Comparative research on three-echelon and two-echelon medicine inventory model with positive lead-time

According to the principle of minimizing total cost, the three-echelon optimized medical inventory model with stochastic lead-time and two-echelon optimized medicine inventory model with fixed lead-time are established. The relationship between lead-time and inventory cost is studied by Matlab software. It shows that the variety of lead-time has an important effect on medicine inventory systems. Numerical simulation and sensitivity analysis of two models are presented by Lingo software. Based on analysis, it is concluded that the two-echelon model with lead-time results in inventory cost savings, and keeps the quality of care as reflected in service levels when compared with the three-echelon network structure.

Infinitesimal dividing modeling method for dual suppliers inventory model with random lead times

As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.

Multi-objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

This study presented a multi-objective linear fractional inventory (LFI) problem with generalised intuitionistic fuzzy numbers. In modelling, the authors have assumed the ambiances where generalised trapezoidal intuitionistic fuzzy numbers (GTIFNs) used to handle the uncertain information in the data. Then, the given multi-objective generalised intuitionistic fuzzy LFI model was transformed into its equivalent deterministic linear fractional programming problem by employing the possibility and necessity measures. Finally, the applicability of the model is demonstrated with a numerical example and the sensitivity analysis under several parameters is investigated to explore the study.

Inventory Model with Supply Disruption Risk and Service Level Constraint

We develop a newsvender model with service level constraint for oneproduct and multi-supplier system, where the supplies are susceptible to disruption risks. We prove the convexity of the programming problem,and provide the necessary and sufficient conditions for the optimal order quantities. Through analysis or numerical experiments we observe the effects of the disrupt risk and the service level constraint on the optimal policy. We propose some managerial insights in managing the multi-source supply chain with disruption risks.

Research on Three-Echelon Inventory Model and Algorithm for Valuable Spare Parts in Weapon Equipment

According to the current situation of repair and supply for valuable spare parts in the weapon equipment of the PLA,using the research results of the repairable spare parts inventory theory,an inventory model of the valuable spare parts in three-echelon repair and supply system is established by expanding the classical METRIC model and theory,and the genetic algorithm is utilized to solve the model.In the algorithm,the chromosome representation and initial population production,the crossover and mutation operators are designed.By using an example,a simulation analysis is carried out to verify the model's correctness.

Mathematical Modelling for a Multi-Product Inventory Routing Problem with Split Delivery

In this article, a multi-product inventory routing problem is studied. One-depot and many retailers in a finite time period are considered, and split delivery is allowed as well for the addressed problem. The objective is to minimize the overall cost including vehicle cost, inventory holding cost and transportation cost while the delivery schedule and the quantity of each product for each retailer have to be decided simultaneously. A mathematical model is presented for solving the addressed optimally and example is illustrated as well.

Impact of Capacity Parameters on Flexible Inventory Control Decision Model

From the mathematical point of view,the flexible inventory control model is proved in the practical problem application and the rationality of the capacity parameter selection and calculation.The purpose is to actively respond to demand fluctuations when there is a demand forecast error or a missing part of the demand information,and to avoid the risk of passive variable demand forecasting to set the immutable inventory capacity.At the same time,the game is controlled by the flexible and variable inventory control strategy and the customer’s willingness to demand.The paper mainly studies the influence of the setting of capacity parameters on the booking-limit decision and its benefits under the control of flexible space with variable total capacity.Through the two trends of capacity increase flexibility and capacity reduction flexibility in the flexible inventory control model,the mathematical performance and marginal utility methods are introduced to change the performance of the booking-limit control decision model under different scenarios.The correlation analysis between the capacity limit level and the return under the optimal Bookinglimit decision,and the above two flexibility parameters are obtained.

Multi-Item Fuzzy Inventory Model Involving Three Constraints: A Karush-Kuhn-Tucker Conditions Approach

In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. This model is solved with shortages and the unit cost dependent demand is assumed. Hence the cost parameters are imposed here in fuzzy environment. This model has been solved by Kuhn-Tucker conditions method. The results for the model without shortages are obtained as a particular case. The model is illustrated with numerical example.

Field-Based Automated Survey for Extracting Tree Inventory Attributes and 3-D Models in a Forested Area

Acquisition of tree inventory parameters such as tree position with respect to a local reference coordinate system, tree height, dbh （diameter breast height） and other associated tree attributes is a tedious process, time consuming, costly and labour intensive. An automatic collection and processing in the field could expedite the process of tree inventory survey and data management. The advent of handheld laser equipments such as the MDL LaserAce 300, should allow rapid acquisition of tree attributes. The instrument measures distances, differences in height and horizontal bearing automatically. This paper describes a study about the automated process of retrieving tree positions, their respective attributes and the creation of 3-D model （three-dimensional model）. A software developed in-house known as ASSIST （automated spatial survey information system） was utilized together with the MI）I, LaserAce 300, being the hardware component of the automated system. The capability of MDL LaserAce 9300 in extracting information regarding tree inventory attributes and the 3-D model encompassing the study area was investigated. The results were checked against the data sets acquired by a total station traversing and tacheometric survey respectively. The accuracy of the horizontal and vertical position of points gathered was critically assessed. The accuracy of the MDL LaserAce 300 was found to be less than ±2 m for both planimetric （horizontal） and vertical （height） in the construction of the 3-D model. The study demonstrates the effectiveness of a field-based automation system as a viable option to support forest application requirement.

