Maximum Inventory Level Research Articles

A prescription for efficiency: optimizing the surgical item inventory management practices in a healthcare facility

PurposeThe primary objective of this article is to examine current procurement, inventory control and management practices in modern healthcare, with a particular focus on the procurement and management of surgical supplies in a prominent public, highly specialized healthcare sector.Design/methodology/approachThis study was conducted in three phases. In Phase 1, the study team interacted with various hospital management stakeholders, including the surgical hospital store, examined the current procurement process and identified challenges. Phase 2 focused on selecting items for a detailed study and collected the qualitative and quantitative details of the store department of the healthcare sector chosen. A detailed study analyzed revenue, output/demand, inventory levels, etc. In Phase 3, a decision-making framework is proposed, and inventory control systems are redesigned and demonstrated for the selected items.FindingsIt was observed that the demand for many surgical items had increased significantly over the years due to an increase in disposable/disposable items, while inventories fluctuated widely. Maximum inventory levels varied between 50 and 75%. Storage and availability were important issues for the hospital. It is assumed the hospital adopts the proposed inventory control system. In this case, the benefits can be a saving of 62% of the maximum inventory, 20% of the average stock in the system and optimal use of storage space, improving the performance and productivity of the hospital.Research limitations/implicationsThis study can help the healthcare sector administration to develop better systems for the procurement and delivery of common surgical items and efficient resource allocation. It can help provide adequate training to store staff. This study can help improve management/procurement policies, ordering and delivery systems, better service levels, and inventory control of items in the hospital business context. This study can serve as a pilot study to further investigate the overall hospital operations.Practical implicationsThis study can help the healthcare sector administration develop better systems for procuring and delivering common surgical items and efficient resource allocation. It can help provide adequate training to store staff. This study can help improve management/procurement policies, ordering and delivery systems, better service levels and inventory control of items in the hospital business context. This study can serve as a pilot study to further investigate the overall hospital operations.Originality/valueThis study is an early attempt to develop a decision framework and inventory control system from the perspective of healthcare inventory management. The gaps identified in real hospital scenarios are investigated, and theoretically based-inventory management strategies are applied and proposed.

On the zero-inventory-ordering policy in the inventory routing problem

The Inventory Routing Problem (IRP) aims at determining the best distribution plan of a certain commodity from a supplier to a set of customers over a given planning horizon. Customers face a per period consumption and the plan has to be such that they can always satisfy it. The aim is to minimize the total cost of the distribution plan, which is given by the sum of routing and inventory holding cost. A replenishment strategy that has become common in the recent literature is the Maximum Level (ML) strategy, where no restriction is imposed on when the customers are visited and what the quantity delivered is, provided that a maximum inventory level at each customer (corresponding to the customer′s warehouse capacity) is not exceeded. This strategy is highly flexible and this clearly provides cost advantages. However, it might also create inconveniences to customers, who might receive visits when their inventory level is still relatively high. Towards addressing this issue, we study in this paper the Zero-Inventory-Ordering (ZIO) replenishment strategy for the IRP, where customers can be served only when their inventory level is zero. The aim is to analyze the impact of a policy which is more customer-orientedthan the ML. The analysis is made in terms of advantages from the customers′ perspective and disadvantages from the system perspective, i.e., increase of the total cost. We propose a formulation based on two-commodity flow variables, and strengthen it through new valid inequalities tailored for our problem as well as with valid inequalities inherited from the literature on the IRP. We develop branch-and-cut algorithms and experimentally compare the ZIO and ML policies on benchmark IRP instances. The results show that the application of the ZIO policy allows to reduce the inventory costs at the customers without substantially increasing, or even decreasing, the number of visits to them. This comes at the expense of an increase of the total costs. Results also show that the increase in total cost is inversely proportional to the relative weight of the inventory costs at the customers. More precisely, inventory costs at customers are decreased by more than 20% on average while total cost increases, on average, by 17.6% when the inventory costs are high and of 9.2% when inventory costs are low. In addition, we generated new sets of instances in which inventory costs are more aligned with practical applications with respect to what happens in the benchmark IRP instances. Results show how the ZIO policy consistently provides solutions where the inventory cost to customers is lower than the one associated with the ML policy. Also, the gap in total cost reduces when the inventory cost at customers increases.

