Single-period Inventory Model Research Articles

A Distributionally Robust Fuzzy Optimization Method for Single-Period Inventory Management Problems

This paper investigates single-period inventory management problems with uncertain market demand, where the exact possibility distribution of demand is unavailable. In this condition, it is important to order a reliable quantity which can immunize against distribution uncertainty. To model this type of single-period inventory management problem, this paper characterizes the uncertain demand by generalized interval-valued possibility distributions. We present a novel concept about an uncertain distribution set to describe distribution perturbation characterization. First, we introduce a lambda selection of the interval-valued fuzzy variable, and the uncertain distribution set is a collection of all generalized possibility distributions of lambda selection variables. According to the uncertain distribution set, a new distributionally robust fuzzy optimization method is developed for single-period inventory management problems. Under mild assumptions, the robust counterpart of the proposed fuzzy single-period inventory management model is formulated, which is an optimization program with certain linear objectives and infinitely many integral constraints. We discuss the computational issue of integral constraints and reformulate equivalently the robust counterpart as three deterministic inventory submodels under generalized interval-valued trapezoidal possibility distributions. According to the characteristics of three submodels, a domain decomposition method is designed to find the robust optimal solution that can immunize against uncertainty in our single-period inventory management problem. Finally, some computational results demonstrate the efficiency of the proposed distributionally robust fuzzy optimization method.

Operations Management of A Single-Period Inventory Model

Single-period systems: the decision is just a one-time purchasing decision where the purchase is designed to cover a fixed period of time and the item will not be reordered. e.g., the newsvendor and Cash Reserve Plan. The newsvendor tries to decide how many newspapers to stock on the newsstand before observing the demand.

Standardization of laparoscopic trays using an inventory optimization model to produce immediate cost savings and efficiency gains.

Perioperative services comprise a large portion of hospital budgets; the procurement and processing of surgical inventories can be an area for optimization in operational inefficiency. Surgical instrument trays can be customized as procedure-specific or standardized as trays that can be used in numerous procedure types. We conducted an interventional study to determine the cost savings from standardizing laparoscopic surgery instrument trays. A single-period inventory optimization model was used to determine the configuration of a standardized laparoscopic (SL) tray and its minimal stock quantity (MSQ). Utilization of instruments on the general surgery, gynecology, and gynecological oncology trays was recorded, and daily demand for trays (mean, SD) was assessed using daily operating room (OR) case lists. Pre- and post-intervention costs were evaluated by reviewing procurement data and quantifying medical device reprocessing (MDR) and OR processes. The SL tray was trialled in the OR to test clinical safety and user satisfaction. Prior to standardization, the customized trays had a total inventory size of 391 instruments (mean instruments per tray: 17, range: 12-22). Daily demand was an MSQ of 23 trays. This corresponded to a procurement cost of $322,160 and reprocessing cost of $41,725. The SL tray (mean instruments per tray: 15, mean trays/day: 9.2 ± 3.2) had an MSQ of 17 trays/day. The total inventory decreased to 255 instruments, corresponding to a procurement cost of $266,900 with savings of $55,260 and reprocessing cost of $41,562 with savings of $163/year. After 33 trial surgeries, user satisfaction improved from 50% to 97% (p < .05). Standardization to a single SL tray using the inventory optimization model led to increased efficiency, satisfaction, and significant savings through aggregating specific service demands. The inventory optimization model could provide custom solutions for various institutions with the potential for large-scale financial savings. Thus, future work using this model at different centres will be necessary to validate these results.

Several Methods of Inventory Control

This paper would firstly introduce the Single-Period Inventory Model, a basic method of inventory control. By analyzing the Newsvendor Problem which is a simplified situation of storing inventories, this paper would discover a method using normal distribution analysis to solve the problem. Then, the paper would promote the adoption of this method into realistic inventory problems and discuss its utility. Secondly, the topic is expanded to Multi-Period Inventory System. This system focus on a more sophisticated inventory situation, and it could be basically categorized into two models: fixed-order quantity model, and fixed time period model. The paper would discuss the methods of ordering determination of the two models respectively.

