Optimal Policy for Brownian Inventory Models with General Convex Inventory Cost

We study an inventory system in which products are ordered from outside to meet demands, and the cumulative demand is governed by a Brownian motion. Excessive demand is backlogged. We suppose that the shortage and holding costs associated with the inventory are given by a general convex function. The product ordering from outside incurs a linear ordering cost and a setup fee. There is a constant leadtime when placing an order. The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.

Multilocation Inventory Models and their Heuristic Algorithm

In this paper, we first construct multilocation inventory models and design a heuristic approximate algorithm of the inventory models. Finally we analyze timing results for algorithm′s implementation on a parallel computer.

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.

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.

Model-based estimation of above-ground biomass in the miombo ecoregion of Zambia

Background：Information on above-ground biomass（AGB） is important for managing forest resource use at local levels,land management planning at regional levels,and carbon emissions reporting at national and international levels.In many tropical developing countries,this information may be unreliable or at a scale too coarse for use at local levels.There is a vital need to provide estimates of AGB with quantifiable uncertainty that can facilitate land use management and policy development improvements.Model-based methods provide an efficient framework to estimate AGB.Methods：Using National Forest Inventory（NFI） data for a^1,000,000 ha study area in the miombo ecoregion,Zambia,we estimated AGB using predicted canopy cover,environmental data,disturbance data,and Landsat 8 OLI satellite imagery.We assessed different combinations of these datasets using three models,a semiparametric generalized additive model（GAM） and two nonlinear models（sigmoidal and exponential）,employing a genetic algorithm for variable selection that minimized root mean square prediction error（RMSPE）,calculated through cross-validation.We compared model fit statistics to a null model as a baseline estimation method.Using bootstrap resampling methods,we calculated 95% confidence intervals for each model and compared results to a simple estimate of mean AGB from the NFI ground plot data.Results：Canopy cover,soil moisture,and vegetation indices were consistently selected as predictor variables.The sigmoidal model and the GAM performed similarly;for both models the RMSPE was -36.8 tonnes per hectare（i.e.,57% of the mean）.However,the sigmoidal model was approximately 30% more efficient than the GAM,assessed using bootstrapped variance estimates relative to a null model.After selecting the sigmoidal model,we estimated total AGB for the study area at 64,526,209 tonnes（＋/- 477,730）,with a confidence interval 20 times more precise than a simple designbased estimate.Conclusions：Our findings demonstrate that NFI data may be combined with freely available satellite imagery and soils data to estimate total AGB with quantifiable uncertainty,while also providing spatially explicit AGB maps useful for management,planning,and reporting purposes.

MINIMIZING JOB SHOP INVENTORY WITH ON-TIME DELIVERY GUARANTEES

In this paper, we introduce a new job shop model that minimizes a well-motivated inventory measure while assuring on-time job deliveries. For this new problem, we introduce precise notation and formalization. A decomposition scheme is discussed in detail, which is subsequently utilized in a new shifting bottleneck procedure (SBP) for the problem. In addition to SBP, we propose another heuristic method based on successive insertion of operations. Algorithms are fine tuned through experimentation. Moreover, the two heuristic procedures are compared in terms of computation time and solution quality, using disguised actual factory data.

SINGLE-PERIOD TWO-PRODUCT INVENTORY MODEL WITH SUBSTITUTION:SOLUTION AND PROPERTIES

In this paper, we study a single-period two-product inventory model with stochastic demands and downward substitution. The optimal order quantities are presented and some properties are provided. Comparing with newsboy model, we prove that both the profit and the fill rate can be improved by using the substitution policy.

Optimal Decision Rule of the inventory Problem for Deteriorating items with Shortages and Time－varying Demand

In this paper, we consider the general inventory problem for deteriorating items having time-varying demand and shortages. An optimal order policy is obtained for determining the number of reorders and the time of the reorder points and shortage points in order to minimize the total cost of system. Several fundamental theoretical results are established for this model. The corresponding cases for no-deterioration and no-shortage is also discussed. To illustrate the solution procedure,numerical examples are shown for the special case of linear increasing demand.

A LIMITED ORDER CAPACITY STOCHASTIC INVENTORY MODEL WITH A FIXED COST FOR ORDER: THE DISCOUNTED CASE

This paper considers a single-item, periodic-review inventory model with linear ordercosts, a convex function representing expected one-period costs, nonegative i.i.d. demandsand a fixed cost for order. Stockouts are backordered. All data are stationary Both finiteand infinite horizon problems are treated.