The inventory routing problem with split deliveries

AbstractWe study the benefit of introducing split deliveries in the inventory routing problem (IRP), both when the order‐up‐to level (OU) and the maximum level replenishment policies are applied. We first propose a mathematical formulation and solve it by implementing a branch‐and‐cut algorithm. Then, we carry out a worst‐case analysis to show the cost increase we have in the worst case by using unsplit deliveries instead of split deliveries, both for the OU and the maximum‐level replenishment policies. Extensive computational results on benchmark instances allow us to evaluate the benefit of introducing split deliveries. Finally, a sensitivity analysis on customer demands, initial inventory levels, maximum inventory levels and distance to the depot allows us to understand the instance features that make split deliveries effective in IRPs.

Optimal ordering policies in response to a disposable coupon

This study investigates a retailer's ordering strategy under the framework of the economic order quantity (EOQ) model. A supplier offers a retailer a disposable coupon and allows it to place a special order at any time in a promotion period. The promotion period is not necessary short and shortages are allowed throughout the time horizon. In addition to the special order time and the special order quantity, the retailer needs to decide whether to place some regular orders in the promotion period before placing the special order for the purpose of making better use of this coupon. We show that the coupon should be used to the retailer's first order in the promotion period regardless of the duration of the promotion period. Moreover, the retailer's maximum inventory level is higher than that in the classical EOQ model. We find that a longer promotion period can benefit the retailer by endowing it with more flexibility in its decision-making. Therefore, the supplier can improve the cash flow and reduce the overstock by integrating a disposable coupon with a longer promotion period. Numerous managerial insights are obtained from sensitivity analysis and numerical experiments.

Klasifikasi ABC dan Peramalan ARIMA Inventory Usaha Kecil Menengah Stokis Pakaian Muslim

The problem faced by many SMEs is the imbalance between demand and supply. As one of the SMEs, Stockist C-Geulis often faces the problem of unavailable product stock while orders are not yet available. This research aims to identify high-value and high-demand products and predict minimum and maximum inventory levels for the following month. The method for determining high-value products is ABC analysis, while the minimum and maximum inventory predictions use the ARIMA (Autoregressive Integrated Moving Average). The data for stock forecasting uses sales data from January 2019 to June 2021. The results show that ABC analysis based on sales value includes four class A products, three class B products, and eight class C products. The forecast results show that the inventory forecast data for three periods does not meet the assumption of stationarity to the average because a level 1 differentiation process is carried out so that the data becomes stationary. The ARIMA models produced are ARIMA (1,1,1) for Batik C-Geulis products and Busui C-Geulis and ARIMA (1,0,0) for Inner Gamis Hijab products. The supplies provided for Batik C-Geulis products in July 2021 are 37 pcs, Busui C-Geulis are 45 pcs, and Inner Gamis C-Geulis are 49 pcs.

Multi-Server Queuing Production Inventory System with Emergency Replenishment

We consider a multi-server production inventory system with an unlimited waiting line. Arrivals occur according to a non-homogeneous Poisson process and exponentially distributed service time. At the service completion epoch, one unit of an item in the on-hand inventory decreases with probability δ, and the customer leaves the system without taking the item with probability (1−δ). The production inventory system adopts an (s,S) policy where the processing of inventory requires a positive random amount of time. The production time for a unit item is phase-type distributed. Furthermore, assume that an emergency replenishment of one item with zero lead time takes place when the on-hand inventory level decreases to zero. The emergency replenishment is incorporated in the system to ensure customer satisfaction. We derive the stationary distribution of the system and some main performance measures, such as the distribution of the production on/off time in a cycle and the mean emergency replenishment cycle time. Numerical experiments are conducted to illustrate the system performance. A cost function is constructed, and we examine the optimal number of servers to be employed. Furthermore, we numerically calculate the optimal values of the production starting level and maximum inventory level.

A Lot-Sizing Model for a Multi-State System with Deteriorating Items, Variable Production Rate, and Imperfect Quality

Conventional production systems assume that during the manufacturing processes, machines operate without breakdown over an infinite planning horizon and manufacture only products of good quality. Imperfect production processes as a result of machine degradation are common in manufacturing. This paper deals with a problem that concerns the modelling and evaluation of the performance of a multi-state production system that is subject to degradation and its effect on lot sizing. Here, we consider that the cycle starts with a particular production rate until a point when the inventory reaches a certain level after which the failure mode is activated due to the deterioration of certain components, leading to a reduction in the production rate in order to ensure the continuity of supply until the maximum inventory level is reached. Production then stops to restore the machine and the cycle starts again. We have assumed that the rate at which inventory deteriorates is exponential and that demand is constant. A numerical example is used to illustrate the model application, followed by sensitivity analysis. This paper contributes to lot sizing in the area of machine reliability by considering a production system in a degraded state with a non-increasing production rate for deteriorating items with imperfect quality and partial backlogging.