Inventory Model with Stochastic Demand Using Single-Period Inventory Model and Gaussian Process

Proper inventory management is vital to achieving sustainability within a supply chain and is also related to a company’s cash flow through the funds represented by the inventory. Therefore, it is necessary to balance excess inventory and insufficient inventory. However, this can be difficult to achieve in the presence of stochastic demand because decisions must be made in an uncertain environment and the inventory policy bears risks associated with each decision. This study reports an extension of the single-period model for the inventory problem under uncertain demand. We proposed incorporating a Gaussian stochastic process into the model using the associated posterior distribution of the Gaussian process as a distribution for the demand. This enables the modeling of data from historical inventory demand using the Gaussian process theory, which adapts well to small datasets and provides measurements of the risks associated with the predictions made. Thus, unlike other works that assume that demand follows an autoregressive or Brownian motion model, among others, our approach enables adaptability to different complex forms of demand trends over time. We offer several numerical examples that explore aspects of the proposed approach and compare our results with those achieved using other state-of-the-art methods.

Solving a single period inventory model with fuzzy inequality

The purpose of this paper is to present a fuzzy chance-constrained single period inventory model (FCCSPIM) in which the fuzziness appears in the space constraint and objective function is crisp. Here the partial order relation exists in between a random variable and a real number. That means the probability of the event is discussed under vague data. Our approach for the solution process uses mostly fuzzy Zimmermann technique to convert the FCCSPIM into a proper deterministic equivalent. Then the resulting nonlinear deterministic model is solved by using LINGO software. The result indicate that the fuzzy programming approach is effective for the inventory problem. The applications of an optimisation model under uncertainty are used to solve day to day problems. Many methods were developed by using tools of mathematics, probability theory and stochastic process. Here, one new approach of fuzzy programming technique is introduced to obtain a deterministic form.

A distribution-free newsvendor model considering environmental impact and shortages with price-dependent stochastic demand.

In today's competitive and volatile market, demand prediction for seasonal items is a challenging task. The variation in demand is so quick that the retailer cannot face the risk of understocking or overstocking. Unsold items need to discarded, which has environmental implications. It is often difficult to calculate the effects of lost sales on a firm's monetary values, and environmental impact is not a concern to most businesses. These issues concerned with the environmental impact and the shortages are considered in this paper. A single-period inventory mathematical model is formulated to maximize expected profit in a stochastic scenario while calculating the optimal price and order quantity. The demand considered in this model is price-dependent, with several emergency backordering options to overcome the shortages. The demand probability distribution is unknown to the newsvendor problem. The only available demand data are the mean and standard deviation. In this model, the distribution-free method is applied. A numerical example is provided to demonstrate the model's applicability. To prove that this model is robust, sensitivity analysis is performed.

Inventory Waste Management In Micro Scale-Food Industry

Micro-businesses in the culinary industry often experience management constraints. Poor management leads to many losses and wastes, such as inventory waste that arises due to mismatch of production level with demand level. This research aims to learn how the micro-business conditions in the culinary industry in Bandung deal with the problem of inventory waste and find suitable methods to overcome the problem. To carry out the research, we conduct a mix method technique. Data were collected through interviews with respondents who involved in micro-scale culinary businesses in Bandung and also from sales reports of internal data from Yama, a micro-scale company engaged in the culinary business. We analyzed the data using a qualitative method and a single-period inventory model. From the research, we found that the micro-business condition in the culinary industry has currently run their waste inventory management based on intuition without a scientific approach. Also, to solve the wasted inventory problem, the single-period inventory model can reduce the amount of inventory waste and can be implemented. It can significantly increase Yama's opportunity to make a profit and decreasing the possibility of inventory waste due to unsold inventory

Solving a Single Period Inventory Model with Fuzzy Inequality

Solving a Single Period Inventory Model with Fuzzy Inequality

Single cycle supply chain coordination model for fuzzy stochastic demand of perishable items

