Optimal Order Size Research Articles

Economic Order Quantity Method to Enhance Rice Supplies and Food Security in Indonesia

Ensuring adequate food provision to meet human basic needs is of utmost importance. In Indonesia, achieving food security involves meeting the food requirements of all individuals and eliminating the risk of famine. The government's strategy to ensure national food security centers on maintaining a steady supply of rice throughout the year, recognizing its paramount significance. To address this concern, this study aims to enhance rice supplies at Gudang Bulog Baru Tempel Lemahbang 202 Blora by implementing the economic order quantity (EOQ) method. The research findings demonstrate that by utilizing the EOQ method, the optimal rice supply order size would be 15,319.4 tons. This order should be placed 119 times per year, given the 280 business days available. The annual cost of implementing this policy at Gudang Bulog Baru Tempel Lemahbang 202 Blora is estimated to be Rp. 424,484,526. Implementing the EOQ method proves beneficial in minimizing the cost for individual rice orders due to its high frequency throughout the year, which directly affects the total cost. Nevertheless, it is crucial to reassess alternative policies to further reduce the overall cost incurred in both the short and long term if the objective of the EOQ method is cost minimization.Top of Form

Determination of “just-in-time” service and optimal order size in the logistics system of the regional agro cluster

Determination of “just-in-time” service and optimal order size in the logistics system of the regional agro cluster

Discontinuous Economic Growing Quantity Inventory Model

The classical economic growing quantity (EGQ) model is a key concept in the inventory control problems research literature. The EGQ model is commonly employed for the purpose of inventory control in the management of growing items, such as fish and farm animals, within industries such as livestock, seafood, and aviculture. The economic order quantity (EOQ) model assumes that customer demand is satisfied without interruption in each cycle; however, this assumption is not always true for some companies as they do not have continuous operations, except for item storage, during non-working times such as weekends, natural idle periods, or spare time. In this study, we extend the traditional EGQ model by incorporating the concept of working and non-working periods, resulting in the development of a new model called discontinuous economic growing quantity (DEGQ). Unlike the conventional EGQ model, the DEGQ model considers the presence of intermittent operational periods, in which the firm is actively engaged in its activities, and non-working periods, during which only storage-related operations occur. By incorporating this discontinuity, the DEGQ model provides a more accurate representation of real-world scenarios where businesses operate in a non-continuous manner, thus enhancing the effectiveness of inventory control and management strategies. The study aims to obtain the optimal number of periods in each cycle and the optimal slaughter age for the breeding items, and, subsequently, to find the optimal order size to minimize the total cost. Finally, we propose an optimal analytical procedure to determine the optimal solutions. This procedure entails finding the optimal number of periods using a closed-form equation and determining the optimal slaughter age by exhaustively searching the entire range of possible growth times.

Algorithmization of data mining to optimize the process of inventory management at the enterprise in conditions of uncertainty

Currently, in conditions of increasing uncertainty of external economic and geopolitical factors, approaches based on digitalization of analytical processes associated with their intellectualization through the use of mathematical tools are used to make effective management decisions at enterprises. Planning of a wide range of issues regarding the functioning of enterprises in the short term, and especially in the long term, depends on the reliability and relevance of the analytical material. The purpose of the study was to develop a data analysis algorithm for inventory management at an industrial enterprise adapted to the current conditions caused by the uncertainty of a number of identified factors. The article presents an analysis of the state of industry in Russia for 2017–2021. The dynamics of the price index for hotel types of economic activity is given, the pattern of changes in the number of industrial enterprises is reflected. The forecast of the price index for individual industries for 2025 is graphically presented. The main problems faced by the branch of Russian industry are identified and a brief description of their impact on the development of industrial enterprises is given. The applicability of system analysis methods for solving inventory management problems is substantiated. The composition of the Economic ordering quantity model is analyzed and the need for its modernization is argued, taking into account the effects of environmental uncertainty factors to determine the optimal order size. The authors propose a data mining algorithm designed to calculate the optimal order quantity based on a modified Wilson formula with the described assumptions and constraints. The approbation of the calculation based on it is presented. To substantiate the correctness and applicability of the algorithm, a comparison of real and calculated data is given, an expert assessment is carried out on the relevance and possibility of its implementation at industrial enterprises in order to reduce risks when making managerial decisions in terms of warehouse logistics, in particular in inventory management.

