Mathematical Inventory Model Research Articles

A closed-loop supply chain inventory model with stochastic demand, exchange rate, green investment, and carbon tax

In this paper, a mathematical inventory model for a closed-loop supply chain consisting of a single manufacturer and a single retailer is investigated under a stochastic environment and imperfect production. The manufacturer adopts a remanufacturing policy to recover returned products from the market. The model takes into account exchange rate disparities because the supply chain’s participants are in separate countries. The model also considers carbon emissions, which are expected to be produced from storage, transportation, and production. A carbon policy, namely carbon tax, is implemented to manage the overall emissions resulting from the supply chain. To cope with carbon restrictions, the manufacturer has an opportunity to invest in green technologies. The objective of the study is to find optimal shipment quantity, number of deliveries, safety factor, and green investment such that the joint total cost is minimized. An iterative procedure is suggested to solve the proposed problem, and a numerical example is presented for model validation. The findings imply that variations in the production rate and carbon tax have a significant influence on the model’s performance. Aside from that, the results reveal that uncertainty in the exchange rate and production flaws are important factors that must be considered by managers in making inventory decisions, especially those related to the number of deliveries, frequency of deliveries, and the amount of money invested in green technology. Finally, a sensitivity analysis is provided to explain the behavior of the model.

Using Four Metaheuristic Algorithms to Reduce Supplier Disruption Risk in a Mathematical Inventory Model for Supplying Spare Parts

Due to the unexpected breakdowns that can happen in various components of a production system, failure to reach production targets and interruptions in the process of production are not surprising. Since this issue remains for manufactured products, this halting results in the loss of profitability or demand. In this study, to address a number of challenges associated with the management of crucial spare parts inventory, a mathematical model is suggested for the determination of the optimal quantity of orders, in the case of an unpredicted supplier failure. Hence, a production system that has various types of equipment with crucial components is assumed, in which the crucial components are substituted with spare parts in the event of a breakdown. This study’s inventory model was developed for crucial spare parts based on the Markov chain process model for the case of supplier disruption. Moreover, for optimum ordering policies, re-ordering points, and cost values of the system, four metaheuristic algorithms were utilized that include Grey Wolf Optimizer (GWO), Genetic Algorithm (GA), Moth–Flame Optimization (MFO) Algorithm, and Differential Evolution (DE) Algorithm. Based on the results, reliable suppliers cannot meet all of the demands; therefore, we should sometimes count on unreliable suppliers to reduce unmet demand.

Sustainable inventory management for a closed-loop supply chain with energy usage, imperfect production, and green investment

In this paper, a mathematical inventory model for a manufacturer-multi retailer system is proposed to optimize the inventory level and investments under a carbon tax policy. The energy consumed by the production and rework and the emissions resulting from supply chain operations are considered and controlled using a production rate adjustment. To comply with the carbon policy, the manufacturer invests in green production technologies to cut down the emissions. The model aims to minimize the joint total cost by simultaneously determining the shipment frequencies, shipment lot, safety factor, production rate, collection rate and the investment. A numerical example and sensitivity analysis are given to show the application of the model and to study the impact of key parameters on model’s behaviour. The results suggest that by allowing the production rate to be adjusted flexibly, the system can easily control the emissions, energy consumption and the number of defects, so that the total cost can be minimized. The green investment is proven to be effective in reducing emissions and increasing returns on used products, thereby improving the environmental performance of the supply chain.

Low carbon inventory model for vendor‒buyer system with hybrid production and adjustable production rate under stochastic demand

In this study, a mathematical inventory model for a supply chain system made up of a vendor and a buyer under stochastic demand is formulated. The vendor serves as a manufacturer who produces items, while the buyer serves as a retailer who buys the items from the vendor and sells them to end customers. In addition to utilizing regular production as a production base, the vendor also uses green production. Green production adopts green technology, which comprises environmentally friendly inventions that are used to reduce emissions. Green production is more costly than regular production, but it generates lower emissions. The production rate is adjustable, which enables decision makers to control the emissions and production cost. The objective of this study is to find the optimal production allocation, ordering quantity, shipment frequency, safety factor, and production rate such that the joint total cost is minimized. An algorithm is suggested to solve the mathematical problems and its application is validated with a numerical example. The results show that the changes in the emissions, carbon tax, and production cost parameters exhibit significant effects in determining the optimal production allocation. Furthermore, by controlling the production rate flexibly, the supply chain can lessen the emissions released during production and maintain the total cost. Finally, a sensitivity analysis is carried out to explain the usage of the proposed model.

