. Although the cost minimization method is correct and interesting, it does not focus on deriving the backorders level. This paper proposes another simple approach. The proposed method finds both the lot size and the backorders level.