Economic Order Quantity Inventory Model Research Articles

An EOQ Model for Temperature-Sensitive Deteriorating Items in Cold Chain Operations

To improve the inventory management of cold chain logistics, we propose an economic order quantity (EOQ) inventory model for temperature-sensitive deteriorating products. Considering that the products are temperature-sensitive, the deterioration rate of the proposed model is a function of the temperature. In addition, the transportation cost, which is a function of the quantity ordered, is considered in this study. This article aims to find the optimal value of the total profit, selling price, and the length of the ordering cycle. Numerical examples are provided; the sensitivity analysis shows that the total profit is much more sensitive to transportation costs, compared with ordering and holding costs.

Solving a fuzzy backlogging economic order quantity inventory model using volume of a fuzzy Hasse diagram

Solving a fuzzy backlogging economic order quantity inventory model using volume of a fuzzy Hasse diagram

EOQ MODEL FOR DETERIORATING AND AMELIORATING ITEMS UNDER CUBIC DEMAND AND PARTIAL BACKLOGGING

The inventory model aims to determine policies in inventory control. Therefore, the availability needs to be managed as well as possible to obtain optimal performance. This study aimed to produce EOQ models for deteriorating and ameliorating products with shortage and partial backlogging policies. The traditional Economic Order Quantity (EOQ) inventory model was used to develop the model. The search algorithm of the model solution was made to get a solution from the model. In the end, a case study of the model implementation at Minimarket SATUMART, Sidoarjo, is given

A supply and demand economic order quantity inventory model under pythagorean fuzzy environment

A supply and demand economic order quantity inventory model under pythagorean fuzzy environment

Carbon Tax and Inflationary Conditions under Learning Effects: A Green EOQ Inventory Model

AbstractNow a day, green retail operations drive in many fields to improve the quality of deteriorating items during the delivery of the green items to his customer. In the present paper, retailer receives greening items from the seller and stores it. After received lot of greening items, retailer starts packing of greening items to maintain the quality of greening items and safe from some germs. We are considering that the holding units exit carbon units which are harmful to the environments. Retailer includes carbon emission cost and green packing cost and also invests on greening items to control the greening degree of the product. This paper deals a green economic order quantity (EOQ) inventory model with learning effect for decaying greening items under the inflationary condition and credit financing. An expression for the total cost of the retailer has been minimized with respect to cycle length in the environments of green operations. The objective of this paper is to analyze the impact of greening degree and trade‐credit financing with the learning effect and inflationary condition under carbon emissions on the retailer's total inventory cost. An expression for the total cost of the retailer has been minimized with respect to cycle length in the environments of green operations. Conclusively, sensitive analysis has been presented as a consequence of numerical examples.

A constrained multi-item EOQ inventory model for reusable items: Reinforcement learning-based differential evolution and particle swarm optimization

The growing environmental concerns, governmental regulations, and significant cost savings are the primary motivations for companies to consider the reuse and recovery of products in their inventory system. The previous research ignored several realistic features of reusable items inventory systems, such as the presence of multiple products and operational constraints. For the first time, this paper presents a new multiproduct economic order quantity inventory model for an inventory system of reusable products. The goal of the model is to determine the optimal replenishment quantity and reuse quantity of each item so that the system's total cost is minimized. Several operational constraints are considered to provide a more realistic framework, such as the total available budget, warehouse space, and holding cost. Due to the nonlinearity of the presented model, differential evolution (DE) and particle swarm optimization (PSO) algorithms are utilized as two solution approaches. However, these algorithms' performance is highly dependent on their control parameters. Therefore, for the first time, two new variants of these algorithms, called DEQL and PSOQL, are presented in this study, where the control parameters of algorithms are not pre-determined. A powerful reinforcement learning algorithm, Q-learning, adapts these values intelligently. In other words, as a research contribution, this research aims at introducing a new variant of hybrid the DE and PSO algorithms in which a machine learning algorithm controls the value of metaheuristic parameters. The other parameters of the proposed algorithms are tunned employing the Taguchi method. Extensive numerical examples are established in different sizes, and the outputs are discussed in terms of several criteria. Statistical analysis of the results is performed, demonstrating that the proposed reinforcement learning-based parameter adaption has significantly improved algorithms' performance.