A cost analysis on Multi-item Inventory model for Factory Outlets with investment constraint under ranking Asteroid Fuzzy Set

Purpose of the study: A multi-item inventory model for factory outlets in crisp and fuzzy sense are formulated in the fuzzy environment with investment under one constraint has been considered. In this model, demand is constant and is related to the price per unit item. The asteroid fuzzy set is defined and is properties are given.
 Methodology: The parameters involved in this model represented by asteroid fuzzy set. The average total cost is defuzzify by ranking method.
 Main Findings: The analytical expressions for maximum inventory level and average total cost are derived for the proposed model by using nonlinear programming technique. A numerical example is presented to illustrate the results.
 Applications of this study: Ranking Asteroid fuzzy set is considered profitable in small businesses. Here we considered the factory outlet .Also its use is considered to help the small scale entrepreneurs during festival period and pandemic situation.
 Novelty/Originality of this study: In this paper, a novel approach to handle the asteroid fuzzy set is proposed. It uses ranking the cost parameters of the asteroid fuzzy set with the best approximation level. The parameters involved are asteroid fuzzy set and are all ill-defined in nature.

Hypergraph-based joint optimization of spare part provision and maintenance scheduling for serial-parallel multi-station manufacturing systems

This paper studies the joint modeling of spare part provision and maintenance scheduling for Serial-Parallel Multi-station Manufacturing Systems (SPMMS), where the spare part connections are especially investigated. In the SPMMS, multiple types of spare parts are retained for uncertain failures of the stations, and multiple stations may share the spare parts in inventory. To describe the spare part connections among the stations, a hypergraph-based model is introduced. In the system-level maintenance, the SPMMS is formulated to be a multi-connection hypergraph, with the Spare Part Hyperedges (SPH), the cost-saving hyperedges and the capacity-loss hyperedge involved. Based on the multi-connection hypergraph, a Combination-Spread Opportunistic Maintenance (CSOM) policy is proposed. To obtain the optimal alternatives of the maximum inventory levels, the length of the combination window and the length of the spread window, a hierarchical optimization method is developed. The case study and the comparisons show that the proposed hypergraph-based CSOM policy is more cost-effective than the traditional maintenance policy, the station-level maintenance policy and the fixed-group maintenance policy. Finally, the discussion shows that the traditional maintenance model is a special scenario of the hypergraph-based model.

Production sequence determination to minimize the required storage space for the multiple items production system

Purpose: The research studies the production system having multiple items being processed on the same production line. The objectives are to (1) investigate the influence of production sequence on the optimal value of production run size, (2) explore the effect of production sequence on the maximum inventory level, which can affect the storage space required, and (3) propose a method to determine the proper production sequence in order to minimize the required storage space.Design/methodology/approach: Finding that the optimal production sequence, which yields the lowest storage space required, is independent of the production run size, the research problem is divided into two independent subproblems. The first subproblem is to determine the optimal production run size to minimize the total variable cost. Here, the solution obtained from the classical multiple items EPQ model still holds. The second subproblem is to explore the proper production sequence in order to minimize the storage space required. The relationship between the production sequence and the value of maximum inventory level is determined and formulated. To explore the proper production sequence, a genetic algorithm is developed. For the performance evaluation, two experimental studies are conducted. The first experiment is to compare the solution obtained from the proposed method with the optimal solution yielded from the enumeration method on 360 small size problems. The second experiment is conducted on 180 large size problems. The result obtained from the proposed method is compared with the result yielded from the Largest Rho First (LRF) heuristic constructed by arranging the production of each item according to the ratio between the demand rate and production rate.Findings: It has been found that the optimal production sequence is independent of the production run size. Nonetheless, different production sequences yield different required storage spaces. With the proper production sequence, the manufacturer can reduce the total space required to keep its inventory. The proposed genetic algorithm can be applied to determine the proper production sequence in a reasonable amount of time. For the small size problem of 8 and 10 production items, the proposed genetic algorithm provides the solution with the maximum percentage deviation of 0.307 percent from the optimal solution. For the large size problem of 15 production items, the proposed genetic algorithm outperforms the LRF heuristic for all 180 problems. This result is more pronounced when the slack proportion is getting smaller.Research limitations/implications: According to the research model, no shortages are allowed. Therefore, the model is applicable for the production system having the summation value of the ratio between demand rate and production rate for all items not greater than one.Originality/value: Those traditional research involving the determination of optimal production run size and production sequence in the system having multiple items being produced on the same production line differs from each other in their production environments. However, most of them still have the objective function of minimizing the total system cost incurred. To the best of our literature searching, none of them discussed the influence of production sequence on the total inventory level, which directly affects the required storage space, one of the critical issues facing by many manufacturers. The originality of this work is to show that different production sequence yields different total storage space required and proposed the method to determine proper production sequence.

