An optimal critical level policy for inventory systems with two demand classes

Traditional inventory systems treat all demands of a given item equally. This approach is optimal if the penalty costs of all customers are the same, but it is not optimal if the penalty costs are different for different customer classes. Then, demands of customers with high penalty costs must be filled before demands of customers with low penalty costs. A commonly used inventory policy for dealing with demands with different penalty costs is the critical level inventory policy. Under this policy demands with low penalty costs are filled as long as inventory is above a certain critical level. If the inventory reaches the critical level, only demands with high penalty costs are filled and demands with low penalty costs are backordered. In this article, we consider a critical level policy for a periodic review inventory system with two demand classes. Because traditional approaches cannot be used to find the optimal parameters of the policy, we use a multidimensional Markov chain to model the inventory system. We use a sample path approach to prove several properties of this inventory system. Although the cost function is not convex, we can build on these properties to develop an optimization approach that finds the optimal solution. We also present some numerical results. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

我国刑罚制度三十年来的回顾与反思

30年来,我国刑罚制度建设取得了多方面的成就：完整的刑罚体系已基本建成;刑罚体系的设置,处处彰显刑罚人道原则;宽严相济的刑罚裁量制度已建立;有利于惩罚和改造的刑罚执行制度也已建立。但是,还存在一些不足,刑罚体系建设、刑罚执行制度、刑罚裁量制度等都有待进一步完善。     

论消防法中责令停产停业处罚的实施主体

消防法中责令停产停业处罚的决定主体应当包括人民政府和公安消防机构。其中 ,重大的责令停产停业处罚的决定主体应当是地方县级以上人民政府而不是公安消防机构。这是由重大的责令停产停业处罚的严厉性、对经济和社会生活影响的重大性、受处罚组织的特殊性以及处罚实施主体权限的法定性决定的 ,也与地方人民政府的行政管理职能相适应 ,并且符合我国的立法例。责令停产停业处罚的执行主体应当是公安消防机构。     

图像恢复中的稳健交替方向乘子法

交替方向乘子法在解决线性逆问题(包括图像恢复)中取得了良好的效果,但是其效果对惩罚参数的选择非常敏感,不利于具体的应用。提出基于惩罚参数自适应选择原理的稳健交替方向乘子法,对其优化条件和收敛性进行了详细分析。实验表明,在基于Parseval紧框架的图像恢复应用中,该算法不但对惩罚参数的选择表现出良好的稳健性,而且效果优于交替方向乘子法,并优于其他目前热门的算法。     

浅析俄罗斯军事刑罚制度对我国的启示

我国军事刑法与俄罗斯军事刑法都分别在本国的普通刑法中用专章加以规定,相似之处很多。在军事刑罚方面,俄罗斯有很多专门针对军人、军事犯罪的特别刑罚很值得我国借鉴。对比中国和俄罗斯两国的军事刑罚,找出我国在军事刑罚方面的不足之处,借鉴俄罗斯军事刑罚制度中的可取之处,完善我国的军事刑罚制度,使之更适应我国军事、国防的发展需要,有利于预防军事、军人犯罪,提高我国军队战斗力。     

有初始间隙弹性摩擦接触问题的罚有限元法

针对三维有初始间隙带摩擦的弹性接触问题,提出了一种新的迭代求解方法——罚有限元法。根据接触问题局部非线性的特点,将接触区域的法向非嵌入条件及切向连续性条件作为罚因子引入系统的总势能泛函中,由最小势能原理,得出了求解有初始间隙带摩擦弹性接触问题的罚有限元公式系统。最后通过两个数值算例验证方法的正确性和有效性。     

A proof for the longest-job-first policy in one-machine scheduling

We consider a one-machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due-date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.     

一起消防行政处罚案件引出的思考

某消防行政处罚案件引起了"可不可以罚"和"怎么罚"的争论,针对这两个问题,对行政处罚的追究时效和《行政处罚法》的溯及力展开论述,并结合该案件进行分析,明确了处罚的方式,为消防执法实践提供了有益的指导。     

A parallel sequencing algorithm for minimizing total cost

The problem of sequencing jobs on parallel processors when jobs have different available times, due dates, penalty costs and waiting costs is considered. The processors are identical and are available when the earliest job becomes available and continuously thereafter. There is a processor cost during the period when the processor is available for processing jobs. The proposed algorithm finds the sequence (or sequences) with minimum total cost (sum of waiting, penalty and processor costs.). A proof of the algorithm and numerical results are given.     

