Ordering Cost Depletion in Inventory Policy with Imperfect Products and Backorder Rebate

This study presents an inventory model for imperfect products with depletion in ordering costs and constant lead time where the price discount in the backorder is permitted. The imperfect products are refused or modified or if they reached to the customer, returned and thus some extra costs are experienced. Lately some of the researchers explicitly present on the significant association between size of lot and quality imperfection. In practical situations, the unsatisfied demands increase the period of lead time and decrease the backorders. To control customers' problems and losses, the supplier provides a price discount in backorders during shortages. Also, an order’s policies may result in including some imperfect products in arrival lots. A discount on price may be offered by the supplier on the out-of-stock products to manage the backorder problems. The study aims to develop a model with imperfect products by permitting the price discount in backorders, and the cost of ordering is considered a decision variable. First, it is assumed that the demand for lead time is followed by a normal distribution and then stops it and assumed that the first two moments of demand for lead time are known. Further, the minimax distribution method is used to solve this model, and a separate algorithm is designed. In this study, two models are discussed with and without a normally distributed rate of demand. The current study verified with the help of some numerical examples over various model parameters.     

DETERMINING THE NUMBER OF KANBANS IN MULTI-ITEM JUST-IN-TIME SYSTEMS

Kanbans (cards) are one means of controlling Just-in-time production systems. The kanbans serve as production authorization orders and essentially become the information system. The presence of a production ordering kanban for a specific part type constitutes an instruction to the workcenter to produce a “container” of that part. In this paper we assume workcenters produce multiple part types and address the issue of the number of kanbans needed for each part type. Our objective is to minimize the sum of inventory holding and backorder cost. A stochastic model is formulated. Steady-state results are derived for the cases of a few and many part types. Modifications for the case of expediting of backorders are also provided. Simulation results demonstrate the accuracy of the model for a large number of kanbans, but an investigation of a finite population queueing model for small numbers of kanbans is suggested as a worthwhile extension.     

Incorporating planned backorders in a family production context with shelf-life considerations

This paper considers the problem of determining the optimal production rate for each item and the optimal cycle time for the family of items in a family production context with restrictions on the shelf-life of various items in the family. We investigate the impact of incorporating planned backorders into the system. We show that the model with planned backorders reduces to a model without backorders with modified holding costs and shelf-life. Therefore, the model with planned backorders can be analysed using the earlier model developed by Viswanathan and Goyal (1997). We also present several examples to demonstrate how incorporating planned backorders can reduce the total costs.     

On offering economic incentives to backorder

We study a strategy to manage demands that occur when an inventory system is temporarily out of stock: offer the customer facing the unsatisfied demand an economic incentive to backorder. We explore the benefits of this inventory management strategy by analyzing a model of an inventory system with stochastic demand and random supply disruptions, where the probability that a customer facing an unfilled demand will backorder (as opposed to becoming a lost sale) can be influenced by an economic incentive. Our results provide several insights regarding this inventory management strategy and suggest that the benefits of offering backorder incentives can be significant.     

Capacitated lot-sizing problem with production carry-over and set-up splitting: mathematical models

This work proposes mathematical models (MMs) for the capacitated lot-sizing problem with production carry-over and set-up splitting, which can handle two scenarios, namely (1) situation/scenario where the set-up costs and holding costs are product dependent and time independent, and with no backorders or lost sales, and (2) situation where the set-up costs and holding costs are product dependent and time dependent, and with no backorders or lost sales. Previously, in an existing study the authors had developed a MM for the same problem and situation where the set-up costs and holding costs are product dependent and time independent, i.e. our Scenario 1. We compare our proposed models with the model in the existing study that appears to be incorrect.     

允许缺货的可控提前期供应链库存优化与协调

将单个企业的可控提前期库存模型拓展到供应链环境中,并考虑了允许部分缺货后补的情形,分别建立了分散决策和联合决策情形下允许部分缺货后补的可控提前期供应链库存优化模型,并提出价格折扣机制来协调供应链成员的利益.采用数值实验方法,对所建的库存优化模型和协调机制进行了分析,结果表明:随着缺货后补比例的不断减少,供应链必须不断增大订货批量和压缩提前期以提高顾客服务水平;价格折扣机制可以使得允许缺货的可控提前期供应链达到协调的目的.     