Optimizing the surgical instrument tray to immediately increase efficiency and lower costs in the operating room.

Background:Surgical trays are often poorly configured and can be ongoing sources of frustration and excess costs. We conducted an observational study to determine if the use of a customized mathematical inventory optimization model would result in a greater reduction in the number of instruments on a surgical tray than a clinician review of the tray.Methods:Utilization of instruments on the major orthopedic tray at a large academic hospital was documented over 80 procedures. Processes in the medical device reprocessing department and operating room were observed to comprehensively quantify all associated costs. Results of the observations were applied to a customized mathematical model to determine the ideal tray configuration. For comparison, a clinician review was also performed.Results:The mathematical model alone produced an ideal tray size of 47 instruments, a reduction of 41 instruments from the original size of 88 instruments (47% reduction). This represented $34 440 in annual savings. In contrast, the clinician review alone suggested an ideal tray size of 67 instruments (23% reduction), representing $17 640 in annual savings. When clinicians were provided with the additional information from the model, they reduced the tray size to 51 instruments (42% reduction), producing $31 870 in savings. The mathematical model yielded an additional 22% instrument reduction and $14 230 in savings compared with clinician review alone.Conclusion:Our mathematical model is generalizable and can be applied to all specialties and hospitals to determine optimal tray configuration. As such, the financial implications are broad; at our institution, application to all surgical trays would result in $205 000 of savings annually. Surgeons and managers looking to streamline surgical trays should consider this evidence-based approach.

Managing a sustainable integrated inventory model for imperfect production process with type one and type two errors

Unlike previous research, this study develops an integrated inventory model for controllable lead time with defective items, errors in inspection, and variable lead time considering sustainability. The research investigates the effect of controlling lead time and capital investment in the setup cost. We assume that the buyer receives a lot size that may contain some defective items with a known defective probability. The buyer’s inspector conducts a 100% quality inspection and may incorrectly classify a non-defective item as a defective item (type one (I) error) or incorrectly classify a defective item as a non-defective item (type two (II) error). The mathematical inventory model considering carbon emission cost is developed, and the solution procedure is designed using the heuristic algorithm to derive the optimal or near optimal solution. Finally, numerical examples and sensitivity analysis are given to illustrate the results. The results show that the defective rate, and type I type II inspection errors, have a significant impact on the shipment lot. This leads to the changes in the total cost, lead time, and the carbon emissions. Our study provides cost savings of 4.39% and carbon emission savings of 28.44%.Graphic abstract

A closed-loop supply chain inventory model with stochastic demand, hybrid production, carbon emissions, and take-back incentives

This paper considers a two-echelon inventory model for a closed-loop supply chain system containing a manufacturer and a retailer under a stochastic environment with carbon emission reductions. Production and remanufacturing are performed simultaneously in a manufacturer's hybrid production system involving green production and regular production. To encourage the manufacturer to reuse products, the government offers a take-back incentive operating under a collection rate target. Motivated by this offer, the manufacturer significantly improves the system and makes an investment to increase the number of used products collected from the customers. The emissions generated from transportation, production, and storage activities are incorporated into the model and intended to be reduced by a carbon tax regulation. To achieve this, a mathematical inventory model that aims to minimize the joint total cost is built and solved using an efficient procedure. The results show that by controlling the collection rate and the production allocation, the system can minimize the cost and the emissions. Further, the take-back incentive and the manufacturer's investment in collection efforts can effectively increase the return rate of used products, but these policies will lead to an undesirable increase in total emissions.