Emission inventory evaluation using observations of regional atmospheric background stations of China

Any accurate simulation of regional air quality by numerical models entails accurate and up-to-date emissions data for that region.The INTEX-B2006 （I06）,one of the newest emission inventories recently popularly used in China and East Asia,has been assessed using the Community Multiscale Air Quality model and observations from regional atmospheric background stations of China.Comparisons of the model results with the observations for the species SO2,NO 2,O 3 and CO from the three regional atmospheric background stations of Shangdianzi,Longfengshan and Linan show that the model can basically capture the temporal characteristics of observations such as the monthly,seasonal and diurnal variance trends.Compared to the other three species,the simulated CO values were grossly underestimated by about two-third or one-half of the observed values,related to the uncertainty in CO emissions.Compared to the other two stations,Shangdianzi had poorer simulations,especially for SO2 and CO,which partly resulted from the site location close to local emission sources from the Beijing area;and the regional inventory used was not capable of capturing the influencing factors of strong regional sources on stations.Generally,the fact that summer gave poor simulation,especially for SO2 and O 3,might partly relate to poor simulations of meteorological fields such as temperature and wind.

Inflation and time value of money in a vendor-buyer inventory system with transportation cost and ordering cost reduction

The article presents a single-vendor and a single-buyer integrated production inventory system with inflation and the time value of money.The main focus is on the effect of ordering cost reduction dependent on lead time and lead time reduction.Two integrated continuous review models are developed.For both cases,our objective is to minimise the total integrated system cost by simultaneously optimising the order quantity,safety factor,lead time and number of shipments.We take the transportation cost as a function of the shipment lot size and it is taken to be in an all unit-discount cost format.Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedure for solving the proposed inventory system.An efficient algorithm for finding the optimal solution is developed and numerical examples are given to illustrate the model.

A supply chain management in a single-vendor and a singlebuyer integrated inventory model with backorders under imperfect production system

Lead time is an essential factor in any supply chain and inventory management system.In stochastic inventory models,lead time is often viewed as a prescribed constant or a random variable that is not subject to control.In many practical situations,lead times can be controlled by paying additional investment.Using this viewpoint,notion of the crashing cost into stochastic inventory model,in which lead time can be controlled by additional investment.Many researchers have developed various analytical inventory models we have considered the piecewise linear function.So in this proposed model,we derive the mathematical model which is developed by incorporating three types of lead time crashing cost functions(i)exponential function,(ii)polynomial function and(iii)negative exponential function.An integrated inventory model is recognized to find the optimal solutions of order quantity,lead time,total cost for buyer,total cost for vendor and the total number of deliveries from the single-vendor to the single-buyer in one production run.A solution process is suggested for solving the proposed model and numerical examples to illustrate the feature of the proposed model,and examined the effect of the key parameters on the optimal solution and managerial implications are discussed.Numerical examples show that this model offers significant improvements over existing models.A computer code using the software Matlab is developed to derive the optimal solution.The main contribution of this paper is developing a mathematical model and an effective solution procedure to find the optimal solution.Finally,a graphical representation of the computational algorithm is represented by a flowchart in each model.

Sustainable Integrated Inventory Model for Substitutable Deteriorating Items Considering Both Transport and Industry Carbon Emissions

Sustainable integrated inventory management policy focuses on reducing the environmental impact of the manufacturing and transport sector.This study develops an integrated single-manufacturer single-buyer inventory model for substitutable deteriorating items considering transport and industry carbon emissions.This article categorizes carbon emissions into two parts:direct and indirect emissions.We also assume two mutually substitutable items,and substitution is considered on the buyer's side.If one of the items is out of stock,the demand for that item can be partially satisfied by the stock of the other item;else,demand will be lost.The purpose of this study is to minimize the integrated cost of the supply chain with total carbon emissions produced by industry and transport sectors and to determine the optimal number of deliveries,order level and carbon emission quantity.A solution procedure is developed to find the optimal values of the policy.Numerical experiments and sensitivity analyses are presented to demonstrate the proposed model.

Inventory Games with Quantity Discount

Meca,et al.(2004)studied a class of inventory games which arise when a group of retailers who observe demand for a common good decide to cooperate and make joint orders.In this paper,the authors extend their model to the situation where the manufacturer provides the retailers with a price discount on purchases in excess of a certain order quantity.The authors define the corresponding inventory game with quantity discount,and show that the inventory game has a nonempty core.Then,the authors propose a core allocation rule,the demand-proportionality rule,and characterize it by introducing efficiency,the retailer splitting property and continuity.

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

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.

L~■-convexity and its applications in operations

L■-convexity, one of the central concepts in discrete convex analysis, receives significant attentions in the operations literature in recent years as it provides a powerful tool to derive structures of optimal policies and allows for efficient computational procedures. In this paper, we present a survey of key properties of L■-convexity and some closely related results in lattice programming, several of which were developed recently and motivated by operations applications. As a new contribution to the literature, we establish the relationship between a notion called m-differential monotonicity and L■-convexity. We then illustrate the techniques of applying L■-convexity through a detailed analysis of a perishable inventory model and a joint inventory and transshipment control model with random capacities.