A trade off between emergency repair and inventory investment

In this paper we present an emergency repair model. We model a situation where failed parts arrive at a repair shop according to a Poisson process. If the stock on hand of serviceable spare parts exceeds a given emergency trigger level, the failed part is sent into normal repair. Otherwise the failed part is sent into an alternative emergency repair channel. Upon arrival failed parts are exchanged for serviceable spare parts, if available. Otherwise the demand is backordered. A backorder is filled with the first part that becomes available from either one of the repair processes. The repair times (including transportation time) are assumed to be exponentially distributed. We analyze the impact of using emergency repair on two service measures: the fraction of demand that is satisfied from stock on hand and the expected duration of a backorder. We calculate the initial stock level and the emergency trigger level that minimize the total cost for a given emergency repair rate. The proposed policy is compared with two other policies: (1) emergency repair is not used and (2) emergency trigger level is zero. We find that significant service improvements and cost reductions can be obtained by using our emergency repair policy. We also present simulation results showing that the distribution of the repair times has a negligible effect on the relevant service measures. Finally, we compare our results with the results of an emergency supply model by Muckstadt and Thomas [1] Again we observe significant cost reductions when using our policy.     

A Hybrid Inventory System with a Time Limit on Backorders

Traditionally, in ( Q , r ) inventory systems, when a shortage occurs, incoming demands are either filled by emergency orders or backordered. However, the backorder costs are usually time-dependent, hence it is costly to backorder early in the lead time. On the other hand, it is obviously expensive to fill the shortages with emergency orders alone. In this paper, we propose a hybrid inventory control system to handle shortages. A cutoff time τis incorporated with the traditional ( Q , r ) systems. Poisson demands and a constant lead time are assumed. Shortages are covered by emergency orders before τand backordered after τ. The traditional backorder and emergency order systems are special cases of the hybrid system with τ= 0 and τ= lead time, respectively. The optimal control variables Q *, r *, and τ* are determined by minimizing the expected annual cost. Numerical examples to illustrate the model are presented together with discussions on the conditions under which the hybrid system provides cost savings over the two traditional systems.     

Aggregate Backorder Exchange Curves

In an effort to avoid estimating backorder costs in developing an inventory strategy, this paper derives an exchange curve which can be used by upper management to decide on backorder policy. Specifically, the exchange curve shows the trade-off between average dollar value of aggregate inventory versus the maximum allowed backorder delay.     

转运情形下基于订单的缺货水平分析

考虑一个多零件二级存储系统,顾客订单类型有多种且随机到达,得到了不允许分销点之间转运时,订单的平均缺货水平的表达式.对于允许转运的情形,通过分析库存状态与实际需求率之间的关系,构造了求解分销点对零件的实际需求率的迭代算法,并得到了订单的平均缺货水平的近似表达式.数值模拟表明该近似表达式的平均误差为10.91%,转运能使订单的缺货数量平均减少38.15%.     

Fuzzy multi-objective optimisation for master planning in a ceramic supply chain

In this paper, we consider the master planning problem for a centralised replenishment, production and distribution ceramic tile supply chain. A fuzzy multi-objective linear programming (FMOLP) approach is presented which considers the maximisation of the fuzzy gross margin, the minimisation of the fuzzy idle time and the minimisation of the fuzzy backorder quantities. By using an interactive solution methodology to convert this FMOLP model into an auxiliary crisp single-objective linear model, a preferred compromise solution is obtained. For illustration purposes, an example based on modifications of real-world industrial problems is used.     

A dynamic lot sizing problem with multiple customers: customer-specific shipping and backlogging costs

This paper considers a dynamic lot sizing problem faced by a producer who supplies a single product to multiple customers. Characterized by their backorder costs as well as shipping costs, a customer with a high backorder cost has a greater need for the product than a customer with a low backorder cost. We show that the general problem with time-varying customer-dependent backlogging and shipping costs is NP-hard in the strong sense. We then develop an efficient dynamic programming algorithm for an important instance of the problem when there is no speculative motive for backlogging. We also establish forecast horizon results for the case of stationary production and shipping costs, which help the decision maker determine a proper forecast horizon in a rolling-horizon planning process.     

Job-shop like manufacturing system with variable power threshold and operations with power requirements

This paper addresses an important issue in manufacturing by considering the scheduling of a Job-shop like manufacturing system involving a power threshold that must not be exceeded over time. A power profile is attached to operations that must be scheduled. This power profile presents a consumption peak at the start of process in order to model most of real-world machining operations. These operations must be scheduled according to the instantly available power threshold. A mathematical formulation of the problem is proposed; its main goal is to minimise the total completion time of all operations. A set of instances is built based on classical format of instances for the Job-shop problem. As it is time-consuming to obtain exact solutions on these instances with the CPLEX solver, a Greedy Randomised Adaptive Search Procedure hybridised with an Evolutionary Local Search (GRASP × ELS) metaheuristic is designed. The GRASP × ELS is compared with two other metaheuristics: a Variable Neighbourhood Search and a Memetic Algorithm. The GRASP × ELS is also compared with several algorithms developed in the literature for the classical job-shop problem. Results show the relevancy of the metaheuristic approaches both in terms of computational time and quality of solutions.     