Penerapan Metode Continuous Review pada Pusat Oleh-Oleh Keripik Rumah Adat Minang

Pusat Oleh-Oleh Keripik Rumah Adat Minang is a business engaged in the production of sweet potato chips, and selling various types of snacks, this business is located in Medan City, North Sumatra. This study aims to compare the total inventory costs of the company's policies and the Continuous Review method and determine the optimal order size. The data obtained is inventory data for 5 types of snacks in 2021. The method used is the continuous review method, based on the results of calculations for 5 types of snacks, the total inventory cost according to company policy is Rp.792,631,977/year, while the total inventory cost using the continuous review method is Rp.773.799,089/year. The results showed that the continuous review method has an optimal total inventory cost, so the company can save on expenses of Rp. 18,832,888 or 2,37% for 5 types of snacks. To facilitate the calculation in this study was conducted using the help of MATLAB software.

Using digital twins to create an inventory management system

The article considers the application of the inventory management model on the example of a manufacturing enterprise, where it is planned to use a digital twin together with the inventory management system. Inventory management model is a mathematical model that allows you to determine the optimal level of stocks at the enterprise. In a manufacturing enterprise, this model can help optimize the inventory of raw materials, materials, and finished goods, which will reduce costs and reduce risks associated with the lack of necessary raw materials or required quantities of finished goods. With the help of data obtained from the enterprise, the input parameters of the model were obtained, namely the size of resource consumption, stock holding costs, delivery realization costs, and time required for delivery. The model was used to find the parameters such as optimal order size, delivery period, inventory level at which ordering should be carried out.

Optimization of the order size concerning losses from the immobilization of working capital in the reserves of material resources

The article discusses approaches to optimizing stocks in the supply chains of large industrial companies. The relevance of this issue concerns primarily the supply of the most expensive categories of material resources, when calculating the order size it is necessary to additionally take into account losses from the immobilization of working capital (opportunity costs). In practice of home and foreign companies, modifications of the optimal order size formula are widely used, with the help of which companies achieve an economic compromise between the level of availability of stocks in the warehouse and the costs of their purchase and maintenance. At the same time, the losses from immobilization, in some cases, can significantly impact the levels of the company's warehouse stocks (including insurance), and hence the need for logistics infrastructure facilities, such as warehouses, handling equipment etc. To date, there is no unified methodology for assessing losses from the immobilization of working capital in stocks, due to the specifics of companies’ activities in different industries and types of business. In this connection, approaches to the choice of rates for determining the amount of such losses and assessing their impact on the efficiency of companies’ activities are significantly different. Correct accounting of opportunity costs can be used in the development of diversified approaches to planning the need for warehouse stocks, which will allow, on the one hand, to satisfy the orders of internal and external customers, and on the other hand, to prevent the formation of excess stocks. Therefore, the issue of developing industry methods for an adequate assessment of financial losses when working with stocks of material resources is relevant.

The opportunistic newsvendor problem: Defining the optimal purchase quantity of resalable items, whose value may appreciate

With Newsvendor Problem (NvP) we refer to a specific class of inventory management problems, valid for a single item with stochastic demand over a single period. In the standard version, the newsvendor is allowed to issue a single order, before he or she can observe the actual demand. Since the newsvendor can face both overage and underage costs, due to lost sales or residual stock, the objective is to define the optimal order size that maximizes the expected profit. In this paper, we consider a specific version of the NvP, in which the buyer has the opportunity to make a last and single order for opportunistic reasons. Specifically, we consider discontinued, collectible items, for which demand will not vanish and whose value might appreciate. Hence, the objective is to define the optimal quantity that should be purchased, just before the item is retired from the market or sold-out, and that should be sold as soon as the price rises over a predefined target level. An optimal solution, maximizing the expected profit, is obtained both in case of negligible and non-negligible stockholding costs. In the latter case, to obtain the optimal solution in implicit form, some simplifying assumptions are needed. Hence, a thorough numerical analysis is finally performed, as a way to empirically demonstrate both the robustness and the accuracy of the model, in several scenarios differentiated in terms of costs and customers’ demand.