Optimal pricing, ordering, and credit period policies for deteriorating products under order-linked trade credit

<p style='text-indent:20px;'>In the modern global economy, trade credit financing is typical in business transactions for both sellers and buyers. The seller offers a credit period to attract new buyers or stimulate demand, and the buyer takes the opportunity to accumulate revenue. To obtain this benefit, the seller prefers trade credit policies that are dependent on the quantity ordered, referred to as order-linked trade credit. The buyer can obtain the benefits from a fully delayed payment if their order is sufficiently large. Similarly, the seller can sell many products while granting a credit period. Otherwise, the buyer receives only partial trade credit, and the seller can take the opportunity of both cash and credit payments. In this study, an economic order quantity (EOQ) inventory model for deteriorating products, under default risk control-based trade credit, is formulated using a discounted cash flow approach. The seller offers to the buyer order-linked trade credit with price-and credit-period-dependent demand. The optimal selling price, credit period policies, and replenishment cycle time are determined simultaneously, while maximizing the present value of the seller's total profit. Moreover, this research provides numerical examples and sensitivity analysis to illustrate the theoretical results, solution procedure, and gain managerial insights. <b>200</b> words.</p>

A study of an EOQ model with public-screened discounted items under cloudy fuzzy demand rate

This article deals with an economic order quantity inventory model of imperfect items under non-random uncertain demand. Here we consider the customers screen the imperfect items during the selling period. After a certain period of time, the imperfect items are sold at a discounted price. We split the model into three cases, assuming that the demand rate increases, decreases, and is constant in the discount period. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the dense fuzzy, parabolic fuzzy, degree of fuzziness and cloudy fuzzy for a comparative study. The basic novelty of this paper is that a computer-based algorithm and flow chart have been given for the solution of the proposed model. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.

Decaying items inventory models with partial linked-to-order upstream trade credit and downstream full trade credit

In practice, any member of supply chain may offer full or partial trade credit contract to his downstream level. Full trade credit is the case that the latter is allowed to defer whole payment to the end of credit period. In partial trade credit, however, the downstream supply chain member must pay for a proportion of the purchased goods at first, and can delay paying for the rest until the end of credit period. This paper considers a two-level trade credit, where the supplier offers order-quantity-dependent partial trade credit to a retailer, who suggests full trade credit to his customers. An economic order quantity (EOQ) inventory model of a deteriorating item with expiration dates is formulated here. Theoretical results are developed to obtain the optimal solutions to the problem. Numerical examples and sensitivity analysis are performed to justify the proposed models and theoretical results and managerial insights are provided.

ANALISIS PENGENDALIAN PERSEDIAAN BAHAN BAKU DI UKM BATIK SEKAR JATI STAR DENGAN MENGGUNAKAN METODE ABC ANALYSIS DAN ECONOMIC ORDER QUANTITY (EOQ)

SMEs of Batik "Sekar Jati Star" is one of the manufacturing industries engaged in batik making located in Jatipelem Village, Jombang and established since 1999. One of the typical motifs in ukm is jombangan motif that depicts the icon of Jombang city. The problem is management of raw material supplies is not optimal, where so far there is no evaluation and no inventory model method is used. So that the article aims to control the inventory of batik raw materials which include fabric, dye and wax. This inventory control includes the classification of each raw material for making batik using the ABC Analysis method. Next, determine the amount of economical raw material inventory using the Economic Order Quantity (EOQ) method. The results showed that the classification of raw materials using the ABC analysis method shows that the raw materials included in category A are fabric raw materials, category B is dye raw materials, and category C is wax raw materials. Implementation of the results of the classification of raw materials, so that the main priority of control is carried out according to the order of categories. The results of the EOQ inventory model show the monitoring of inventory control of raw materials for fabrics, dyes, wax for a year. Monitoring includes the time and quantity of economic Q, RoP, frequency of purchases, average inventory per week. Furthermore, from the comparison of inventory costs, the results of the EOQ model provide more economical results compared to the raw material inventory management that has been carried out so far for fabrics, dyes and waxes.