考虑补贴水平影响的易逝品动态定价模型

建立了补贴背景下企业对易逝品动态定价的模型,并对其进行分析和求解,得出最优价格和最优期望收益关于补贴水平的一阶和二阶关系,并对企业的最优定价策略和政府对易逝品的补贴水平给出了指导性意见,得到了政府坚持公平原则的动态补贴策略。     

A data reduction method based on the J-integral to obtain the interlaminar fracture toughness in a mode II end-loaded split (ELS) test

Various difficulties arise in the data reduction of the end-loaded split (ELS) test. On one hand, a small Fracture Process Zone (FPZ) at the crack front is assumed in the existing mode II end-loaded split test methodologies based on Linear Elastic Fracture Mechanics (LEFM). However, mode II fracture has been reported to involve large FPZ and a fuzzy crack tip. Furthermore, the ELS test, is usually affected by geometrical non-linearities.This work proposes a closed-form solution based on the J-integral to determine the interlaminar fracture toughness in an ELS test. This solution avoids the need to measure the crack length, and is applicable when a large FPZ is present, as occurs in adhesive bonded joints between CFRP. In addition, because the ELS test involves large vertical deflections, a correction of the formulation for large displacements has been implemented.This new methodology has been compared to other methods available in the literature based on LEFM by means of an experimental campaign of delamination tests using unidirectional CFRP specimens in order to make a first validation of the method.     

Effect of limited capacity on optimal planning parameters for a multi-item production system with setup times and advance demand information

An analytical production/inventory model to optimise the planning parameters lot-size, safety stock and planned lead time is developed for a stochastic single-stage production system with multiple items and limited capacity. Based on queuing analysis, the influence of item specific lot-sizes on the production lead time distribution is modelled. Applying stochastic advance demand information, the expected values for finished-goods-inventory, backorders and service level are explicitly stated. Numerical optimisation is applied to solve the respective cost minimisation problem and a solution heuristic is developed to support this approach. A numerical study provides managerial insights concerning capacity limitation effects on the optimal planning parameters. Higher shop loads, i.e. tighter capacity constraints, are found to significantly increase optimal lot-size and optimal safety stock. Safety stock and planned lead time are substitutes, an increase of both leads to higher FGI and lower backorders, however, the specific trade-off depends on the demand information quality. A sensitivity analysis investigating other (non-) financial system parameters is conducted as well. The main contribution of this paper is that the interaction of different planning parameters, i.e. lot-size, safety stock and planned lead time, for different items is simultaneously studied for a capacity constrained production/inventory system.     

Two-Parameter Approximations For Multi-Echelon Repairable Inventory Models With Batch Ordering Policy

In this paper we present a model for multi-echelon repairable systems with batch ordering policy at the bases. Such an ordering policy is desirable when demand rates and/or the set up cost for ordering are relatively high. Operating characteristics of such a system are analyzed. A two-parameter approximation scheme for the distribution of the number of orders outstanding and consequently backorders is developed, and its performance evaluated. It is found that, under a variety of scenarios including both finite and infinite servers at the repair facility, the approximation scheme is very effective in providing a relatively simple means to determine the stocking levels at both the depot and the bases to minimize the cost of inventory holding and backorders. For the special case when the batch size is one, we confirm the effectiveness of the use of the negative binomial distribution as an approximation for the distribution of orders outstanding, as suggested by recent studies, under a much more general setting.     

带有积压定单的最优模糊存储模型

本文提出一个新的具有积压定单的关于模糊总需求的模糊存储模型。在模糊函数原理下，给出了模糊总存储成本。为了寻找最优解，使用积分均值法白化模糊总存储成本，利用Lingo8．0求解不等式约束问题，我们发现最优解都是确定的实数。此外，当模糊总需求是确定的实数时，我们提出模型的最优解与经典的具有积压定单存储模型具有相同的结果。     

具有有效期易变质品的最优补货策略研究

易变质物品库存管理策略一直是实务界与学术界高度关注的问题,其中具有有效期易变质物品的最优补货策略是研究中的难点。本文研究了有限销售时域内具有有效期易变质物品的库存补货策略,在物品的需求率依赖于物品的库存水平,且物品有效期已知的假设下,本文建立了一个确定易变质物品最优补货策略的优化模型,并给出了具体的求解算法。文章最后给出了数值算例,并对模型中的相关参数作了敏感性分析。