Market demand of the perishable bakery products are volatile. Hence, demand of such items are random variable. The most appealing demand distribution of such items is lognormal demand distribution. Using historical data, the parameters of lognormal distribution are obtained. But, there is a problem of overestimation or underestimation of the parameters. Fuzzy triangular numbers are used to overcome such problems. Single period (newsboy) inventory model is used to obtain an optimal order quantity. The retailers and manufacturers profit is obtained by using the supply chain coordination model. At the end of day, all the remaining items rotted. Hence, there is no gain from unsold items. Also, the some items are defective at the time of purchase. Thus, loss sharing strategy is proposed between manufacturers and retailers. All of these aspects are incorporated in the supply chain coordination model. The data is collected from Koregaon Park, Pune market, India to illustrate the methodology.

Single stage fuzzy supply chain model with Weibull distributed demand for milk commodities

The newsvendor model is very simple, but it is very important to study problems of supply chain coordination. This model is also called a single-cycle inventory model. In a short cycle, it is very difficult to forecast the demand. The effect of good prediction reduces inventory shortage, increases the profit and enhances competitiveness. This type of product is characterized by strong uncertainty, that means demand always changes. This creates challenges for decision makers. For newly developed products, it is very difficult to obtain the statistical demand distribution of a product. Here, we consider the demand of the milk products, which are fluctuating in nature. Hence, demand is a random variable. It is assumed that demand follows Weibull distribution. Also, there is some uncertainty in demand. It leads to the over estimation or under estimation of the parameters of the distribution. Fuzzy triangular numbers are used to obtain the uncertain demand. The lifetime of the items are very short. Thus, unsold items are sent back to the manufacturers. The retailers and manufacturers profit is obtained under decentralized and centralized supply chain. Also,the proposed single period (newsboy) inventory model is used to obtain an optimal order quantity. The proposed methodology is illustrated for milk product from Aundh market Pune, India.

Sustainable sourcing including capacity reservation for recycled materials: A newsvendor framework with price and demand correlations

Critical raw materials like rare-earth elements are essential inputs for the production process of many electronic products, but also for environmentally-friendly green-energy technology products. The market for these materials faces high uncertainty associated with their supply. The use of recovered raw materials can help to mitigate the risk and simultaneously pave the way towards a circular economy. We investigate a sourcing strategy faced by a manufacturer considering the possibility to source critical raw materials from a supplier offering recycled material. As the recycling efficiency of these materials is still an ongoing research, and return flows from end-of-life products are highly volatile, we also rely on virgin material. We develop a single-period inventory model with procurement from a supplier offering recycled material according to a capacity reservation contract and a reactive supplier (spot market) offering virgin material. We consider uncertainties of demand, prices and recycling quantities as well as potential dependencies, in particular dependencies between prices for virgin and recycled materials and prices and demand. We provide results on the optimal policy structure and obtain a closed-form solution as a bound of the optimal procurement quantity. Our analysis gives us first insights on the effect of different economic parameters on the ordering decision. In an extensive numerical analysis we then study the impact of correlation on our results in order to derive managerial implications. We show that considering correlation when using such a sourcing strategy is especially important in environments with high demand uncertainty, high virgin material prices and yield uncertainty.

Newsboy problem with birandom demand

Estimation of accurate product demand in a single period inventory model (SPIM) is an essential prerequisite for successfully managing the supply chain in large and medium merchandise. Managers/ decision makers (DMs) often find it difficult to forecast the exact inventory level of a product due to complex market situations and its volatility caused by several factors like customers uncertain behavior, natural disasters, and uncertain demand information. In order to make fruitful decisions under such a complicated environment, managers seek applicable models that can be implemented in profit maximization problems. Many authors studied SPIM (also known as newsboy problem) considering the demand as a normal random variable with fixed mean and variance. But for more practical situations the mean demand also varies from time to time yielding two-folded randomness in demand distribution. Thus, it becomes more difficult for DMs to apprehend the actual demand having two-folded random/birandom distribution. A blend of birandom theory and newsboy model has been employed to propose birandom newsboy model (BNM) in this research to find out the optimal order quantity as well as maximize the expected profit. The practicality of the projected BNM is illustrated by a numerical example followed by a real case study of SPIM. The results will help DMs to know how much they should order in order to maximize the expected profit and avoid potential loss from excess ordering. Finally, the BNM will enhance the ability of the managers to keep parity of product demand and supply satisfying customers’ needs effectively under uncertain environment.

