An Inventory Model for Items with Two Parameter Weibull Distribution Deterioration and Backlogging

In this paper an inventory model is developed with time dependent power pattern demand and shortages due to deterioration and demand. The deterioration is assumed to follow a two parameter Weibull distribution. Three different cases with complete, partial, no backlogging are considered. The optimal analytical solution of the model is derived. Suitable numerical example has been discussed to understand the problem. Further sensitivity analysis of the decision variables has been done to examine the effect of changes in the values of the parameters on the optimal inventory policy.

POLYNOMIAL DYNAMIC PROGRAMMING ALGORITHMS FOR LOT SIZING MODELS WITH BOUNDED INVENTORY AND STOCKOUT AND/OR BACKLOGGING

This paper addresses a dynamic lot sizing problem with bounded inventory and stockout where both no backlogging and backlogging allowed cases are considered. The stockout option means that there is outsourcing in a period only when the inventory level at that period is non-positive. The production capacity is unlimited and production cost functions are linear but with fixed charges. The problem is that of satisfying all demands in the planning horizon at minimal total cost. We show that the no backlogging case can be solved in O（T^2） time with general concave inventory holding and outsourcing cost functions where T is the length of the planning horizon. The complexity can be reduced to O（T） when the inventory holding cost functions are also linear and have some realistic properties, even if the outsourcing cost functions remain general concave functions. When the inventory holding and outsourcing cost functions are linear, the backlogging case can be solved in O（ T^3 logT） time whether the outsourcing level at each period is bounded by the sum of the demand of that period and backlogging level from previous periods, or only by the demand of that period.

An EPQ model with variable production,probabilistic deterioration and partial backlogging under inflation

This paper develops an economic production quantity(EPQ)model under the effect of inflation and time value of money.The rate of replenishment is considered to be a variable and the generalized unit production cost function is formulated by incorporating several factors,such as raw material,labour,replenishment rate,advertisements and other factors of the manufacturing system.The selling price of a unit is determined by a mark-up over the production cost.We have considered three types of continuous probabilistic deterioration function,and also considered that the holding cost of the item per unit time is assumed to be an increasing linear function of time spent in storage.In addition,shortages are allowed and partially backlogged.This model aids in minimizing the total inventory cost by finding the optimal cycle length and the optimal production quantity.The optimal solution of the model is illustrated with the help of numerical examples.

Two-warehouse inventory model for non-instantaneous deteriorating items with optimal credit period and partial backlogging under inflation

This paper analyses an inventory model for non-instantaneous deteriorating items under a two-warehouse system with the effect of inflation and time value of money.We propose the model from the seller’s prospective by incorporating the fact that granting the trade credit from the seller to its buyer not only increases sales and revenue but also opportunity cost and default risk.Moreover,in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The purpose of this study is to determine the optimal credit period and the optimal order quantity such that the total profit of the seller is maximised.Some numerical examples are presented for illustrating the proposed inventory model.Furthermore,sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.

An EOQ model for non-instantaneous deteriorating items with timedependent demand under partial backlogging

This article discusses an economic order quantity model for non-instantaneous deteriorating items in which the demand is assumed to be a linear function of time over an infinite planning horizon.In addition,the salvage value associated with the deteriorated units is also considered.The shortages are allowed and partially backlogged.A mathematical model is framed to obtain the replenishment policy which aids the retailer to minimize the total inventory cost.The objective of this work is to minimize the total inventory cost and to find the optimal length of replenishment and the optimal order quantity.The theory developed in this article is illustrated using numerical examples.A computational algorithm is designed to find the optimal solution.Sensitivity analysis is carried out to study the changes in the effect on the optimal solutions and some managerial insights are obtained.

An inventory model for non-instantaneous deteriorating items with multivariate demand and backlogging under inflation

In this paper,a deterministic inventory model for non-instantaneous deteriorating items with price-and time-dependent demand with inflation is developed.The demand is continuous and differentiable function of price and time.Shortages are allowed and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time.The objective is to find the optimal replenishment cycle such that present value of total profit is maximized,for any given selling price.We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model that can be easily implemented by practitioners.Comparisons of the present model with various cases are presented as the special case.Numerical examples are used to illustrate the theoretical results and the sensitivity analysis with respect to major parameters on the optimal solutions is also performed.