An Improved Inventory Coordination Model in a Multi-stage Multi-customer Supply Chain

To solve the inventory coordination model in a multi-stage, multi-customer supply chain, this paper first analyzes the third model （integer powers of two multipliers at each firm） studied by Moutaz Khouja （2003）, and the authors take a numerical example to prove that the third model is irrational to miss feasible solution. Then this paper puts up a new improved model （integer multiplier at each firm）, and takes the example to prove it gives better results than the integer powers of two multipliers at each firm.

Analysis of the inflection points of height-diameter models

The inflection point is an important feature of sigmoidal height-diameter(H-D)models.It is often cited as one of the properties favoring sigmoidal model forms.However,there are very few studies analyzing the inflection points of H-D models.The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset.The six models were the Wykoff(WYK),Schumacher(SCH),Curtis(CUR),HossfeldⅣ(HOS),von Bertalanffy-Richards(VBR),and Gompertz(GPZ)models.The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution.The distributions of the estimated inflection points were similar between the two-parameter models WYK,SCH,and CUR,but were different between the threeparameter models HOS,VBR,and GPZ.GPZ produced some of the largest inflection points.HOS and VBR produced concave H-D curves without inflection points for 12.7%and 39.7%of the tree species.Evergreen species or decreasing shade tolerance resulted in larger inflection points.The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape.Furthermore,HOS could produce concave H-D curves for portions of the landscape.Based on the studied behaviors,the choice between two-parameter models may not matter.We recommend comparing seve ral three-parameter model forms for consistency in estimated inflection points before deciding on one.Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one.Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.

Dominant woody plant species recognition with a hierarchical model based on multimodal geospatial data for subtropical forests

Since the launch of the Google Earth Engine(GEE)cloud platform in 2010,it has been widely used,leading to a wealth of valuable information.However,the potential of GEE for forest resource management has not been fully exploited.To extract dominant woody plant species,GEE combined Sen-tinel-1(S1)and Sentinel-2(S2)data with the addition of the National Forest Resources Inventory(NFRI)and topographic data,resulting in a 10 m resolution multimodal geospatial dataset for subtropical forests in southeast China.Spectral and texture features,red-edge bands,and vegetation indices of S1 and S2 data were computed.A hierarchical model obtained information on forest distribution and area and the dominant woody plant species.The results suggest that combining data sources from the S1 winter and S2 yearly ranges enhances accuracy in forest distribution and area extraction compared to using either data source independently.Similarly,for dominant woody species recognition,using S1 winter and S2 data across all four seasons was accurate.Including terrain factors and removing spatial correlation from NFRI sample points further improved the recognition accuracy.The optimal forest extraction achieved an overall accuracy(OA)of 97.4%and a maplevel image classification efficacy(MICE)of 96.7%.OA and MICE were 83.6%and 80.7%for dominant species extraction,respectively.The high accuracy and efficacy values indicate that the hierarchical recognition model based on multimodal remote sensing data performed extremely well for extracting information about dominant woody plant species.Visualizing the results using the GEE application allows for an intuitive display of forest and species distribution,offering significant convenience for forest resource monitoring.

Generalized Height-Diameter Models for Pinus montezumae Lamb. and Pinus pseudostrobus Lindl. Plantations in Michoacan, Mexico

Tree height (H) in a natural stand or forest plantation is a fundamental variable in management, and the use of mathematical expressions that estimate H as a function of diameter at breast height (d) or variables at the stand level is a valuable support tool in forest inventories. The objective was to fit and propose a generalized H-d model for Pinus montezumae and Pinus pseudostrobus established in forest plantations of Nuevo San Juan Parangaricutiro, Michoacan, Mexico. Using nonlinear least squares (NLS), 10 generalized H-d models were fitted to 883 and 1226 pairs of H-d data from Pinus montezumae and Pinus pseudostrobus, respectively. The best model was refitted with the maximum likelihood mixed effects model (MEM) approach by including the site as a classification variable and a known variance structure. The Wang and Tang equation was selected as the best model with NLS;the MEM with an additive effect on two of its parameters and an exponential variance function improved the fit statistics for Pinus montezumae and Pinus pseudostrobus, respectively. The model validation showed equality of means among the estimates for both species and an independent subsample. The calibration of the MEM at the plot level was efficient and might increase the applicability of these results. The inclusion of dominant height in the MEM approach helped to reduce bias in the estimates and also to better explain the variability among plots.

