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Inventory system behaviour for growing items with the owned facility, rented facility and linear growth function (Sebatjane and Adetunji [6])
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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 invent...
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In online purchasing, customers may return products due to dissatisfaction with the quality of the product, and receive a refund based on the return policy, which is determined by online distributors. Online distributors can offer generous policies to attract more customers, but at the cost of reducing total profits. In this paper, the effect of th...
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... Therefore, an arrangement is needed to determine the number of orders, considering the expiration time and available warehouse capacity. Many papers have included the discount factor in the model along with warehouse or capacity constraint or other factor, such as in [8], [9], [10], [11], [12], [13], [14] and [15]. For example, in [8], a mathematical model was developed to accommodate delays in payments, discounts, capacity constraints, and shortages. ...
... For example, in [8], a mathematical model was developed to accommodate delays in payments, discounts, capacity constraints, and shortages. A model for growing products with incremental discounts, storage capacity, and budget was considered [9]. Models with several types of discount factors were developed in those papers along with factors such as partial credit policy and capacity constraint ( [10]), probabilistic model ( [11]), and deterioration ( [12], [13], [14], [15]). ...
... And the number of items to be ordered at the beginning of each cycle is 72, 52, and 105 units, so the purchase price used for item 1 is 12 (because 1 ≤ 201), item 2 is 15 (because 2 ≤ 131), and item 3 is 8 (because 3 ≤ 301), so the total inventory cost that the company must incur is 19,488.32. Furthermore, it will be checked whether the order quantities for the first, second, and third items satisfy the constraints in Equation (8) and Equation (9). Based on this, ordering using a joint order policy does not exceed the warehouse capacity and capital provided by the company. ...
Article History: In general, companies have inventory stored in warehouses to be used or sold in the future. To optimize inventory, companies require a model to determine the appropriate order quantity and optimal reorder timing to minimize total inventory costs. To stay within the set capacity, several factors need to be considered in inventory management, such as a product's shelf life, warehouse capacity, and capital. On the other hand, suppliers may offer discounts, and companies tend to take advantage of them. However, they must consider the warehouse capacity and capital availability. This paper constructs two probabilistic multi-item inventory models, considering discounts, expiration, warehouse capacity, and capital constraint. The first model considers all-unit discounts, while the second deals with incremental discounts. We consider three items to be managed and examine three replenishment policies, namely individual order, joint order, and a combined policy of individual and joint order, to minimize the total inventory cost. Sensitivity analysis is performed on the joint order policy to determine the influence of parameter values' changes on the reorder time and total inventory cost.
... Research has been conducted on inventory systems that account for factors such as all-units discount and expiration dates, as shown in the publications [3], [4], and [5]. [6] provided economic order quantity model for expanding items with budget constraints, a storage facility that can accommodate them, and incremental quantity discounts. A probabilistic multi-item inventory model introduced by [7]. ...
... routing for order pickers) and strategic decision such as warehouse layout. Order batch also can be related to maximum order quantity can be stored in the capacitated warehouse [8], [9], and [10]. According to [11] the objective of the order batching strategy is to minimize the picking route distance in a manual sorting system particularly. ...
Order picking is the process of retrieving items from storage to meet a specific customer order, which is known to be the most labor-intensive and costly function among all the warehouse functions. This function is also important in that it has a critical impact on downstream customer service especially in facing the current covid-19 pandemic. This research aims to provide information, description and more comprehensively identifies the design and control of warehouse order picking by using empirical literature review. In this research, the stages are Identification of potential study, Study Selection based on criteria, quality assessment, data extraction, and data analysis. A systematic literature review identified 37 relevant articles for the research purpose. These articles focus on the design and control of warehouse order picking, aiming to enhance e-commerce transactions.
... The models consider sending a certain number of equally sized batches to retailers. Hidayat et al. [10] and Sitanggang et al. [11] integrated incremental discount policies for the acquisition of growing items from a supplier. Sebatjane and Adetunji [12] developed a growing inventory model where some of the growing items have poor quality and a lower selling price after a 100% screening process. ...
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.
... Their model obtains the optimal order quantity and cycle length, minimizing the total costs in both rented and owned facilities. After that, Hidayat et al. [16] extended the work of Sebatjane and Adetunji [15] by combining the limited on-hand budget and warehouse capacity. ...
