Optimal order quantity considering carbon emission costs, defective items, and partial backorder

In today's competitive business situation, the supplier frequently offers his or her retailers a permissible delay period to stimulate sales. In addition, the capacity of any warehouse is limited in practice; thus, the retailer needs an additional rented warehouse to store the excess units when the order quantity exceeds the capacity of the own warehouse. Furthermore, with the globalization of the marketing policy, the supplier may provide the retailer a discounted price if the quantity of purchase is large enough. Green inventory management reduces the environmental impacts of a business without lacking its profit. Considering all of the factors mentioned above, in this paper, we study a green economic order quantity model with capacity constraint under order-size-dependent trade credit and all-units discount along with minimizing carbon for a cleaner environment. The paper discusses all the potential cases, which may occur in green inventory models with carbon emission cost under different allowable delay in payments. Shortages are allowed and partially backordered. The main objective is to determine the sustainable optimal ordering strategies for retailers and decide whether a rented warehouse (RW) is to obtain ordering and replenishment policies for a retailer such that the retailer’s annual profit is maximized. First, we prove that the conditions of the objective functions have interior minimizer value and the closed-form optimal solution is found. Next, an algorithm is developed to determining the global optimal solution of the problem. Finally, some management insights are drawn by observing the applicability of the developed algorithm and also by performing sensitivity analyses on different parameters.

Study’s Excerpt/Novelty This study introduces a novel economic order quantity (EOQ) model for managing non-instantaneous deteriorating items under two-phase demand rates and linear holding costs, incorporating constant partial backlogging and two-level pricing strategies within a trade credit framework. The model uniquely addresses the complexities of time-dependent quadratic demand before deterioration and constant demand afterward, providing optimal solutions for maximizing total profit by determining the best timing for positive inventory, cycle length, and order quantity. The research not only establishes the theoretical existence and uniqueness of these optimal solutions but also demonstrates practical implications through numerical examples and sensitivity analyses, highlighting the critical impact of deterioration rates on inventory management and profitability. Full Abstract This research developed an economic order quantity model for non-instantaneous deteriorating items with two-phase demand rates, linear holding cost, constant partial backlogging rate and two-level pricing strategies under trade credit policy. It is assumed that the holding cost is linear time-dependent, the unit selling price before deterioration sets in is greater than that after deterioration sets and the demand rate before deterioration sets in is considered as continuous time-dependent quadratic, after which it is considered as constant up to when the inventory is completely exhausted. Shortages are allowed and partially backlogged. The purpose of the model is to determine the optimal time with positive inventory, cycle length and order quantity such that the total profit of the inventory system has a maximum value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions have been established. Some numerical examples have been given to illustrate the theoretical result of the model. Sensitivity analysis of some model parameters on the decision variables has been carried out and suggestions towards maximising the total profit were also given. , it is seen that the higher the rate of deterioration the lower the optimal time with positive inventory ( ), cycle length order quantity and the total profit and vice versa. This implies that the retailer needs to take all the necessary measures to avoid or reduce deterioration to maximise higher profit. Based on the results application of the model led to an increase in revenue.

Due to increasing global warming and environmental consciousness, to avoid/reduce carbon emission is a challenge in today's business scenario. In this study, a three stage (buyer-distributer-vendor) economic order quantity strategy is presented. The objective of this study is to analyse the carbon emissions caused during transportation and holding of the inventory. In order to increase the utility of the proposed model, besides all cost parameters, carbon emission costs and transportation costs at every step of supply network are also considered as fuzzy and denoted by fuzzy numbers. Shortages are allowed and backlogged unconditionally for this study. The optimal solution are obtained by using (a non derivative) arithmetic geometric inequality method. Further the optimization model is studied under the following policies (i) without considering carbon emission and (ii) with carbon emission. Here closed form solutions are obtained. Proposed models are analysed environmentally and economically for the decision variables. A numerical example is used to demonstrate the work in a better way and obtained results are compared under both policies. Finally, the results of two models proved that, the model with carbon emission is better for cost reducing and environmental consciousness both. Sensitivity analysis is also performed with respect to all important parameters.

In this paper, economic order quantity (EOQ) models without shortages for single item and multi-items are presented. Here, the holding cost of the item is a continuous function of the order quantity. The costs involved in this model are imprecise in nature. The main contributions of this research are as follows: The proposed EOQ model is discussed in two cases by describing the model in an uncertain environment. In case-1, EOQ models with fuzzy parameters (like ordering cost, holding cost, and unit product cost) are considered. Here all the fuzzy parameters are represented by trapezoidal fuzzy numbers. The said EOQ model is carried out by using the signed-distance method. In case-2, EOQ models with interval parameters (like ordering cost, holding cost, unit product cost, and the total money investment for the quantities) are considered. This proposed model is solved by using interval linear programming problem (ILPP) technique based on the best and the worst optimum values of the objective function. Numerical examples are given to exemplify the proposed model and also the results of different models are compared.KeywordsEOQTrapezoidal fuzzy numberInterval numberSigned-distance methodInterval linear programming problem (ILPP)