Optimization of Inventory Level Using Fuzzy Probabilistic Exponential Two Parameters Model

Inventory control is an important factor in trading activities. Inventory control aims to ensure product availability. Several factors affect the level of inventory including the level of demand factor, maximum inventory, and the level of deterioration. If the influencing factors cannot be defined with certainty and follow a certain statistic distribution then the fuzzy probabilistic approach can be applied. This research discusses the problem of optimizing the inventory of red chillies at the retail level. The level of deterioration is assumed to follow an exponential distribution and demand follows a Pareto distribution. Statistical parameters are estimated using the Maximum likelihood method and cost parameters are expressed by triangular fuzzy numbers. Based on the calculation results for several beta values, the highest total cost is 405143.6 rupiah, a maximum inventory level of 15 kg, and an order cycle time of 0.923 days.

Economic Production Quantity Model for Deteriorating Items with Weibull Deterioration Rate over the Finite Time Horizon

In the present paper we have considered a production supply chain and developed two models for production supply cycle. These models are (i) The optimum total cost model and (ii) The maximum inventory level model. We have assumed constant demand rate for deteriorating inventory and considered three parameter Weibull distributions for deterioration rate with finite time horizon. We have also considered three different level of production in one cycle with shortages allowed. In real world of production and manufacturing market, EPQ models are playing role of an effective tool. The objective of our work is to find optimal production quantity and minimize total cost per cycle. Our work will be useful for the organizations which are going to launch new product in the market or newly established production organizations where at starting organizations are not aware about the production size and changing their production level according to the market demand. These models will help to avoid surplus stock or shortages in business organizations and reduce holding cost; deterioration cost etc. The objective of this paper is to find optimal total cost and optimal production quantity for one cycle. At last numerical example and sensitivity analysis is given to illustrate the result. We have used Mathematica 0.9 to solve equations, calculation and plotting graph.

A Combined Maintenance Strategy Considering Spares, Buffer, and Quality

This paper studies an innovative maintenance model for an upstream machine in a common production system. Multiple system-wise features are integrated in the model, including maintenance, spare parts, buffer inventory, and product quality. The objective is to minimize the system expected cost rate by determining the optimal inspection interval, preventive maintenance threshold, corrective maintenance threshold, reorder level of spare parts, maximum stock level of spare parts, and maximum inventory level of the buffer. In this maintenance model, both the hazard rate and the product qualification rate can trigger maintenance activities. The well-known proportional hazard model (PHM) is adopted to describe the state of the upstream machine. The effect of machine state on product quality is explicitly characterized. Due to the complexity of the mathematical model, simulation and a genetic algorithm are employed to determine the optimal solution. A case study of bearings is presented to demonstrate the performance of the proposed maintenance policy. The results show that this policy is practical and can reduce system cost significantly.

Truck Scheduling Model in the Cross-docking Terminal by using Multi-agent System and Shortest Remaining Time Algorithm

One most important and critical problem in a cross-docking system is truck scheduling. Many studies in it assumed that the temporary storage is unlimited which is in the real world, the temporary storage is limited. Many studies focus on minimizing total completion time. Meanwhile, studies that focus on minimizing temporary storage are hard to find, although this aspect is very important. Due to its complexity, especially in the cross-docking system with multiproduct characteristics, manual scheduling is almost impossible to achieve its goals. Many studies used several techniques, such as genetic algorithm (GA) and mixed integer programming where these methods are computationally expensive. Based on this problem, in this work, we propose new truck scheduling model in a cross-docking terminal with limited temporary storage constraint. This model is developed by using multi-agent system. The main contribution of this work is proposing the multi-agent-based truck scheduling model with limited temporary storage capacity constraint and temporary truck changeover permit. In it, there are three agents: inbound-trucks scheduler agent, outbound-trucks scheduler agent, and material handler agent. The shortest remaining time (SRT) algorithm is adopted in every agent. Based on the simulation result, this proposed model is proven competitive compared with the existing FIFO based models and integer-programming based model. Compared with the integer-programming model, it creates 41.8 percent lower in maximum inventory level. Compared with the FIFO based model, it creates 52.1 to 55.1 percent lower in maximum inventory level. In total time aspect, it creates 0.2 to 2.2 percent lower than the FIFO based model. It creates 7.2 percent higher in total time compared with the integer-programming based model.