... Next, we compute the partial derivation of the objective function (16) with respect to the slaughter date (t) and set it equal to zero, as follows: ...
... w 0 = 45 g; h = 0.002 $/year; D = 100, 000, 000 g; z = 0.0001 $/g/day; K = 5000 $/cycle; p = 0.01 $/g; a = 0.001 $/L/d·g; and r = 1 $/bird Based on the proposed solution method, the optimal value of the slaughter age is t * = 44 (see Figure 6). Then, substituting t * into Equations (16) and (19), the other optimal results are determined, as follows: y * = 419 newborn chickens, and TC * = 878991.3 USD. ...
Determining the optimal slaughter age of fast-growing animals regarding the mortality rates and breeding costs plays an important and major role for companies that benefit from their meat. Additionally, the effects of carbon dioxide (CO2) emissions during the growth cycle of animals are a significant concern for governments. This study proposes an economic order quantity (EOQ) for growing items with a mortality function under a sustainable green breeding policy. It assumes that CO2 production is a practical polynomial function that depends on the age of the animals as well as the mortality function. The aim of the model is to determine the optimal slaughter age and the optimal number of newborn chicks, purchased from the supplier, to minimize the total costs. We propose an analytical approach, with five simple steps, to find the optimal solutions. Finally, we provide a numerical example and some model management insights to help practitioners in this area.
... Growing inventory items include poultry and cattle. Hidayat's (2020) proposed scheme modifies three presumptions of the classical EOQ (i.e) purchased objects do not proliferate, infinite capacity, and an unlimited budget. Inventory models for growing items that take into account quality aspects, allowable shortages with complete backorder, and holding costs during both the growth and consumption periods, a model of nonlinear programming is developed in Alfares and Afzal (2021). ...
In this article, a multi-echelon supply chain for growing and deteriorating items, where the grower has a lot of live newborn items (growing) is discussed. The grower transfers the matured inventory to the processor in each shipment. The processor begins to process the stock as a ready-sale product in the market. The processor also delivers the processed inventory to the retailer in each shipment in the non-processing period of his cycle length. Then the processor offers trade credit to the retailer and makes the retailer agree to share a portion of his profit with him. The product’s life cycle when in the hand of the retailer is certain and it expires after some time t. Carbon emission during processing is considered while packing and preserving the livestock for sale. Depending on these assumptions, there are six possibilities to discuss profit values. Sensitivity analysis was also brought to verify the optimal determined values. The profit-sharing sharing method’s outcome benefits the processor and the retailer more.
... (17) Holding costs are incurred in the three stages of the supply chain. (18) In the processor stage, the inventory and holding costs of the growing items during the slaughter process are neglected. ...
This research develops an optimization model for growing items in a supply chain with three stages: farmer, processor, and retailer while considering imperfect quality, mortality, shortages with full backordering, and carbon emissions. In the farmer stage, during the growing period, not all articles survive until the end of the period, so a density function of the probability of survival and death of the growing articles is taken into account. Moreover, it is considered imperfect quality in the retailer’s stage because as the supply chain goes down, there exists a greater probability of product defects. Here, the end customer (consumer) can detect poor-quality aspects such as poorly cut, poorly packed, expired products, etc. An inventory model that maximizes the expected total profit is formulated for a single type of growing items with price-dependent polynomial demand. An algorithm is developed to solve the optimization problem generating the optimal solution for order quantity, backordering quantity, selling price, and the number of shipments that maximizes the expected total profit per unit of time, and a numerical example is used to describe the applicability of the proposed inventory model. Finally, a sensitivity analysis has been carried out for all the input parameters of the inventory model, where the effect of each of the parameters on the decision variables is shown to extract some management knowledge. It was found that holding costs in the three stages of the supply chain have a substantial impact on the total profit per unit of time. In addition, as the demand scale parameter increases, the company must raise the selling price, which directly impacts the expected total profit per unit of time. This inventory model has the advantage that it can be applied to any growing item, including animals or plants, so it helps the owners of farms or crops to generate the most significant possible profit with their existing resources.
