Optimal maintenance policies with lead times and repair

Maintenance policies with lead times and repair are discussed. We first discuss ordering policy with repair and refer to inspection-ordering policy. In each policy, as a criterion of optimality, we apply cost effectiveness which balances system effectiveness and cost, and obtain the optimal policies. It is shown that, under certain conditions, there exists a finite and unique optimal policy.     

Optimum repair limit policies with a time constraint

In this paper, we discuss the optimum repair limit policies with a time constraint. We apply the expected total discounted cost as a criterion and obtain the optimum policies which minimize it. We show that, under certain conditions, there exists a finite and unique optimum policy. Finally, we present a numerical example using a mixed Weibull distribution.     

Some replacement policies with minimal repairs and repair cost limit

Some extended replacement policies based on the number of failures, incorporating the concept of repair cost limit are discussed. Three models are considered as follows: (a) a unit is replaced at the nth failure, or when the estimated minimal repair cost exceeds a particular limit c; (b) a unit has two types of failures and is replaced at the nth type 1 failure, or type 2 failure, or when the estimated repair cost of type 1 failures exceeds a predetermined limit c—type 1 failures are minimal; failures, type 2 failures are catastrophic failures and both occur with constant probability; (c) a unit has two types of failures and the type 1 and type 2 failures are age dependent—the unit is replaced at the nth type 1 failure, type 2 failure, or when the estimated repair cost due to type 1 failures exceeds a predetermined limit c. Introducing costs due to replacements, inspections, and minimal repairs, an optimal number of minimal repairs before replacement is obtained, which minimizes the expected cost rate. Some particular cases are also derived. Finally, the application of these models to computer science is discussed.     

Comparison of group replacement policies under minimal repair

Three replacement policies for a group of identical units are compared. ( 1 ) Units are periodically replaced all together. Between the periodic group replacements, minimal repairs are performed at failures. ( 2 ) The group replacement interval is divided into repair and waiting intervals. Minimal repairs are performed at failures during the repair interval, but no repair is made in the waiting interval, and the unit remains failed until the group replacement time comes. ( 3 ) Each unit undergoes minimal repair at failure during the repair interval. Beyond the interval, no repair is made until a number of failures. The expected cost rate expressions under each policy are derived. It is shown that the third policy is better economically than the other two policies. Numerical examples are given to demonstrate the results.     

An ordering policy with lead time

An ordering policy in which a working item can be replaced by an item supplied by order with load time is considered. We discuss the optimum ordering policy minimizing the expected cost per unit time for an infinite time span. It is shown in n, theorem that there exists a finite and unique optimum policy under suitable conditions. A sub-optimum policy is also presented.     

Stochastic and fuzzy ordering with the method of minimal transformations

We analyze the methods of stochastic and fuzzy comparison and ordering of random and fuzzy variables. We find simple formulas for computing a number of comparisons and establish the interrelations between various comparisons. We propose and study a new approach to comparing histograms of discrete random (fuzzy) variables based on computing a “directed” minimal transformation that maps one of the compared variables into another. We apply the method of minimal transformations to solving the problem of optimal reduction of discrete random (fuzzy) variables to unimodal form which is considered in the context of ranking the histograms of universities constructed by USE (Unified State Exam) results. We propose a model of “perfect” admission for high school graduates and show that the distribution of admitted graduates to a university in this model will be unimodal under sufficiently general assumptions on the preference function.     

A note on optimal policies for two group scheduling problems with deteriorating setup and processing times

Conventionally, job processing times are known and fixed. However, there are many situations where the job processing time deteriorates as time passes. In this note, we consider the makespan problems under the group technology with deteriorating setup and processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. For both linear functions, we show that the makespan problems remain polynomially solvable. In addition, the constructive algorithms are also provided.     

Single period stochastic inventory problems with ordering or returns policies

In recent years, there has been an increasing adoption of returns policies in the coordination of the supply chain, where market demand is always assumed to be satisfied by manufacturing or by ordering from suppliers. However, many industries face the important decision of how to balance their inventory level. This problem has long been studied in financial institutions such as banks. This study presents an optimal inventory policy under a given stochastic demand such as a uniformly distributed demand, single-item, and single period review inventory system. The optimal inventory control policy obtained in this study is called a four-point policy: that is, when the entity’s inventory level is below a reorder point, the entity must increase his stock level by ordering and order up-to a fixed level (second point); when the entity’s inventory level is over a return point (third point); the stock level must be decreased by returns and decreased to a fixed level (fourth point); otherwise, nothing should be done. We also analyze the (K, S)-convex properties of the inventory cost function.     