An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

Ordering Policies of a Deteriorating Item in an EOQ Model under Upstream Partial Order-Quantity-Dependent Trade Credit and Downstream Full Trade Credit

In the classical inventory systems, the retailer had to settle the accounts of the purchased items at the time they were received. But in practice, the supplier applies some strategic tools, such as trade credit contract, to enhance his sales channel and offers delay period to his customers to settle the account. Any member of the supply chain may offer full or partial trade credit contract to his downstream level. Full trade credit is the case that the latter is allowed to defer the whole payment to the end of the credit period. In partial trade credit, however, the downstream supply chain member must pay for a proportion of the purchased goods at first and can delay paying for the rest until the end of the credit period. This paper considers a two-level trade credit, where the supplier offers order-quantity-dependent partial trade credit to a retailer, who suggests full trade credit to his customers. An economic order quantity (EOQ) inventory model of a deteriorating item is formulated here, and the Branch and Reduce Optimization Navigator is applied to find the optimal replenishment policy. The sensitivity of the variables on different parameters has been analyzed by applying some numerical examples. The data reveal that increasing the credit periods of the retailer and the customers can decrease and increase the retailer’s total cost, respectively.

A profit jump inventory model for imperfect quality items with receiving reparative batch and order overlapping in dense fuzzy environment

This paper presents an economic order quantity (EOQ) inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a dense fuzzy environment Here, the imperfect items are identified by screening and are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterwards, the items are returned to the supplier to be reworked. Also, discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error free. An order overlapping scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. However, we assume the total monthly demand quantity as the dense fuzzy number because of learning effect. Moreover, first of all a profit maximization deterministic model is developed and solve by classical method. Fuzzifying the final optimized function via dense fuzzy demand quantity we have employed extended ranking index rule for its defuzzification. During the process of defuzzification we make an extensive study on the paradoxical unit square of the left and right deviations of dense fuzzy numbers. A comparative study is made after splitting the model into general fuzzy and dense fuzzy environment. Finally numerical and graphical illustrations and sensitivity analysis have been made for its global justifications.

Economic Order Quantity Model for Growing Items with Incremental Quantity Discounts, Capacitated Storage Facility, and Limited Budget

The development of the inventory model started when Harris introduced the classic inventory model. It was firstly published by Wilson using the optimization method. He derived a mathematical equation model to obtain economic order quantities. Later, this model is known as the classic Economic Order Quantity (EOQ) or Wilson Model. The classic inventory EOQ model has some limitations. The model assumed that order items do not have physical changes during a planning period. This assumption becomes the weakness of the classical EOQ inventory model. Many items have material changes during a planning period, such as amelioration, deterioration, and growth. This research proposed a new mathematical model. The model relaxes three implicit assumptions of the classical EOQ: (1) the ordered items do not grow; (2) unlimited capacity; and (3) unlimited budget. A solution procedure to solve the model was developed and illustrated with a numerical example. A numerical example was performed to compare the result between the reference model and the new model. The number of ordered items per cycle time increased by 7%, and cycle time increased by 28%. It increased because the proposed model tends to choose large purchased quantities to get a cheap price. It caused the number of ordered items per cycle time to be larger and the cycle time to be smaller than the reference model. This research also provided sensitivity analysis. It showed the response of decision variables to some changes in input parameters.

Determining the Efficiency of Fuzzy Logic EOQ Inventory Model with Varying Demand in Comparison with Lagrangian and Kuhn-Tucker Method Through Sensitivity Analysis

This paper considers an EOQ inventory model with varying demand and holding costs. It suggests minimizing the total cost in a fuzzy related environment. The optimal policy for the nonlinear problem is determined by both Lagrangian and Kuhn-tucker methods and compared with varying price-dependent coefficient. All the input parameters related to inventory are fuzzified by using trapezoidal numbers. In the end, a numerical example discussed with sensitivity analysis is done to justify the solution procedure. This paper primarily focuses on the aspect of Economic Order Quantity (EOQ) for variable demand using Lagrangian, Kuhn-Tucker and fuzzy logic analysis. Comparative analysis of there methods are evaluated in this paper and the results showed the efficiency of fuzzy logic over the conventional methods. Here in this research trapezoidal fuzzy numbers are incorporated to study the price dependent coefficients with variable demand and unit purchase cost over variable demand. The results are very close to the crisp output. Sensitivity analysis also done to validate the model.