Models-3模式中增加移动源清单对模拟效果的影响

采用空气质量模式Models-3,在原有点源和面源污染源输入清单的基础上,加入移动污染源,对辽宁地区2004年12月24—27日大气污染物时空分布进行数值模拟。结果表明:加入移动污染源后,辽宁主要城市污染物SO2、NO2和PM10模拟效果有所提高,NO2模拟效果提高最为显著;从总体模拟效果来看,SO2和NO2模拟效果较好,而PM10模拟值相对较差。

Application of Inventory Theory in Service Stations

A service station plays an important role in the petroleum product distribution terminal. With the increase in petroleum consumption in China, the inventory theory should be applied in the stock control of service stations. In this paper the inventory theory including its background and characteristics is introduced. At the same time, the application of the theory in some trades today, especially in petroleum trade, is analyzed. Then (s, S) stochastic model is advanced, which is established according to the principle of operational research and, based on this model, a sample is given, which discusses the details of application in the stock control of service stations. The sample is simplified but implies the validity of the model in optimizing the storage of petroleum products in the market.

The inventory of the carbon stocks in sub tropical forests of Pakistanfor reporting under Kyoto Protocol

The United Nations Framework Convention on Climate Change （UNFCCC） requires reporting net carbon stock changes and anthropogenic greenhouse gas emissions, including those related to forests. This paper describes the status of carbon stocks in sub tropical forests of Pakistan. There are two major sub types in subtropical forests of Pakistan viz a viz Subtropical Chir Pine and Subtropical broadleaved forests. A network of sample plots was laid out in four selected site. Two sites were selected from sub tropical Chir Pine （Pinus roxburghii） forests and two from Subtropical broadleaved forests. Measurement and data acquisition protocols were developed specifically for the inventory car- ried out from 2005 to 2010. In total 261 plots （each of lha.） were established. Estimation of diameter, basal area, height, volume and biomass was carried out to estimate carbon stocks in each of the four carbon pools of above- and below-ground live biomass. Soil carbon stocks were also determined by doing soil sampling. In mature （-100 years old） pine forest stand at Ghoragali and Lehterar sites, a mean basal area of 30.38 and 26.11 m2.ha-1 represented mean volume of 243 and 197 m3·ha-1, respectively. The average biomass （t.ha-1） was 237 in Ghoragali site and 186 tha-1 in Lehterar site, which is equal to 128 and 100 t·ha-1 including soil C. However, on average basis both the forests have 114.5± 2.26 t.ha-1 of carbon stock which comprises of 92% in tree biomass and only 8% in the top soils. In mixed broadleaved evergreen forests a mean basal area （m2.ha-1）was 3.06 at Kherimurat with stem volume of 12.86 and 2.65 at Sohawa with stem volume of 11.40 m3.ha-1. The average upper and under storey biomass （t·ha-1） was 50.93 in Kherimurat site and 40.43 t.ha-1 in Sohawa site, which is equal to 31.18 and 24.36 t ·ha-1 including soil C stocks. This study provides a protocol monitoring biomass and carbon stocks and valuable baseline data for in Pakistan＇s managed and unmanaged sub-tropical forests.

Mapping the potential distribution suitability of 16 tree species under climate change in northeastern China using Maxent modelling

Knowledge on the potential suitability of tree species to the site is very important for forest management planning.Natural forest distribution provides a good reference for afforestation and forest restoration.In this study,we developed species distribution model(SDM)for 16 major tree species with 2,825 permanent sample plots with natural origin from Chinese National Forest Inventory data collected in Jilin Province using the Maxent model.Three types of environmental factors including bioclimate,soil and topography with a total of 33 variables were tested as the input.The values of area under the curve(AUC,one of the receiver operating characteristics of the Maxent model)in the training and test datasets were between 0.784 and 0.968,indicating that the prediction results were quite reliable.The environmental factors affecting the distribution of species were ranked in terms of their importance to the species distribution.Generally,the climatic factors had the greatest contribution,which included mean diurnal range,annual mean temperature,temperature annual range,and iosthermality.But the main environmental factors varied with tree species.Distribution suitability maps under current(1950-2000)and future climate scenarios(CCSM4-RCP 2.6 and RCP 6.0 during 2050)were produced for 16 major tree species in Jilin Province using the model developed.The predicted current and future ranges of habitat suitability of the 16 tree species are likely to be positively and negatively affected by future climate.Seven tree species were found to benefit from future climate including B etula costata,Fraxinus mandshurica,Juglans mandshurica,Phellodendron amurense,Populus ussuriensis,Quercus mongolica and Ulmus pumila;five tree species will experience decline in their suitable habitat including B.platyphylla,Tilia mongolica,Picea asperata,Pinus sylvestris,Pinus koraiensis;and four(Salix koreensis,Abies fabri,Pinus densiflora and Larix olgensis)showed the inconsistency under RCP 2.6 and RCP 6.0 scenarios.The maps of the habitat suitability can be used as a basis for afforestation and forest restoration in northeastern China.The SDMs could be a potential tool for forest management planning.