Repair-limit risk-free warranty policies with imperfect repair

The current competitive market environment requires manufacturers to continuously provide better service and support. As a result, warranty considerations emerge as a significant instrument for increasing product marketability. In this paper, we propose a new warranty policy, the repair-limit risk-free warranty with a threshold point on the number of repairs, where replacement is deemed to be more cost effective thereafter. Consumers are better off with this than with a traditional free-repair policy since they could be compensated with a new product in case of premature failures. As for the manufacturers, it not only offers extra marketing incentives, but also reduces the possibility of high-cost lawsuits due to the products with "proven" bad quality. Some useful results of the warranty cost of imperfectly repaired products are derived through a censored quasi-renewal process.     

Online scheduling of two job types on a set of multipurpose machines with unit processing times

We study a problem of scheduling a set of n jobs with unit processing times on a set of m multipurpose machines in which the objective is to minimize the makespan. It is assumed that there are two different job types, where each job type can be processed on a unique subset of machines. We provide an optimal offline algorithm to solve the problem in constant time and an online algorithm with a competitive ratio that equals the lower bound. We show that the worst competitive ratio is obtained for an inclusive job-machine structure in which the first job type can be processed on any of the m machines while the second job type can be processed only on a subset of m/2 machines. Moreover, we show that our online algorithm is 1-competitive if the machines are not flexible, i.e., each machine can process only a single job type.     

Coordinating orders in a two echelon supply chain with controllable lead time and ordering cost using the credit period

In this research, a coordination mechanism based on a credit period in a two echelon supply chain with one buyer and one supplier, is designed. The buyer is faced with uncertain demand by coping with normal distribution. Both lead time and ordering cost for receiving his order can be reduced at an added cost; in other words, they are controllable. The optimization models with and without integration are proposed. Then a way to coordinate orders in supply chain based on the credit period so that the total cost of supply chain would be minimized is designed. By using this mechanism we also discuss how the credit period is to be determined in order to achieve channel coordination and a win-win outcome. Finally, numerical examples are solved to illustrate the theoretical results and obtain the managerial insights.     

以最小换乘次数和站数为目标的公交出行算法

提供两点乘车的最优公交路径是ATIS的核心功能。文中建立了以最小换乘次数为第一目标,最小途经站数为第二目标的公交出行最优路径模型。提出了可行路径的最小换乘次数动态规划算法,依此确定换乘次数上界;设计了搜索算法确定最优公交线路序列,分析了线路相交的四种情况,给出了换乘点选择方法,由公交线路序列和换乘点共同组成最优路径。     

Reverse logistics network design with stochastic lead times

This work is concerned with the efficient design of a reverse logistics network using an extended version of models currently found in the literature. Those traditional, basic models are formulated as mixed integer linear programs (MILP-model) and determine which facilities to open that minimize the investment, processing, transportation, disposal and penalty costs while supply, demand and capacity constraints are satisfied. However, we show that they can be improved when they are combined with a queueing model because it enables to account for (1) some dynamic aspects like lead time and inventory positions, and (2) the higher degree of uncertainty inherent to reverse logistics. Since this extension introduces nonlinear relationships, the problem is defined as a mixed integer nonlinear program (MINLP-model). Due to this additional complexity, the MINLP-model is presented for a single product-single-level network. Several examples are solved with a genetic algorithm based on the technique of differential evolution.     

带有两次订购机会且两阶段需求相关的Newsboy模型

首先建立需求形式为一般随机变量情形下零售商的两次订购决策模型,并从理论上证明了在两个阶段需求相互独立情形下,零售商期望利润函数的下凹性及最优订购策略的存在唯一性,从而弥补了已有模型在寻求最优订购策略时采用数值方法所存在的缺憾;然后,建立两阶段需求相关情形下带有两次订购的Newsboy模型,给出了模型的分析解.数值实例验证了模型的求解过程,并得到了相关管理启示.     