Lateral Thinking in the Process of Logistics Students’ Education Using the Example of the EOQ Model

This paper explores the possibility of using lateral thinking to enhance student learning in higher education. Teams of students formed during classes using the „six think- ing hats” method, a concept developed by (de Bono, 1985), analyse a problem posed by the lecturer. This problem involves solving a commonly used economic rule considered in a deterministic environment, the so-called economic order quantity (EOQ) model. Students divided into research teams first solve the problem classically, using elements of differential calculus. In the next stage, they solve the problem using process analysis, re-engineering principles, and a computer application. The most important feature of this stage is the analysis of the problem, so to speak, from the end, i.e., from the definition of the goal, which is to determine the optimal order size of goods in the supply chain at minimum cost. The six thinking hats method is extremely helpful at this stage. The key benefits for students using this type of teaching are related to verifying previous thinking in solving the problem and adopting a creative approach to solving the task. Empirical studies confirm that this type of teaching increases the attractiveness of the class and the satisfaction of acquiring creative thinking skills and provides the satisfaction of solving a complex research problem in a team. Student surveys with a small sample (<30 students) confirmed those benefits. According to the compiled statistics, about 60% of the respondents believe that teamwork reduces the time needed to complete the task, while about 70% of students believe that teamwork teaches creative thinking, and the presented way of solving the problem can be used in practical activities of business entities. The current world situation and pandemic threats cause the suspension of classes for students. The method developed allows for distance learning, known as e-learning. Students form groups and connect via Skype. Using an online platform, they share lessons developed through the use of a thinking hat. The Excel spreadsheet used in the method allows solutions to be communicated online, making it easier for students to communicate at a distance. The developed method does not require complex e-learning applications and platforms. Students work at home using their private computer equipment and make the right decisions without much effort. With the threat of viral infection, it is crucial to focus on interesting activities without having to interact with the outside world.

ЛОГІСТИЧНІ МОДЕЛІ ОПТИМІЗАЦІЇ ПРОЦЕСУ ЗАБЕЗПЕЧЕННЯ ПІДПРИЄМСТВА МАТЕРІАЛЬНИМИ РЕСУРСАМИ

The article examines the peculiarities of optimizing the process of providing enterprises with material resources based on the complex use of logistic models. The need to quickly respond to the needs of consumers, which are constantly changing, caused increased interest in this issue both in scientific circles and in the applied sense. The tasks of ensuring the efficiency of material flows can be conventionally divided into those related to the movement of production and technical products, and tasks related to the movement of goods. To solve these problems, the article proposes to use modeling methods that involve the definition of the objective function. Having this data and information about the input parameters of the material flow, it is possible to obtain a solution to the problem with the highest level of efficiency. The article systematizes a number of logistical problems related to material flows that are typical for most enterprises. The problem of choosing the optimal order size using the Harris (Wilson) formula is considered in detail on the example of real data. According to this model, total costs should be minimal, the occupied volume of the warehouse should not exceed the actual volume of the warehouse, and the costs of purchase and storage should not exceed the available budget of the enterprise. Also, the solution to the problem of choosing a "Make-or-Buy" raw material supply system was implemented: to buy or to manufacture independently. Solving the "Make-or-Buy" problem allows you to make quick decisions when changing the production capabilities of both the manufacturer and the supplier. At the same time, the main goal remains cost minimization. Both problems were implemented using MS Excel "Solution Search" tools and have appropriate graphic support. Thus, having the input parameters of the problem and the objective function, the considered models allow generating mathematically justified and effective management decisions. The use of information technologies significantly accelerates and facilitates the process of using the specified models and allows creating a system of constant monitoring of changes in the company's needs for material resources.

PERENCANAAN PERMINTAAN BAHAN BAKU DAN PENENTUAN UKURAN PEMESANAN (LOT SIZE) OPTIMAL DI GUDANG KIMIA MARUNDA

<p><em>This research was conducted on companies that store and distribute chemical raw materials (sodium sulfate) to industrial companies. The problem that occurs is that the company does not have a medium-term raw material demand plan to determine the optimal order size to suppliers as storage in the warehouse. Given that ordering is also important to note because it has an impact on the total cost of inventory from ordering costs and holding costs. The purpose of this study is to forecast to find out the demand for raw materials in the future so that the company has an estimate for planning future demand for raw materials and calculates several ordering methods (lot size) to get the optimal order size.</em></p><p><em>Solving problems using forecasting methods (Moving Average, Weight Moving Average, Exponential Smooth), and lot size methods (Economic Order Quantity, Period Order Quantity, Least Unit Cost, Part Period Balancing). The results of the analysis, forecasting to determine the demand for raw materials for the next year using the Exponential Smooth method because it has the smallest MAD MSE MAPE value, and the ordering lot size using the Part Period Balancing method because it has the minimum total inventory cost of Rp. 14,128,706,027 or 23.5% more efficient than the usual ordering used by companies.</em></p>