P77. Optimizing the spine surgery instrument trays to immediately increase efficiency and lower costs in the operating room

<h3>BACKGROUND CONTEXT</h3> Spine surgery is increasingly scrutinized in a climate of rising health care costs given its cost per procedure compared to other specialties. Fortunately, there are many sources of inefficiency that can be addressed without compromising patient care. Surgical trays are often poorly configured and have considerable economic implications as they comprise a large portion of perioperative budgets. Instruments are typically added on an ad-hoc basis, based on surgeon request, which can result in excessively large and inefficient trays. A solution must take into account the conflicting issues of clinical need, costs, ease of batching, prevention of adverse clinical events, and minimization of wear-and-tear on instruments. Clinician review and cost-analysis of surgical trays are two methods historically used to address this challenge, although they have shortcomings. We conducted an interventional quality improvement study to determine if a customized mathematical inventory optimization model would result in greater reduction of instruments than a clinician review. <h3>METHODS</h3> This was a single-site quality improvement study conducted at a large academic hospital which performs over 750 laminectomy procedures annually. Two trays are required: 1) Laminectomy Tray (LT) and 2) Basic Neurosurgery Tray (BNT). As such, the focus of our study was to optimize these two trays. A trained observer was present in the operating room (OR) during 25 randomly selected laminectomy procedures. Processes in the MDRD and OR were observed to comprehensively quantify associated costs. The results of the observations were applied to a mathematical model to determine ideal tray configuration. In addition, a clinician review (CR) of the trays was performed for comparison. <h3>RESULTS</h3> The mathematical model produced an ideal tray size of 29 for the LT, representing a reduction of 41% from the original size of 49. For the BNT, the mathematical model produced an ideal tray size of 23 instruments, a reduction of 50% instruments from the original size of 46. Combined, this represented $20,934 in annual savings. In contrast, CR alone suggested an ideal tray size of 35 (29% reduction) for the LT and 37 (19%) for the BNT instruments, and $11,197 in annual savings. <h3>CONCLUSIONS</h3> Superior reduction of surgical trays used for laminectomy was achieved using a mathematical model when compared to CR alone. The mathematical model yielded an additional 10% instrument reduction and $9,737 in savings compared to clinician review alone. Our model comprehensively optimizes the surgical trays by incorporating several cost drivers important to major processes involved in surgical tray assembly, processing and OR utilization. This model may be generalizable to all specialties and hospitals to determine optimal tray configuration. The financial implications are broad; at our institution, application of the mathematical model to all surgical trays would result in projected costs savings of $312,476 annually. Surgeons and managers looking to manage costs should consider this evidence-based approach. <h3>FDA DEVICE/DRUG STATUS</h3> This abstract does not discuss or include any applicable devices or drugs.

A mathematical inventory model for a single-vendor multi-retailer supply chain based on the Vendor Management Inventory Policy

A mathematical inventory model for a single-vendor multi-retailer supply chain based on the Vendor Management Inventory Policy

Inventory and sales decisions in a vendor–buyer system with imperfect items and learning in inspection

ABSTRACT In this study, we propose a joint economic lot-sizing model to include learning process along with errors in inspection and full backordering system. We aim to study pricing and inventory decisions in a two-level supply chain involving a single vendor and a single buyer in which the demand is sensitive to price and company’s advertisement efforts. The mathematical inventory model is developed analytically and solved using a proposed algorithm. The objective of the model is to maximise joint total profit by simultaneously determining optimal shipment size, number of deliveries, backorder quantity and product selling price. A numerical example is provided to show the application of the model and to investigate the impact of key parameter’s changes on model behaviour. By comparing the integrated/centralised model to the independent/decentralised model, we note that the integrated/centralised model provides better profit to the system, along with lower selling price and smaller amount of backorder.