Optimal ordering decision for deteriorating items with expiration date and uncertain lead time

The ordering policy for the retailers and the suppliers is a function of deterioration, product expiration date, the supplier’s uncertain lead time, available capital constraint and the retailer’s seasonal pattern demand. We develop a deteriorating inventory replenishment model of the system and present an algorithm to derive the retailer’s optimal replenishment cycle, shortage period, order quantity and the supplier’s managing cost. Numerical example and sensitivity analysis are given to illustrate the model.     

Echelon stock formulation for multi-stage lot-sizing with component lead times

Material requirements planning of batch production in multi-stage manufacturing systems is discussed where component parts may have significant non-zero production or purchasing lead time. The presence of such lead time poses a synchronization problem for the rolling horizon planning of component part production in the system. The synchronization problem is analysed, discussed and modelled first for the case of assembly product structures where a component has a unique successor component. The analysis is then extended to the more complex case of general product structures where a component may have multiple successor components. The associated general structure multi-stage lot-sizing problem is then formulated as a mixed integer linear program first in terms of conventional stock, and then reformulated in terms of echelon stock. The echelon stock quantity of a component is its lead-time adjusted total system stock, counted both as a stand-alone component and as part of successor components. The echelon stock formulation permits the derivation of valid inequalities that can be used in an optimal solution method, and facilitates the development of a fast heuristic method for the capacitated problem     

Optimum sweeps of simple polygons with two guards

A polygon P admits a sweep if two mobile guards can detect an unpredictable, moving target inside P  , no matter how fast the target moves. Two guards move on the polygon boundary and are required to always be mutually visible. The objective of this study is to find an optimum sweep such that the sum of the distances travelled by the two guards in the sweep is minimized. We present an O(n²)$O(n^2)$ time and O(n)$O(n)$ space algorithm for optimizing this metric, where n   is the number of vertices of the given polygon. Our result is obtained by reducing this problem to finding a shortest path between two nodes in a graph of size O(n)$O(n)$.     

Balancing stocks and backlogs with stochastic lead times: A special case

The paper gives compact, finite horizon and asymptotic results concerning an inventory system, that allows backlogging, with constant demand and costs but stochastic lead times, not necessarily i.i.d., under two special conditions. The special conditions are: (1) no crossovers of orders; (2) there are both shortage and stock build-up between any two consecutive orders. It is shown that the minimal total expected cost, namely, of holding inventory, shortages and replenishments, as well as the optimal replenishment times depend, among other parameters, only on the lead time variances as representatives of the stochastic component of the model. The results are direct extensions of the deterministic EOQ model and lend themselves to tractable sensitivity analysis. Further possible developments are discussed.     

Consistency and repair for XML write-access control policies

XML access control policies involving updates may contain security flaws, here called inconsistencies, in which a forbidden operation may be simulated by performing a sequence of allowed operations. This article investigates the problem of deciding whether a policy is consistent, and if not, how its inconsistencies can be repaired. We consider total and partial policies expressed in terms of annotated schemas defining which operations are allowed or denied for the XML trees that are instances of the schema. We show that consistency is decidable in PTIME for such policies and that consistent partial policies can be extended to unique least-privilege consistent total policies. We also consider repair problems based on deleting privileges to restore consistency, show that finding minimal repairs is NP-complete, and give heuristics for finding repairs. Finally, we experimentally evaluate these algorithms in comparison with an exact approach based on answer-set programming.     

Estimating order lead times in hybrid flowshops with different scheduling rules

In this study, we consider a problem of estimating order lead time in hybrid flowshops, where orders arrive dynamically. When an order arrives at the shop, the time duration between the arrival and completion (i.e., lead time) of the order is to be estimated. For good estimation, not only the order specification and the inventory status but also the scheduling method used in the shop should be taken into account. In this study, we consider three most common dispatching rules, i.e., FCFS, EDD, and SPT, for the shop scheduling, and develop three distinct estimation methods for the corresponding dispatching rules. A series of computational experiments were carried out and the results show that the proposed methods outperform the existing benchmarks in terms of two accuracy measures.