Donating to a good cause: Optimal coordination design of a dyadic supply chain with socially aware consumers

Socially aware consumers care about giving to a good cause through their purchases. In reality, though, while some consumers respond favourably to companies' social responsibility initiatives, others apprehend because they do not trust the company or the effectiveness of the cause. That variability in consumers’ perceptions and purchase decisions inevitably adds to demand uncertainty. This paper studies the optimal design of a coordination mechanism for a socially responsible dyadic supply chain (SC) with a manufacturer supporting a cause-related marketing campaign (CMC) and a retailer selling to socially aware consumers. Unlike in pertinent literature, we take demand as uncertain due to consumers’ diverse and unpredictable responses to announced CMC. In a Stackelberg game setting, we determine the optimal donation size (a percentage of the selling price) for the manufacturer and the retailer’s optimal order size. We show that a two-part tariff (TPT) contract coordinates the SC. The numerical experiments demonstrate that the proposed TPT contract incentivizes the manufacturer to reach out to socially aware consumers by pledging to a charity. We also show that the proposed coordination model can achieve a Pareto-improving solution.

Managing panic buying-related instabilities in supply chains: A COVID-19 pandemic perspective

Global supply chains (SCs) have been severely impacted by the COVID-19 pandemic on several levels. For example, SCs suffered from panic buying-related instabilities and multiple disruptions of supply, demand, and capacity during the pandemic. This study developed an agent-based model (ABM) to predict the effects of panic buying-related instabilities in SCs and offered strategies to improve them. The ABM model includes a simulation and optimization model of a typical SC of an essential product manufacturer (i.e., toilet paper SC) for the analysis of scenarios and strategies to observe improvements in SCs. Among the four strategies identified, the findings suggest boosting production capacity to the maximum and ensuring optimal reorder points, order sizes, and trucks helped the essential product manufacturers reduce panic buying-related instabilities in their SCs.

Presenting a Multi‐Echelon and Multi‐Product Model for Inventory Control considering Shortages Using a Heuristic Algorithm

In the present study, a mathematical model is provided for inventory management in a three‐level supply chain including a supplier, a manufacturer, and a distributor, taking into account the potential for product deficiency. Significant parameters such as the optimal order size for raw materials, optimal production rate, optimal allowed deficiencies at each supply chain level, the of the vehicles and the number of times the products are delivered between the supply chain components have been provided aiming at minimizing inventory management costs in the supply chain. The problem was solved using a heuristic algorithm. The proposed model is implemented for 20 different numerical examples. According to the results, the difference between the solutions obtained from the algorithm and the solutions obtained from the optimal values with the real variables is an average of 1.52%.

Alignment between an ABC classification and results from an optimization approach

The paper analyzes a multi-item inventory system, using independent (R,Q) policies. The aim is to minimize the average stock level while keeping a weighted (across items) fill rate service level at a given target. The paper explores whether the optimal order sizes and the optimal safety factors are aligned with the ABC classification. Our results show that A items should be ordered more frequently followed by B items and C items. Concerning the optimal safety factors, our results depend on the weights applied in the specification of the weighted service level. If all items have equal weight, A items should have the lowest safety factors followed by B and C items. If the weights are the demand rates, the ranking of the safety factors follows the ratios between the demand rate and the unit purchase price, and the higher this ratio is, the higher is the optimal safety factor. However, this ranking is completely aligned with the ABC classification given that the demands are transformed into monetary units.