Retailer’s inventory decisions with promotional efforts and preservation technology investments when supplier offers quantity discounts

In this paper, we formulate a mathematical inventory model for deteriorating items with a constant rate of deterioration. The supplier offers the retailer successive discount on purchase of goods if the order size crosses predefined quantity levels. Retailer uses preservation techniques to reduce the deterioration rate. In order to increase the sales, retailer implements promotional strategies. Market demand of the product is influenced by promotional efforts, stock level and selling price of the product. The objective is to find optimum order quantity, cycle time, promotional cost, preservation cost and selling price in order to maximize total profit for the retailer. A numerical example is given to validate the mathematical model. Sensitivity analysis has been carried out to analyze the effect of change of other inventory parameters on decision variables and total profit. Results indicate that due to preservation technology we can see remarkable decrease in the deterioration rate hence cycle time increases and retailer can set a cheaper selling price to increase sales. Promotional efforts help the retailer to enhance sales of the product. Moreover, depending upon the product demand and order size, quantity discounts help retailer to reduce the purchase cost and hence overall profit of retailer increases.

Development of new hybrid discrete-time perishable inventory model based on Weibull distribution with time-varying demand using system dynamics approach

In the 20th century, there has been a significant development in logistics systems owing to market globalisation. From this perspective, our study focuses on designing novel models of inventory systems to reflect these real-time systems with improved accuracy and eventually design optimal control systems. Many mathematical inventory models lack details. Most of the existing models in the literature neglect the inclusion of closing days despite the shortening of the shelf-lifes of perishable items daily. In this study, a hybrid dynamic discrete-time inventory model with random lifetime perishable products, first in–first out (FIFO) and last in-first out (LIFO) issuing policies, positive lead time, and time-varying demand, including closing days, is developed. It is assumed that the demand is an external input to the model, and thus, it is easy to implement or test various market scenarios. The developed model is fitted to real data obtained from the research on the formation of botulinum toxin on packaged cubed melons and microbial spoilage at various incubation temperatures. Our study shows that the implementation of the Weibull distribution in modelling perishability can improve the accuracy of reflecting the performance of real physical inventory systems. We compare the developed model to an existing one in the literature, considering different issuing policies: FIFO, LIFO, and their combination. The study also includes a comparative analysis of the fixed and random lifetimes of products in terms of closing days.

A Closed-loop Supply Chain Inventory Model Considering Limited Number of Remanufacturing Generation and Environmental Investigation

This study presents a mathematical inventory model in the Closed-loop Supply Chain (CLSC) system. We investigate a CLSC system that consists of a retailer, a manufacturer and a 3rd party collection dealer. The model aims to minimize the annual joint total inventory cost for the three parties and determine several decision variables, including number of shipments, manufacturer shipment lot size and number of remanufacturing generations. The number of remanufacturing generations is one of our concerns since we consider a type of product that could not be remanufactured in an unlimited number of time. Thus, how many times the product should be remanufactured becomes important. In this study, we also investigate the environmental impacts in term of carbon emissions, energy usage, as well as annual disposed items. The model can guide companies in the related industry to plan a system of CLSC inventory management with environmental considerations.

Learning effect on an optimal policy for mathematical inventory model for decaying items under preservation technology with the environment of COVID-19 pandemic

Learning effect on an optimal policy for mathematical inventory model for decaying items under preservation technology with the environment of COVID-19 pandemic

Inventory Policies for Non-instantaneous Deteriorating Items with Preservation technology investment under Price-sensitive Time-dependent demand

In this paper, we formulate a mathematical inventory model for non-instantaneous deteriorating items under price-sensitive and quadratic time-dependent demand. Products in the inventory system are ...

A novel mathematical inventory model for growing-mortal items (case study: Rainbow trout)

• Developing a novel mathematical inventory model for growing-mortal items. • Studying the proposed model for trout fish production in a two-echelon supply chain (case study). • Applying revenue-sharing contract as well as revenue and cost sharing contract into proposed model. • Proposing a new feeding function for rainbow trout. • Providing managerial insights into trout production in a coordinated supply chain. Unlike the extensive inventory models for both ameliorating and deteriorating items, incorporating some specific features of these products have mostly been neglected. To fill this research gap, providing an appropriate mathematical inventory model for both ameliorating and deteriorating items is of paramount importance. In this regard, this paper proposes a novel mathematical inventory model for products called growing-mortal items in a two-echelon supply chain consisting of one supplier and one farmer. The proposed inventory model is more precise than analogous inventory models due to the fact that the specific growth function for the item is considered as well as mortality rate. As a case study, the model is applied to rainbow trout, which can be used for other types of growing-mortal items. Moreover, a feeding function is first-ever proposed for rainbow trout regarding the case study. The goal of this paper is to study the growth period in the supplier and then in the farmer sites to maximize the profit of the supplier as a leader and farmer as a follower under a Stackelberg game. To demonstrate how to reduce the inventory system costs by two coordination mechanisms, namely revenue-sharing and revenue and cost sharing, the model is solved under centralized and decentralized cases. Finally, sensitivity analysis on key parameters is also conducted to derive some managerial insights.