赋予公安派出所消防行政处罚权限的探索

有关法规未明确公安派出所的消防行政执法权限,这在一定程度上影响了公安派出所的消防监督工作。论述了赋予公安派出所消防执法处罚权限的必要性,分析了赋予公安派出所消防执法权限应注意的问题,提出应全面规范公安派出所消防执法处罚权限,以充分发挥其消防监督作用,预防和减少火灾事故的发生。     

A penalty for concave minimization derived from the tuy cutting plane

A wide variety of optimization problems have been approached with branch-and-bound methodology, most notably integer programming and continuous nonconvex programming. Penalty calculations provide a means to reduce the number of subproblems solved during the branch-and-bound search. We develop a new penalty based on the Tuy cutting plane for the nonconvex problem of globally minimizing a concave function over linear constraints and continuous variables. Computational testing with a branch-and-bound algorithm for concave minimization indicates that, for the problems solved, the penalty reduces solution time by a factor ranging from 1.2 to 7.2. © 1994 John Wiley & Sons, Inc.     

Improved convergence rate results for a class of exponential penalty functions

An improved theoretical rate of convergence is shown for a member of the class of exponential penalty function algorithms. We show that the algorithm has a superlinear convergence rate.     

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

We consider a stochastic counterpart of the well-known earliness-tardiness scheduling problem with a common due date, in which n stochastic jobs are to be processed on a single machine. The processing times of the jobs are independent and normally distributed random variables with known means and known variances that are proportional to the means. The due dates of the jobs are random variables following a common probability distribution. The objective is to minimize the expectation of a weighted combination of the earliness penalty, the tardiness penalty, and the flow-time penalty. One of our main results is that an optimal sequence for the problem must be V-shaped with respect to the mean processing times. Other characterizations of the optimal solution are also established. Two algorithms are proposed, which can generate optimal or near-optimal solutions in pseudopolynomial time. The proposed algorithms are also extended to problems where processing times do not satisfy the assumption in the model above, and are evaluated when processing times follow different probability distributions, including general normal (without the proportional relation between variances and means), uniform, Laplace, and exponential. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 531–557, 1997.     

Flexible supply contracts for short life‐cycle goods: The buyer's perspective

In this paper we analyze a two‐period supply contract which allows for order adjustment by the buyer. The buyer is required to place orders for two periods. After observing initial demand, the buyer is then allowed to adjust the second order, paying a per unit order adjustment penalty. We describe the optimal behavior of the buyer under such a contract, both in determining the initial order quantities and in subsequently adjusting the order. We compare the solution to a contract where no adjustment is allowed and to the case where adjustment is allowed without penalty. We demonstrate that flexible contracts can reduce the potentially negative effect of correlation of demand between two periods. Further, we investigate how the duration of the first period vis‐à‐vis the second period affects the profitability of the buyer as a function of the degree of correlation. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 25–45, 2002; DOI 10.1002/nav.10002     

An efficient cyclic coordinate method for optimizing penalty functions

In this study, a simple and efficient cyclic coordinate search procedure is used to optimize penalty functions. Since the contours of the penalty function are very ill-behaved, an accurate line search is very difficult to achieve. Due to accumulated errors in line search, this makes “simple-minded” search directions just as good as more sophisticated directions, and actually better since they require a smaller effort per iteration. Of course this is only true if the search procedure is able to “ride” along steep ridges, and meanwhile move an appreciable distance towards the optimal, if at all possible. Computational results on the cyclic coordinate method seems to support this point of view, and shows robustness, reliability, and efficiency of the method.     

Inducing coordination in supply chains through linear reward schemes

Decentralized decision‐making in supply chain management is quite common, and often inevitable, due to the magnitude of the chain, its geographical dispersion, and the number of agents that play a role in it. But, decentralized decision‐making is known to result in inefficient Nash equilibrium outcomes, and optimal outcomes that maximize the sum of the utilities of all agents need not be Nash equilibria. In this paper we demonstrate through several examples of supply chain models how linear reward/penalty schemes can be implemented so that a given optimal solution becomes a Nash equilibrium. The examples represent both vertical and horizontal coordination issues. The techniques we employ build on a general framework for the use of linear reward/penalty schemes to induce stability in given optimal solutions and should be useful to other multi‐agent operations management settings. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Use of dimensionless ratios to determine minimum-cost inventory quantities

The iteration usually necessary for simultaneous determination of minimum-cost order quantity and reorder point in (Q, r) inventory systems may be eliminated by a graphical technique employing dimensionless ratios. This technique is illustrated for three different types of stock-out penalty.     

具有模糊系数约束的多目标线性规划

研究了一类具有模糊系数约束的多目标线性规划问题.根据各目标函数的梯度方向来量化目标之间的冲突程度,以此提出了一种确定目标权重的新方法,然后基于惩罚函数运用梯度上升算法求问题的有效解.最后给出了一个数值例子.     

Optimal project compression with due-dated events

The paper proposes an algorithm for the determination of the solution of the activities to be shortened and the amount by which they are to be shortened in order to minimize the total cost of project completion. This cost involves a linear penalty for tardienss of a set of key events and a linear cost of activity compression from its normal duration. The procedure is a generalization of the work of Fulkerson.     

Inventory control of a multiproduct system with a limited production resource

Optimal control of the production of several products subject to restricted production resources is considered. Linear production, holding and penalty costs are assumed although this is crucial only for production costs. Excess demand results in lost sales. A single point plays an important role in the definition of the optimal policy.