Прогнозування запасів промислового підприємства в умовах волатильності попиту

The aim of the article is to provide tools for obtaining reliable forecasts of the level of inventories of the enterprise in conditions of volatility in demand for products. Most types of demand for industrial products are unstable, so it is important to form stocks based on demand forecasts to reduce logistics risks. The results of the analyses. Analytical tools for forecasting maximum level of inventories in conditions of volatility of demand for products of machine-building enterprises have been developed, which provides an opportunity to obtain the most reliable sales forecast and estimate the maximum required stocks for a certain type of demand. The method, which is obtained by analytical tools, is based on a three-stage algorithm: a) identification of trends in a time series of sales; b) obtaining optimal sales forecasting models; c) plotting of interval forecasts of product sales and risk assessment of the formation of its maximum stocks. The developed methodology identifies logistics risks, which depend on sales forecasts, for nine machine-building enterprises of Ukraine. A method for statistical assessment of logistics risks of machine-building enterprises by confidence intervals has been developed, in which maximum stocks are determined by two confidence intervals of sales forecasts, and the risk of error is associated with the appropriate levels of reliability of these intervals. It is proposed to build the upper limits of two confidence intervals, for example, 95% and 99%, according to the forecast inventory level estimates, and to consider them as maximum inventory level estimates with corresponding probabilities. The risk of stock shortages is defined as the probability of going beyond the upper limit of the corresponding interval. It is proved that the dynamics of monthly or quarterly sales of enterprises can be typed by four patterns: the presence of seasonal fluctuations and trends; the presence of purely seasonal fluctuations without a pronounced trend; no seasonal fluctuations, but the presence of a trend; no seasonal fluctuations and trends. Conclusions and perspectives for further research. It is proved that the volatility of monthly or quarterly sales volumes of enterprises can be typed by four patterns: 1) the presence of seasonal fluctuations and trends; 2) the presence of purely seasonal fluctuations without a pronounced trend; 3) no seasonal fluctuations, but the presence of a trend; 4) no seasonal fluctuations and trends. Based on this, the theoretical and methodological principles and analytical tools for forecasting the maximum stocks of an industrial enterprise in conditions of demand volatility were improved. Keywords: seasonality, volatility, inventory level forecasting, maximum stocks, demand forecasting.

A Benders Decomposition Approach for the Multivehicle Production Routing Problem with Order-up-to-Level Policy

The production routing problem (PRP) arises in the applications of integrated supply chain which jointly optimize the production, inventory, distribution, and routing decisions. The literature on this problem is quite rare due to its complexity. In this paper, we consider the multivehicle PRP (MVPRP) with order-up-to-level inventory replenishment policy, where every time a customer is visited, the quantity delivered is such that the maximum inventory level is reached. We propose an exact Benders’ decomposition approach to solve the MVPRP, which decomposes the problem as a master problem and a slave problem. The master problem decides whether to produce the product, the quantity to be produced, and the customers to be replenished for every period of the planning horizon. The resulting slave problem decomposes into a capacitated vehicle routing problem for each period of the planning horizon where each problem is solved using an exact algorithm based on the set partitioning model, and the identified feasibility and optimality cuts are added to the master problem to guide the solution process. Valid inequalities and initial optimality cuts are used to strengthen the linear programming relaxation of the master formulation. The exact method is tested on MVPRP instances and on instances of the multivehicle vendor-managed inventory routing problem, a special case of the MVPRP, and the good performance of the proposed approach is demonstrated.