Inventory rationing for the News-Vendor problem with a drop-shipping option

• We extend the News-Vendor model by including the inventory rationing problem. • We provide optimality conditions of the expected profit and derive other additional structural properties. • We analyze two rationing policies. We consider a single-period inventory model for a bricks-and-clicks business. Store inventory can be used to fulfill both store demand and internet demand. Drop-shipping is used as an additional option for internet sale. We analyze two rationing policies for store inventory: a threshold policy and a fixed-portion policy. We formulate the expected profit for both and prove concavity . There exists an optimal order quantity for store inventory and an optimal stock rationing level below which the manager starts to use drop-shipping for internet demand. Numerical examples show that considering the rationing problem for the single-period inventory model, which is ignored in some earlier works, can result in remarkable differences.

Inventory control and supply chain management: A green growth perspective

Green growth is becoming an important mode for the sustainable operation of economy and society in the world. All countries are developing innovative methodologies to achieve green growth. Particularly, inventory and pricing are important technologies for companies’ leadership to make decisions. The increasingly polluted environment has made sustainable utilization of resources and environmental protection more urgent, however, there is very little literature studying inventory and pricing from a green growth perspective. To fill this gap, we consider both inventory and pricing decisions for companies under different green growth mechanisms. We first consider the single period inventory model with a remanufactured supplier and the government subsidy for single and dual sourcing system, respectively, further derive the optimal order decisions for the retailer. Then, we assume the customers are environmentally sensitive and there is a green supplier in the market, examine the optimal pricing decisions for the retailer using the two-stage optimization method. We explore the value of the recycling supplier and government subsidy in the numerical study; furthermore, we examine the influences of the green degree of product on the optimal price decisions for different products. One interesting finding is that the retailer should order more green products no matter how expensive it is, as long as the customers in the market are environmentally sensitive.

A Single Period Production Inventory Model in Interval Environment with Price Revision

In the present competitive market, in case of some products like smartphone, it is observed that after few days of launching a new product, a same type of product by some other company becomes available with a cheaper selling price or with more accessories within the same selling price. In this situation, customers normally go for the new product rejecting the older one. So always there is a possibility that some units of product remain unsold. This compels the company for a revision in selling price. This paper aims to develop such kind of production inventory models. Here demand of the product depends upon the selling price of the product, promotional effort and time. Now-a-days, specially for those kind of products, demand mainly depends on these three parameters in real life situation. When demand becomes zero, company sets a new selling price and the remaining products are depleted at a constant demand. So obviously it is going to be a single period inventory model. As a real life production process can not be hundred percent perfect, during the production process, some defective items are also produced which are reworked after the regular production process. Also, in order to reflect practical situation, inventory cost parameters are taken as interval numbers. As a result the corresponding optimization problem becomes interval valued which has been solved by using quantum-behaved particle swarm optimization technique. The main objective of this paper is to determine the optimal production run time that maximizes the total profit of the company.

Bounds for the solution to the single-period inventory model with compound renewal process input: An application to setting credit card limits

Motivated by a desire to calculate the optimal credit limit for a credit card account in terms of the card-holder’s purchasing behaviour, we consider a single-period inventory model in which the total value of all attempted purchases increases in jumps throughout the period. If a purchase does not cause the limit to be exceeded, then that purchase is approved and the total value of approved purchases is increased by its value. On the other hand, if the limit is exceeded, then the purchase is rejected and the total value of approved purchases remains at its previous level.We derive an equation for the Laplace–Stieltjes transform of the expected total value of approved purchases at the end of the period. Unfortunately this equation appears to be intractable, a situation that we address by providing upper and lower bounds. We provide numerical examples that show that these upper and lower bounds can be close, which leads to good upper and lower approximations for the optimal limit.