Metropolitan Housing Development in Urban Fringe Areas-A Case Study of Three Metropolitan Cities of South Africa: Johannesburg, Ekurhuleni and Tshwane

Purpose:The metropolitan cities of Johannesburg,Ekurhuleni and Tshwane play an important role in the economy of the Gauteng province in South Africa.The region constitutes to 22.4 percent of the total population of South Africa and has a strong presence and contributes in areas of manufacturing sector,financial and business services,retail and wholesale trade,etc.The rapid urban population,increase in the informal settlements and socio-economic opportunities has resulted in considerable urban sprawl in and around the urban fringe areas of these metropolitan cities.The urban fringe areas of these metros often come under the influence of rapid urbanization process and pressures.Coupled with the economical and potential land dynamics and lack of priority of spatial development guidelines,these areas attract rapid and haphazard development from communities and developers.Research Design/Methodology:This research is based on a qualitative approach through a comprehensive literature review that included content analysis of key documents on housing sector such as IDPs(Integrated Development Plans),Municipal Annual Reports,Growth Development Strategies,and among other sectoral documents on housing sector.Some of the key priority issues considered in the housing sector included:eradication of housing backlogs,spatial restructuring of housing,provision of choice in terms of location,tenure and housing typology.Findings:The current paper discusses the approaches of metropolitan housing development processes in three metropolitan cities of South Africa from Gauteng region,namely:Johannesburg,Ekurhuleni and Tshwane.The paper discusses the existing housing sectoral scenario along with the fringe areas in three cities with focus on:formal and informal settlements,housing segregation and the backlogs,current institutional arrangements,role of public private participation,and scope for alternate mechanisms.The paper concludes in discussion on sustainable development options for housing development in urban fringe areas.

Partial backlogging inventory model with price and stock level dependent demand,time varying holding cost and quantity discounts

This article deals with an increasing total profit for inventory optimal ordered quantity and partial backlogging with the holding cost depending on the storage time period,and the rate of market demand is assumed to fluctuate as a function,based on level of stock and selling price.Thereafter,using the concept of a Hessian matrix,we have proved the concave nature of the profit function for the case where maximum cost is obtained.Finally,in order to validate the derived models,numerical examples and sensitivity analysis are explained.Through numerical test,we show that the proposed algorithms give quite satisfactory solutions.Hence,it can be concluded that the total profit can be increased by allowing shortage and partial backlogging.

An EOQ model of non-instantaneous deteriorating items with price,time-dependent demand and backlogging

This paper considers an inventory model with non-instantaneous deteriorating item in which demand rate is a function of selling price and time,taking account of time value of money.This paper aids the retailer in maximising the total profit by determining optimal replenishment policies.Shortages are allowed which are partially backlogged.This model also takes into cognizance the fact that in business activities nowadays customers are given delay in payments.Under these assumptions,a mathematical model is formulated over a finite planning horizon and then some useful theoretical results have been framed to characterise the optimal solutions.The necessary and sufficient conditions for the existence and the uniqueness of the optimal solutions are also derived.An algorithm is designed to find the optimum solutions of the proposed model.Numerical examples are included to illustrate the algorithmic procedure and the effects of key parameters are studied to analyse the behaviour of the model.

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.

一种SYN-Flooding攻击的防范对策

针对SYN Flooding攻击的特点,分析了常用的几种防御SYN Flooding攻击的方法,指出其防御方法的不足,提出一种FIFO淘汰防御方法,进行了攻击 防御实验,取得较好效果.

A Note on an Economic Lot-sizing Problem with Perishable Inventory and Economies of Scale Costs:Approximation Solutions and Worst Case Analysis

This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.

异地分布式多SCRUM项目产品Backlog分解过程影响因素分析

将异地分布和SCRUM方法相结合,分析产品Backlog分解过程,提出分解过程的几种重要影响因素:优先级设置、团队地理位置、任务稳定性、团队间差异、任务工作量估算。采用问卷调查的方法收集数据,然后用SPSS软件进行数据分析,研究各因素对产品Backlog分解过程的影响。研究结果表明,优先级和任务的稳定性以及工作量估算对产品Backlog分解过程有显著影响,而团队的地理位置和团队差异则没有显著影响。研究结果有助于SCRUM开发团队更好地完成产品Backlog的工作。

高效制定并使用Scrum开发的产品Backlog

Scrum开发过程框架中,产品Backlog是产品所要具备的所有功能的总纲,是Scrum过程的核心。产品Backlog就类似于传统顺序开发模型中的需求分析,但它不需要完全的确定和细化产品的需求,也不用形成完整使用说明,它用的是另一种恰到好处的方式。本文从三个方面讨论如何高效制定并使用产品Backlog,并举一个考务系统的Scrum开发实例进行深入说明,希望可以为刚转型Scrum的传统开发团队提供参考。

Exploiting Virtual Elasticity of Production Systems for Respecting OTD-Part 1: Post-Optimality Conditions for Ergodic Order Arrivals in Fixed Capacity Regimes

Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arrivals, may compromise the observance of on-time supplies for some orders. The purpose of this paper is to evaluate the conditions of post-optimality for stochastic order rate governed production systems in order to observe OTD. Instead of a heuristic or a simulative exploration, a Cartesian-based approach is applied to developing the necessary and sufficient mathematical condition to solve the problem statement. The research result demonstrates that increasing speed of throughput reveals a latent capacity, which allows arrival orders above capacity limits to be backlog-buffered and rescheduled for OTD, exploiting the virtual manufacturing elasticity inherent to all production systems to increase OTD reliability of non JIT-based production systems.