The Online Distribution System of Inventory-Routing Problem with Simultaneous Deliveries and Returns Concerning CO2 Emission Cost

This study attempts to consider CO2 emission cost to propose an online distribution system of inventory-routing problem with simultaneous deliveries and returns (IRPSDRCO2). The proposed IRPSDRCO2 mathematical models will be developed to find the total inventory routing cost, the CO2 emission cost, the optimal delivery routes, the economic order quantities, the optimal reordering points, the optimal service levels, the optimal common review interval, and the optimal maximum inventory levels for all retail stores delivered in these scheduled routes. The proposed IRPSDRCO2 model further applies the savings method, the target insert heuristic method, the target exchange heuristic method, and the repeated target heuristic method to find the optimal solution and the related scheduled routing plan. The sensitivity analyses will be conducted for this proposed IRPSDRCO2 model based on different parameters to provide very helpful decision-making information for a distribution system design. The performance of the proposed repeated target heuristic method is demonstrated to be better than most of four other combination methods regarding both the inventory routing cost and CPU running time. Consequently, it should be very helpful for logistics firms to design their distribution system by following the structure and the detailed procedure flow of the online distribution system developed by this study.

MODEL PENENTUAN STRATEGI PENGELOLAAN PERSEDIAAN BAHAN BAKU DENGAN METODE ANALYTICAL NETWORK PROCESS (ANP) (Studi Kasus di PT. LMM)

The success of raw material planning depends on the exact number of material of raw material needed; therefore the production will run properly. Base on this fact, the research conducted at PT Laser Metal Mandiri in PPIC department as the object this research focuses on how to overcome problem related to raw inventory, specifically making priority to strategy management raw material lack so that the production will keep running. In order to determine strategy management either tangiable or intangiable, Analytic Network Process (ANP) applied in this research that those analysis will show correlation among elements comprehensively. The criteria in this research comprise four aspects such as marketing or selling (C1), production (C2), purchasing (C3), and financing (C4), while the alternatives cover monthly demand (raw material) management (A1), maximum inventory level of raw material (A2), maximum-minimum production level (A3), and tracking management for certain sold product (A4). Based on the ANP method with software Super Decisions to A1 value of 0,095158, A2 value of 0,025463, A3 value of 0,026573, A4 value of 0,035432 dan A5 value of 0,064446.Keywords: Raw Material Planning, Strategy Management, Analytic Network Process (ANP), correlation, criteria

Are Procured Quantities of Implants Adequate and Appropriate? Modeling Procurement, Inventory, and Consumption of Contraceptive Implants During Rapid Uptake.

Donors and others are concerned that implants procured under the Family Planning 2020 Initiative exceed the number sought by clients, resulting in accumulating stocks. To explore this issue, we examined 3 questions across 9 countries: (1) How accurate were procurement quantities given requirements for filling supply chains for the rapidly growing implant programs? (2) Is there a standard factor that can be applied to consumption data to predict procurement volumes required? (3) How accurately do demographic estimates mirror dispensed-to-client data? We created a model incorporating public-sector supply chain system parameters to calculate system "imputed" inventory and the system "filled-to-max" inventory. Comparing results determined the adequacy of the procurement quantities. The proportion of consumption that the filled-to-max inventory represented through time suggests whether a standard factor can be applied to consumption to predict necessary procurement volumes. We compared demographic estimates to consumption data to determine the usability of the former in predicting demand. According to model results, 3 of the 9 countries came close to procuring accurate quantities over the study period between 2010 and 2017, 4 had procurement volumes lower than what was required to fill the supply chain to maximum inventory requirement levels, and 2 had volumes that exceeded the need. We found no standard factor for relating inventory quantities to consumption rates across countries, given that inventory needs can vary based on system design parameters and the rates of growth or decline in consumption. Finally, we observed that our demographic estimates were on average lower than the dispensed-to-client data in the 6 countries for which these data were available. Study results show that the significant investments in procurement quantities for the rapidly growing implant programs were justified based on consumption and system design. This research should assure observers that rapid increases in implant procurement quantities (where data are available) have generally not resulted in overstocks of the system to date. It suggests that the relationship between procurement quantities and consumption levels cannot be accurately assessed without understanding the country supply chain, inventory control parameters, and current and future demand.

Periodic review inventory model for Gumbel deteriorating items when demand follows Pareto distribution

For the importance of deteriorating in units, this paper presents a Constraint Deteriorating Probabilistic Periodic Review Inventory Model (CDPPRIM), a model which is applicable under some assumptions: (1) the demand is a random variable that follows Pareto distribution without lead time, (2) some costs are varying and shortage is permitted, (3) the deterioration rate follows Gumbel distribution, and (4) there is a constraint on varying deteriorating cost.Here, the objective function under a constraint is imposed in crisp and fuzzy environment. A Newton’s method is used to solve the system of nonlinear equations. The objective is to find the optimal values of four decision variables (maximum inventory level, stock-out time, the deteriorating time, and review time), which minimize the expected annual total cost under the assumptions. Finally, the model is followed by an application.