Most researchers established their inventory lot-size models under trade credit financing by assuming that the supplier offers the retailer fully permissible delay in payments and the products received are all non-defective. However, in the real business environment, it often can be observed that the supplier offers the retailer a fully permissible delay in payments only when the order quantity is greater than or equal to the predetermined quantity Q d . In addition, an arriving order lot usually contains some defective items due to imperfect production processes or other factors. To capture this reality, the paper extends Huang (2007) economic order quantity (EOQ) model with partially permissible delay in payments to consider defective items. We formulate the proposed problem as a profit maximization EOQ model in which the replenishment cycle time is the decision variable. Then we use the arithmetic-geometric mean inequality approach to determine the optimal solution under various situations. An algorithm to obtain the optimal solution is also provided. Finally, the numerical examples and sensitivity analysis are given to illustrate the results.

The economic ordering quantity (EOQ) model has been widely applied to inventory management. However, some assumptions in the model are unrealistic in practice. One of the assumptions is that all produced units are of good quality. This article deals with an EOQ model for products with imperfect quality under an announced price increase, where the defectives are screened out by a 100% inspection process, and which can be sold as a single batch at the end of the inspection process. The optimal ordering policies associated with three kinds of effective times of the price increase are obtained. A numerical example is then provided to illustrate the proposed model. Besides, based on the numerical example, the effects of some important parameters on the optimal order quantity and the corresponding saving in cost are also investigated.

Inventory control is a very important element in the management of pharmaceutical supplies. Inventory control at Hospital “X” in Palopo City is currently using the consumption method, which has the risk of running out of medicine (stock out). Methods that can minimize this risk are the ABC, EOQ, and ROP analysis methods. The research aims to group drug items into 3 ABC groups based on investment value, find out the optimal order quantity using the economic order quantity (EOQ) calculation, and determine the time to reorder drugs using the reorder point (ROP) calculation. This type of research is non-experimental and uses mixed methods; data collection is done retrospectively for quantitative data and directly for qualitative data. The results of the analysis of the ABC method of branded generic drug included in group A were 18 types (12%) with an investment value of 70.17% of the total investment value, group B, namely 22 types (14.67%) with an investment value of 20.38 % of the total investment value, and group C drugs, namely 110 types (73.33%) with an investment value of 9.46% of the total investment value. Based on the EOQ calculation analysis, the optimal number of orders for group A branded generic drugs varied between 683 and 34 units. The results of the calculation and analysis using the ROP method show that the reorder point for group A branded generic drugs varies between 234 and 7 for each drug unit.

This paper considers logistics decision support system which deals with transportation mode selection considering transportation and carbon emission cost. Transportation and carbon emission costs vary with the choice of transportation modes and to become competitive companies need to find proper transportation modes for their logistics services. However, due to the restricted capacity of transportation modes, it is difficult to balance transportation and carbon emission costs when designing logistics network including transportation mode choice for each service. Therefore this paper aims to analyze the trade-off relationship between transportation and carbon emission cost in mode selection of intermodal transportation and to provide optimal green logistics strategy. In this paper, the logistics decision support system is designed based on mixed integer programming model. To understand the trade-off relationship of transportation and carbon emission cost, the system is tested with various scenarios including transportation of containers between Seoul and Busan. The analysis results show that, even though sea transportation combined with trucking is competitive in carbon emission per unit distance travelled, the total cost of carbon emission and transportation for the sea transportation may not have competitive advantage over other transportation modes including rail and truck transportation modes. The sea-based intermodal logistics service may induce detours which have negative impacts on the overall carbon emission. The proposed logistics decision support system is expected to play key role in green logistics and supply chain management.

Typical economic order quantity models of inventory feature demand rate as a constant parameter and do not allow for backordering. Furthermore, the purchasing cost of the ordered materials is considered constant. In reality, the demand rate is related to the unit purchasing cost and other factors, such as time and availability of products in the market. A quantity discount is regularly applied to encourage ordering more products by decreasing the price. In some situations, carbon dioxide emissions are carefully scrutinized and a program to handle these. Greenhouse gases are put in place. Hence, for this research, the rate of demand in the model was assumed proportional to the unit purchasing cost and partial backordering was allowed as a fixed parameter. Because plants emit greenhouse gases (carbon dioxide), we considered mitigation efforts. A mathematical model and computational procedures are shown with the solution algorithms that demonstrate the capability of the model. An example problem was solved with the model and sensitivity analysis was conducted to inform the managerial insights offered.

On 2019 and 2022, a year before and after the Covid-19 pandemic, indicates fluctuating conditions in net profit and increasement in operational costs of F&B Department Hotel Indigo Bali Seminyak Beach. This writing aims to present a solution to reduce operational costs and increase the percentage of net profit. The method used is assistance in implementing cost leadership and the EOQ (Economic Order Quantity) approach in price break cases. By implementing cost leadership strategy and EOQ (Economic Order Quantity) in price break cases, the F&B Department of Hotel Indigo Bali Seminyak Beach will get optimal order quantities and the best prices from suppliers, reduce operational costs, and set lower selling prices.