Analysis of Stress Backlogs during Case-File Processing in Forensic Science Laboratory

Case-file backlogs were identified as one of the cause factors affecting the competitiveness of the forensic science laboratory (FSL). Backlogs represent case-files?that remain unprocessed or unreported within a selected time interval (year, week or month) which leads to increased customer complaints, rework, cost of analysis, degradation of biological samples, etc. Case-file backlogging was quantified in three consecutive years (2014 to 2016), using the following parameters: case-files received and case-files processed, difference of which gives case-files backlogged. There was a need to define time interval for a case-file to be regarded as backlogged (that is, one week), results of which can translate into backlogged case-files per month or year. A data collection tool was established and used for three work stations (forensic chemistry, biology/DNA and toxicology laboratories). The tool includes starting and ending date for each?time interval, in which the numbers of case-files received and processed were entered followed by computing the backlogs. It was observed that, case-files reported?increased between 2014 and 2016 leading to a decrease in backlogged case-files.?The annual percentage of the case-files backlogged was highest for forensic?toxicology. The highest number of case-files backlogged was observed for forensic?chemistry, followed by forensic biology/DNA. The number of case-files?backlogged per analyst per year was highest in 2014 and dropped continuously?towards 2016, being comparably higher in forensic biology/DNA and chemistry.?Probability density functions (PDFs) and cumulative distribution functions (CDFs)?of backlogs data indicated that a large number of backlogs created in previous?weeks were eliminated. It was concluded that the effect of case-file backlogging on FSL competitiveness can be minimized by continued management effort in backlog elimination.

高效制定并使用Scrum开发的产品Backlog

Scrum开发过程框架中,产品Backlog是产品所要具备的所有功能的总纲,是Scrum过程的核心。产品Backlog就类似于传统顺序开发模型中的需求分析,但它不需要完全的确定和细化产品的需求,也不用形成完整使用说明,它用的是另一种恰到好处的方式。本文从三个方面讨论如何高效制定并使用产品Backlog,并举一个考务系统的Scrum开发实例进行深入说明,希望可以为刚转型Scrum的传统开发团队提供参考。

Maintenance Capacity Planning: Determination of Maintenance Workforce

Determining the size of maintenance workforce is an essential element of maintenance planning. It is important for performing maintenance programs perfectly. However, it is a complex and challenging problem since it involves the consideration of several important factors. The mathematical model developed in this paper aims at finding out the optimal size of the maintenance workforce taking into account all of the important factors that affect this size. It is based on determining the needed number of workers with different skill levels and from different sources to meet maintenance workload of different grades that is to be performed in a specified planning horizon with minimum cost acquired.

Two-warehouse inventory model with non-instantaneously deteriorating items,stock-dependent demand,shortages and inflation

In this paper,a two-warehouse economic order quantity(EOQ)model for noninstantaneously deteriorating items with stock-dependent demand under the effects of inflation and the time value of money is presented.Also in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The objective of this model is to minimize the total inventory cost of the retailer by finding the optimal intervals and the optimal order quantity.An algorithm is designed to find the optimum solution of the proposed model.Numerical examples are given to demonstrate the results.Sensitivity analysis of the model with respect to several system parameters has been carried out and some managerial inferences are obtained.

Analysis and optimization of an EOQ inventory model with promotional efforts and back ordering under delay in payments

In this paper,economic order quantity(EOQ)inventory model is considered subject to promotional efforts.We adopt a demand function which is dependent on sales teams’initiatives in which shortages are allowed which are completely backlogged under the condition of permissible delay in payments with timedependent holding cost.The main objective of this paper is to determine the optimal replenishment schedule and optimal order quantity to maximize the total profit.Expressions for various optimal indices are provided.First,we prove that a unique optimal replenishment schedule exists.Second,we present an effective iterative algorithm to obtain the optimal solution.Furthermore,we establish some useful theorems to characterize the optimal solution to determine the values of replenishment schedule and optimal order quantity.Third,we prove that the total profit is a concave function via differential calculus and present numerical examples using SCILAB 5.5.0 to illustrate the model.Finally,we extend the numerical example by performing a sensitivity analysis of the model parameters and discuss managerial insights.This study suggests to the management of firms to determine the optimal order quantity,optimal inventory cycle length and sales teams’initiatives/promotional effort in order to achieve their maximum profits.