... However, since the exact solution cannot be necessarily achieved in even small-size problems, their claim cannot be validated. Similarly, Hidayat et al. (2020) took notice of capacitated storage facility and limited budget in their growing inventory model. In order to manage the complexities raised by incorporating these two constraints, they applied a linear growth function. ...
Growth outlines the behavior of a class of inventories whose weight and size increase during their storage. Fast-growing young animals such as broiler chickens, ducks, and calves are examples of this class, prevalent in many food industries. Despite their presence in various food supply chains, studying these items in the context of inventory control, supply chain, and operations management is still in its early stage. This study provides the essential grounds of the knowledge in this area and further reviews the related research developments to provide the researchers with clear insights into the structure of the current literature, its main gaps, and promising directions for future research. In order to guarantee the comprehensiveness of our review, we have incorporated a systematic search procedure to identify the relevant literature. Through this procedure, 23 papers were identified that were used in our further analysis throughout the paper. Our investigations show that the literature on growing inventories is very confined, and this body of the literature gets even more limited when it comes to the problems in the context of the supply chain. Our findings introduce the topic as a promising direction in inventory and supply chain management with high potential for insightful future research works.
... Then Sebatjane and Adetunji [8] proposed a growing items model considering the incremental discounts. Hidayat et al. [9] proposed an optimization model for growing items with incremental quantity discounts, capacitated storage facility, and limited budget. Luluah et al. [10] proposed a model for growing items with incremental discount and imperfect quality on the farmer side. ...
This research develops an optimization model for determining the order quantity for growing items by considering the imperfect quality and incremental discount by involving three supply chain members: farmers, processors, and retailers. The farmers are responsible for caring for the newborn items until they reach their ready-to-eat weight. The processors perform two roles, namely processing and screening. In the processing role, the processors process the grown items by a slaughtering and packaging process. Afterward, they inspected the processed items and categorized the items into good and poor quality. Finally, they shipped the end products to retailers. The retailers are responsible for selling good-quality items to the final consumers. This research considers two kinds of poor quality. First is the poor quality of growing items in terms of mortality rate. The second is the poor quality of final products on the processor side. The processed items with poor quality are then sold to the secondary market at lower prices in one batch at the end of the period. This model also considers the incremental discounts offered by vendors to farmers and retailers to consumers for specific amounts of purchases. The model's objective function is to maximize the total supply chain profit, with the number of orders quantity, cycle time, and the number of batches delivery set as the decision variables. The sensitivity analysis results show that the most sensitive parameter in the model is the probability that the live items survive throughout the growth period.
... Research on inventory systems that consider factors such as expiry date, joint orders, and all unit discounts have been carried out, for example, [5,6,7,8], and [9]. Research on inventory control models that considers limited warehouse capacity on deterministic demand has been carried out by [10], while probabilistic demand has been carried out by [11] and [12]. Inventory models with probabilistic demand are considered more representative of actual conditions [13]. ...
... From the studies of [10,11], and [12] that have been done, all of them have not included the perishable factor as consideration for determining optimal ordering lot size. A study considers multi-item, space capacity, and perishable items but does not include discount, with the probabilistic nature presented in uniform distribution [16]. ...
The characteristics considered in this study are probabilistic demand, perishable products, and warehouse constraints for multi-item inventory models. This condition occurs in several industries that consider perishable factors and warehouse constraints, namely companies that produce food, food sales agents, and retail that sell goods to end customers. The Karush-Kuhn-Tucker Condition approach was used to solve the warehouse capacity problem to find the optimum point of a constrained function. The results of the developed inventory model provide two optimal ordering times, namely ordering time-based on warehouse capacity and joint order time, and the two ordering time values will be compared to determine which ordering time is optimal. In addition, the sensitivity analysis to the model was done to analyse the total inventory costs in a planning horizon, the time between goods ordering from one cycle to the next cycle, and the number of items that will expire. The parameters to be changed for the sensitivity test were warehouse constraint, a fraction of good condition goods, holding costs per unit per period, and all unit discount factors. The sensitivity analysis was done to see the behaviour of the total cost, time to order changes, and the quantity of perished products. The result of model testing and sensitivity analysis showed that total cost, based on joint order, is sensitive to the fraction of good condition products, discount, and holding cost. The joint order was not sensitive to the warehouse capacity. In general, the model was perceived as able to describe the behaviour of the model components.