An Analysis of Optimal Order Decision for Substitutable Perishable Products at Different Loss Rates

Loss rate was here used to characterise products' life cycles given that perishable products produced through different processes have different life cycles. In addition, products with different loss rates may also be interchangeable to the end user. In this paper, we first established two realistic models with the goal of maximising the expected profit. We here proved that the optimal size of each order and maximum expected profit exist and are unique in both models. After the numerical analysis, we concluded that the rate of loss of models with or without substitutes has the same impact as each other on the optimal order size and the maximum expected profit, and the trends in the variation in the cost of each order are also the same. Furthermore, the trends in the variations with substitutes are relatively slow. The model with substitutes was found to facilitate management decisions through the substitution coefficient, and the boundary value was consistent with the value of the model without substitutes.

An analysis of optimal order decision for substitutable perishable products at different loss rates

Loss rate was here used to characterise products' life cycles given that perishable products produced through different processes have different life cycles. In addition, products with different loss rates may also be interchangeable to the end user. In this paper, we first established two realistic models with the goal of maximising the expected profit. We here proved that the optimal size of each order and maximum expected profit exist and are unique in both models. After the numerical analysis, we concluded that the rate of loss of models with or without substitutes has the same impact as each other on the optimal order size and the maximum expected profit, and the trends in the variation in the cost of each order are also the same. Furthermore, the trends in the variations with substitutes are relatively slow. The model with substitutes was found to facilitate management decisions through the substitution coefficient, and the boundary value was consistent with the value of the model without substitutes.

MEDICINE INVETORY CONTROL BY CONSIDERING EXPIRY PERIODS AND PRODUCT RETURNS USING THE ALWAYS BETTER CONTROL (ABC) ANALYSIS AND THE HANDLEY WITHIN MODEL OF ECONOMIC ORDER QUALITY (EOQ) AT PHARMACIES IN INDONESIA

This study aims to control medicine inventories by considering the expiration period and the product return using The Always Better Control (ABC) analysis and The handley within model of Economic Order Quantity (EOQ). The results of this study indicate that there are 21% of medicines or 22 types of medicines belonging to group A with the use of 74.64%. for group B there were 25% drugs or 28 types of drugs with a budget use of 15.31% of all medicines. Meanwhile, there are 55% of medicines or 60 types of medicines belonging to group C with the use of a budget of 10.05% of the total medicines and the calculation using the EOQ method by considering the expiration period and product returns in this research has a more optimal order size compared to the previous method so that it can minimize expired medicines and estimate which medicines will expire at the end of the cycle so that the total cost of supplies at the pharmacy is more optimal.

Optimalization HDPE Pipe Raw Material Using Simulation Model in PT. X

PT. X is an industrial company engaged in the production of pipes. In producing HDPE pipes, the company uses various raw materials ordered from foreign suppliers. The raw material needed in the HDPE pipe production process is HDPE plastic seeds. The company orders raw materials to meet existing demand, inventory stocks often experience differences with demand and orders are made if there is not enough supply to meet demand, Shipments of materials in containers via sea transport with a square off time of 1 month. In practice the number of orders is determined based on the number of requests in 1 month. In this study the method used is a simulation to determine the optimal HDPE raw material order quantity with total inventory cost (Total Cost Inventory) as a comparison, the order size determination is also carried out using the probabilistic EOQ method. The optimal order size with the Q system for a reorder point of 60,000 kg is 80,000 kg and a total inventory cost of 378,465,389, -.

Imperfect and variable production cost in three-layer supply chain system incorporating deterioration and screening effect

This paper develops a three-layer supply chain for defective and non-defective types of produced items by supplier and manufacturer. The condition of the chain that without any financial liability on the manufacturer, defective items will be sent back to the supplier after screening. In the subsequent stage, the retailer accepts the non-defective items produced by the manufacturer after the screening and sends back the defective items to the manufacturer. Hence the retailer receives the perfect quality items for selling to the customers, but the retailer considers the effect of the deterioration of items. This model also considers the impact of several business strategies such as; optimal order size of raw materials, production rate, unit production cost, idle time costs of the supplier, and manufacturer in a collaborative marketing system, etc. to determine the optimum average profit of the integrated model. This study discusses the selling price of the retailer, demand rate of the customer, purchase cost of supplier and holding cost, which can be a significant breakthrough in expanding the profit of the business in real terms. Numerical example and sensitivity analysis are presented to illustrate the phenomenon of theoretical study and demonstrate the managerial implication of the model.