Analysis of an Inventory System for Items with Stochastic Demand and Time Dependent Three-Parameter Weibull Deterioration Function

In recent times, mathematical models have been developed to describe various scenarios obtainable in the management of inventories. These models usually have as objective the minimizing of inventory costs. In this research work we propose a mathematical model of an inventory system with time-dependent three-parameter Weibull deterioration and a stochastic type demand in the form of a negative exponential distribution. Explicit expressions for the optimal values of the decision variables are obtained. Numerical examples are provided to illustrate the theoretical development.

Some non-linear height–diameter models performance for mixed stand in forests in Northwest Iran

This study evaluated the total height of trees based on diameter at breast height by using 23 widely used height-diameter non-linear regression models for mixed-species forest stands consisting of Caucasian oak,field maple,and hornbeam from forests in Northwest Iran.1920 trees were measured in 6 sampling plots(every sampling plot has 1 ha area).The fit of the best height–diameter models for each species were compared based on R2,Root Mean Square Error(RMSE),Akaike information criterion(AIC),standard error,and relative ranking performance criteria.In the final step,verification of results was performed by paired sample t-test to compare the observed height and estimated height.Results showed that among 23 height-diameter models,the best models were obtained from the top five ones including Modified-logistic,Prodan,Sibbesen,Burkhart,and Exponential.Comparison between the actual observed height and estimated height for Caucasian oak showed that Modified–Logistic,Prodan,Sibbesen,Burkhart,and Exponential performed better than the others,respectively(There were no statistically significant differences between observed heights and predicted height(p≥0.05)).Prodan,Modified-Logistic,Burkhart,and Loetch evaluated field maple tree height correctly,and Modified-Logistic,Burkhart,and Loetch had better fitness compared to the others for hornbeam,respectively.Although other models were introduced as appropriate criteria,they could not reliably predict the height of trees.Using the Rank analysis,the Modified-Logistic model for the Caucasian oak and Prodan model for field maple and hornbeam had the best performance.Finally,to complement the results of this study,it is suggested to assess how environmental factors such as elevation,climate parameters,forest protection policy and forest structure will modify height-diameter allometry models and will enhance the prediction accuracy of tree heights prediction in mixed stands.

Longitudinal height-diameter curves for Norway spruce, Scots pine and silver birch in Norway based on shape constraint additive regression models

Background： Generalized height-diameter curves based on a re-parameterized version of the Korf function for Norway spruce （Piceo abies （L.） Karst.）, Scots pine （Pinus sylvestris L.） and silver birch （Betula pendula Roth） in Norwa are presented. The Norwegian National Forest Inventory （NFI） is used as data base for estimating the model parameters. The derived models are developed to enable spatially explicit and site sensitive tree height imputatio in forest inventories as well as future tree height predictions in growth and yield scenario simulations. Methods： Generalized additive mixed models （gamm） are employed to detect and quantify potentially non-linear effects of predictor variables. In doing so the quadratic mean diameter serves as longitudinal covariate since stand ag as measured in the NFI, shows only a weak correlation with a stands developmental status in Norwegian forests. Additionally the models can be locally calibrated by predicting random effects if measured height-diameter pairs are available. Based on the model selection of non-constraint models, shape constraint additive models （scare） were fit tc incorporate expert knowledge and intrinsic relationships by enforcing certain effect patterns like monotonicity. Results： Model comparisons demonstrate that the shape constraints lead to only marginal differences in statistical characteristics but ensure reasonable model predictions. Under constant constraints the developed models predict increasing tree heights with decreasing altitude, increasing soil depth and increasing competition pressure of a tree. / two-dimensional spatially structured effect of UTM-coordinates accounts for the potential effects of large scale spatial correlated covariates, which were not at our disposal. The main result of modelling the spatially structured effect is lower tree height prediction for coastal sites and with increasing latitude. The quadratic mean diameter affects both the level and the slope of the height-diameter curve and both effects are positive. Conclusions： In this investigation it is assumed that model effects in additive modelling of height-diameter curves which are unfeasible and too wiggly from an expert point of view are a result of quantitatively or qualitatively limited data bases. However, this problem can be regarded not to be specific to our investigation but more general since growth and yield data that are balanced over the whole data range with respect to all combinations of predictor variables are exceptional cases. Hence, scare may provide methodological improvements in several applications by combining the flexibility of additive models with expert knowledge.