Development and simulation analysis of a new perishable inventory model with a closing days constraint under non-stationary stochastic demand

Abstract The food waste in grocery retail is a worldwide problem. Many mathematical inventory models for perishable items do not have a closing days constraint, although the age of perishable items also increases on closing days in grocery stores. We develop a new age-based inventory model with a closing days constraint. This stochastic multi-item inventory model includes total stock capacity constraints, a positive lead time, a periodic inventory control, a target customer service level and mixed FIFO and LIFO issuing policies for perishable items with a fixed lifetime under a non-stationary random demand. We show in a comparative simulation study under a rolling planning that the closing days constraint improves order decisions and reduces waste quantities and costs in grocery stores.

Development of Inventory Model for Health Care System in Multi-Speciality Hospitals Using Arena

In 21st century healthcare organization is one of the significantly growing service organizations to the public in India but operational cost is increasing everyday which makes the people unaffordable. Hence, inventory management is essential to minimize the operational cost effectively in health care system. The aim of this study is to provide decision support for operation theatre in-charge in maintaining appropriate levels of drugs and consumables. The mathematical inventory model for accounting various elements of inventory cost is essential which enables the OT in-charge for making decisions to reduce inventory cost. The OT inventory system has been simulated to find average inventory and inventory turnover for critical products. The simulation results provides insight on average inventory to be maintained for the above three critical products as 14, 36 and 5 units respectively and also provides imminent on utilization of critical recourses in OT of the selected multi-specialty hospital.

A review of mathematical inventory models for reverse logistics and the future of its modeling: An environmental perspective

The responsible management of product return flows in production and inventory environments is a rapidly increasing requirement for companies. This can be attributed to economic, environmental and/or regulatory motivations. Mathematical modeling of such systems has assisted decision-making processes and provided a better understanding of the behavior of such production and inventory environments. Therefore, this paper reviews the literature on the modeling of reverse logistics inventory systems that are based on the economic order/production quantity (EOQ/EPQ) and the joint economic lot size (JELS) settings, so as to systematically analyze the mathematics involved in capturing the main characteristics of related processes. The literature is surveyed and classified according to the specific issues faced and modeling assumptions. Special attention is given to environmental issues. In addition, there are indications of the need for the mathematics of reverse logistics models to follow current trends in ‘greening’ inventory and supply-chain models. Finally, the modeling of waste disposal, greenhouse-gas emissions and energy consumption during production is considered as the most pressing priority for the future of reverse logistics models. An illustrative example for modeling reverse logistics inventory models with environmental implications is presented.

Development of analytical models of optimizing an enterprise’s logistics information system supplies

The creation of an efficient enterprise’s logistics information system requires a set of mathematical decision support models. The existing inventory models that are used in warehouse logistics have low adequacy with the real logistics processes.The research examines the reasons for the low efficiency of the basic warehouse logistics models and analyzes their development. When determining the form of the total cost function in the EOQ model, the costs of delivery and storage related to different moments of time were not taking into account. Failure to fulfill this requirement is one of the main factors affecting the adequacy of the mathematical inventory models, which are based on the EOQ model.The developed mathematical models, representing the refined Wilson’s model, allow to justify the consignment delivery using several vehicles. The conditions for applying the model to the order cost, depending on the consignment size were determined. The algorithm for determining the optimal number of vehicles for the consignment delivery was developed.Using the developed mathematical models will allow making the best decisions in warehouse logistics. The findings to the EOQ model development can be used for other inventory models that will create an effective information logistics system.