Economic order quantity model with deterioration factor and all-units discount

Inventory related with the illiquid assets for a company and its amount must be carefully calculated. Inventory cost usually consists of purchasing, ordering, holding and shortage cost; however, when there is a possibility that the goods are damage, deteriorated or exceed its expiration date, the so-called deteriorated cost must be considered in the total inventory cost. In this paper we consider an economic order quantity (EOQ) inventory model by considering the possibility of goods to be deteriorated or damage or exceed its expiration date. We also consider an all-units discount scheme offered by the supplier that affect the inventory cost formation in this model. Numerical examples are given to illustrate the model and sensitivity analysis of the shortage cost is also provided. Higher shortage cost will make the total inventory cost higher and the optimal order quantity is obtained by taking the cheapest price the supplier has offered.

An EOQ Inventory Model for Time-varying Deteriorating Items with Cubic Demand under Salvage Value and Shortages

In this paper, an Economic Order Quantity (EOQ) inventory model is developed for time-varying deteriorating items. Researchers are constantly developing deteriorating inventory models to become more realistic. Many items like paddy, wheat, potato, onion, radioactive substance etc. are becoming damage over time. So time dependent deterioration is more realistic than a constant rate of deterioration of goods used in the present market. The assumption of constant demand rate may not be always appropriate for many inventory items like milk, vegetables etc, the age of these items has a negative impact on demand dure to loss of quality of such products, on the other hand, demand is becoming increased initially when new branded fashionable products like cosmetics, mobile, computer etc are launched in the market. So the demand rate is considered as a cubic function of time and time dependent holding cost. We also want to give importance on salvage value of an inventory system. The model is solved with salvages value associated to the units deteriorating during the cycle. Shortages are allowed and fully backlogged. Finally the model is illustrated with the help of a numerical example, some particular cases are derived and a comparative study of the optimal solutions towards different nature of demand is also presented graphically.

A trade credit policy in an EOQ model with stock sensitive demand and shortages for deteriorating items

Here, an economic order quantity (EOQ) inventory model with stock dependent demand under multiple cases of permissible delay for deteriorating items has been derived. In corporate world, the proper stock level attracts the consumers and has a positive impact on sale. In this sense the demand rate is stock dependent which attracts the consumers to purchase more. Trade credit on payment works as a publicity tool. The shortage occurs and partially backlogged in which backlogging rate is exponentially decreasing. Convexity of the optimal solution for different cases of trade credit has been discussed. The model is exemplified numerically for different cases. The impact of demand parameter, deterioration rate, backlogging parameter and interest earn rate on critical time as well as on total system cost are mentioned by sensitivity analysis. Aim of this paper is to find optimum cost. Mathematica 11.3 is used here.

A Trade Credit Policy in an EOQ Model with Stock Sensitive Demand and Shortages for Deteriorating Items

Here, an economic order quantity (EOQ) inventory model with stock dependent demand under multiple cases of permissible delay for deteriorating items has been derived. In corporate world, the proper stock level attracts the consumers and has a positive impact on sale. In this sense the demand rate is stock dependent which attracts the consumers to purchase more. Trade credit on payment works as a publicity tool. The shortage occurs and partially backlogged in which backlogging rate is exponentially decreasing. Convexity of the optimal solution for different cases of trade credit has been discussed. The model is exemplified numerically for different cases. The impact of demand parameter, deterioration rate, backlogging parameter and interest earn rate on critical time as well as on total system cost are mentioned by sensitivity analysis. Aim of this paper is to find optimum cost. Mathematica 11.3 is used here.

An Economic Order Quantity inventory model for a product with a circular economy indicator

Circular economy approach is receiving an increasing attention as an alternative to the current linear economic model with the ambition of positive impact on the environment while contributing to economic growth. In this paper, an Economic Order Quantity inventory model in a circular economy is presented. We assume that the product can be manufactured with a variable level of circularity measured by an index. The information provided by a given circularity indicator allows the consumers to make responsible decisions about what they buy. Governments can influence the transition to a circular economy through regulations, taxes and subsidies, while companies seek to maximize their profits by taking these considerations into account in decision-making. Hence, we argue that the circularity level has impact on the demand, cost and selling price of the product and propose various linear and nonlinear relationships. Therefore, additionally to the order quantity, the circularity level is also a decision variable in our model. The optimal parameters are determined analytically and numerical Examples are provided. From the company’s perspective, the obtained results demonstrate that making circular products can be justified financially.