EOQ models with stockouts for disassembly systems

Abstract. Effective and efficient inventory management is crucial for the sustainability of businesses in the culinary industry. Brebes Lembang Restaurant, as a culinary business providing food and beverages, requires proper inventory management to increase efficiency and reduce costs.This study aims to determine the Economic Order Quantity (EOQ) method in managing chicken broiler raw material inventory at Brebes Lembang Restaurant and to evaluate the effectiveness of the EOQ method in improving inventory management efficiency.This study employs a mixed-method approach, combining qualitative and quantitative methods. Data were collected through interviews, observations, and analysis of secondary data. Data analysis used the EOQ method to determine the optimal order quantity and minimum total cost.The resultsshow that Brebes Lembang Restaurant has effectively applied the EOQ method in managing chicken broiler raw material inventory. The analysis reveals that the EOQ method can improve inventory management efficiency and reduce total costs.This study concludes that the EOQ method can be used as a tool to support inventory management of chicken broiler raw materials at Brebes Lembang Restaurant. The findings of this study are expected to contribute to the development of inventory management theory and practice in the culinary industry. Abstrak. Pengelolaan persediaan bahan baku yang efektif dan efisien sangat penting bagi keberlangsungan usaha di bidang kuliner. Rumah Makan Brebes Lembang sebagai salah satu usaha kuliner yang bergerak di bidang penyediaan makanan dan minuman, memerlukan pengelolaan persediaan bahan baku yang tepat untuk meningkatkan efisiensi dan mengurangi biaya. Penelitian ini bertujuan untuk mengetahui metode Economic Order Quantity (EOQ) dalam pengelolaan persediaan bahan baku ayam gantung di Rumah Makan Brebes Lembang, serta untuk mengetahui efektivitas metode EOQ dalam meningkatkan efisiensi pengelolaan persediaan. Penelitian ini menggunakan metode campuran, yaitu kombinasi antara metode kualitatif dan kuantitatif. Data yang dikumpulkan melalui wawancara, observasi, dan analisis data sekunder. Analisis data menggunakan metode EOQ untuk mengetahui jumlah pesanan optimal dan biaya total yang minimal. Hasil penelitian menunjukkan bahwa Rumah Makan Brebes Lembang telah menggunakan metode EOQ dengan baik dalam pengelolaan persediaan bahan baku ayam gantung. Hasil analisis menunjukkan bahwa metode EOQ dapat meningkatkan efisiensi pengelolaan persediaan dan mengurangi biaya total. Penelitian ini menyimpulkan bahwa metode EOQ dapat digunakan sebagai alat bantu dalam pengelolaan persediaan bahan baku ayam gantung di Rumah Makan Brebes Lembang. Hasil penelitian ini diharapkan dapat memberikan kontribusi pada pengembangan teori dan praktik manajemen persediaan di bidang kuliner.

This paper presents EOQ (Economic Order Quantity) model with stock- level dependent demand and different types of holding cost function. We show that the total relevant inventory cost per unit time is convex with respect to cycle time. Mathematical models are established to determine optimal order quantity and total relevant inventory cost. Numerical examples are provided for two different models i.e. (i): Instantaneous replenishment with inventory dependent holding cost and (ii) Instantaneous replenishment with quadratic time dependent carrying cost. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. The second order approximation is used for finding closed form optimal solution. Mathematica 5.2 software is used to find numerical results.

Carbon emission calculation during power transmission and substation construction provides valuable insights into the trend of carbon emissions and the development of low-carbon power grids. In this regard, this study divides the power transmission and substation construction process into production, transportation, and construction stages based on the sources of carbon emissions and employs a life cycle assessment to calculate the total carbon emissions using the carbon emission factor method for typical 500 kV projects. The results show that in the construction process the production stage contributes the most carbon emissions, with material and equipment production for power transmission accounting for 78% and 14% of the total emissions, respectively. The transportation and construction stage contribute 1% and 7% of the total emissions, respectively. For substations, material and equipment production contribute 67% and 30% of the total emissions, respectively. The transportation and construction phases contribute 1% and 2% of the total emissions. Through the qualitative and quantitative analysis of the carbon emission results, the construction scale and the topography and geology have significant impacts on carbon emissions from power transmission and substation projects. Finally, some targeted recommendations for carbon emission reduction for power transmissions and substations are proposed based on the influencing factors of each stage of the construction.

This article presents mathematical and statistical methods applicable to inventory management. Inventory analysis using ABC curves is used to identify priority items, the most expensive items, and those with the highest turnover (demand). Based on this information, it is possible to determine, through inventory control models, the optimal order quantity and frequency that minimize the total storage costs of these items. Using the Economic Order Quantity (EOQ) model and the (Q, r) model, inventory control models, the minimization of a company's inventory costs in Londrina, Paraná, Brazil was simulated. The comparison of the results provided by the models was discussed. Specifically, it was observed that for some inventory items, it would theoretically be possible to achieve savings margins of over 50% on inventory expenses for this company.