Development of a single period inventory planning model for perishable product redistribution

Considering that more than 100 million EU citizens face the risk of poverty or social exclusion, while at the same time 35% of perishable food in the EU is unnecessarily discarded at supermarkets, the redistribution of the perishable food surpluses could provide an economically feasible solution towards the confrontation of poverty and the minimization of food waste. Under this context, the purpose of this paper is to propose a novel quantitative decision-making tool that optimizes a retailer’s replenishment policy for perishable products while minimizing the amount of perishable items discarded after they approach their expiration dates, through the timely donation of a part of their net stocks.

The impact of abusing return policies: A newsvendor model with opportunistic consumers

Consumers may return a product for a variety of reasons, such as the product having the wrong color or size, having poor functionality, being damaged during shipment, or simply prompting regret for an impulsive purchase. Retailers generally provide lenient return policies not only because they may signal high quality but also because they act as risk relievers for consumers’ purchasing decision processes. However, increasing product returns have become particularly challenging for the efficient management of inventory. As such, at the crux of a holistic inventory model lies the understanding of consumer return behavior. In this study, we introduce a variant of the classical single-period inventory (newsvendor) model with returns, in which heterogeneous consumers decide, based on their post-purchase valuation of the product, whether to return the product after using it. From the perspective of the retailer, such deliberate returns may abuse the return policy, which in turn may exacerbate reverse logistics and environmental costs. To that end, we incorporate demand uncertainty and consumer valuation uncertainty by explicitly gauging return probabilities and differentiated salvage values into a newsvendor model. We derive analytical results for the profit-maximizing order quantity for a single-period product that comes with a retailer return policy and exclusively identify the impact of return type as abused or normal. Also offered are closed-form optimal solutions in the cases where market demand is exponentially or uniformly distributed. Structural and numerical results lend managerial insight into how optimal ordering amount, profit, return rates and salvage values change with the price, return window, and hassle cost of returning the product.

Diseño de un modelo para la administración de inventarios en un cultivo de fresa, basado en el modelo de pedido para un solo periodo y las métricas 6 sigma

La administración de inventarios es parte de las actividades fundamentales de toda empresa, por tanto, de su adecuadomanejo dependerán los resultados de actividades posteriores. Los modelos de inventario parten del supuesto general deque los productos presentan un tiempo de vida ilimitado, sin embargo, en algunos sistemas existe una generación de costosadicionales, asociados al deterioro de la calidad de los productos, llamados perecederos. A partir de las condicionesproductivas, de gestión de inventarios y de control de desperdicio, el presente estudio incluye una propuesta de diseño deun modelo para la administración de inventarios en un cultivo de fresa, basado en un modelo de inventario para productosperecederos, conocido como el modelo de pedido de un solo periodo y la aplicación de métricas 6 sigma, para la consideracióny control del nivel de desperdicio y las limitantes de capacidad productiva del cultivo. A partir del modelamientoplanteado, se realiza una prueba de verificación del funcionamiento teórico del mismo El modelo a nivel teórico es funcional,permitiendo evidenciar en un periodo de planeación de un mes, que el modelo permite establecer adecuadamente lacantidad óptima de recolección recomendada; relacionando capacidad esperada de recolección respecto a capacidad realdisponible; así como a partir de la cantidad de desperdicio en el cultivo en un periodo determinado, permitiendo establecercontroles en el cultivo, teniendo en cuenta el factor de calidad seis sigma y su aplicación como indicador de ocurrenciasde desperdicio, que permite garantizar a nivel teórico la planeación y momentos de renovación de cultivo.