Finding the Kth shortest path in a time‐schedule network

We consider the problem of finding the Kth shortest path for a time‐schedule network, where each node in the network has a list of prespecified departure times, and departure from the node can take place only at one of these departure times. We develop a polynomial time algorithm independent of K for finding the Kth shortest path. The proposed algorithm constructs a map structure at each node in the network, using which we can directly find the Kth shortest path without having to enumerate the first K − 1 paths. Since the same map structure is used for different K values, it is not necessary to reconstruct the table for additional paths. Consequently, the algorithm is suitable for directly finding multiple shortest paths in the same network. Furthermore, the algorithm is modified slightly for enumerating the first K shortest paths and is shown to have the lowest possible time complexity under a condition that holds for most practical networks. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Decomposition algorithms for minimal cut problems

Consider a network G(N. A) with n nodes, where node 1 designates its source node and node n designates its sink node. The cuts (Z_i, =), i= 1…, n - 1 are called one-node cuts if 1 ? Z_i,. n q Z_i, Z₁-_? {1}, Z_i ? Z_i+1 and Z_i and Z_i+l differ by only one node. It is shown that these one-node cuts decompose G into 1 m n/2 subnetworks with known minimal cuts. Under certain circumstances, the proposed one-node decomposition can produce a minimal cut for G in 0(n² ) machine operations. It is also shown that, under certain conditions, one-node cuts produce no decomposition. An alternative procedure is also introduced to overcome this situation. It is shown that this alternative procedure has the computational complexity of 0(n³).     

The probability of the existence of a feasible flow in a stochastic transportation network

Stochastic transportation networks arise in various real world applications, for which the probability of the existence of a feasible flow is regarded as an important performance measure. Although the necessary and sufficient condition for the existence of a feasible flow represented by an exponential number of inequalities is a well‐known result in the literature, the computation of the probability of all such inequalities being satisfied jointly is a daunting challenge. The state‐of‐the‐art approach of Prékopa and Boros, Operat Res 39 (1991) 119–129 approximates this probability by giving its lower and upper bounds using a two‐part procedure. The first part eliminates all redundant inequalities and the second gives the lower and upper bounds of the probability by solving two well‐defined linear programs with the inputs obtained from the first part. Unfortunately, the first part may still leave many non‐redundant inequalities. In this case, it would be very time consuming to compute the inputs for the second part even for small‐sized networks. In this paper, we first present a model that can be used to eliminate all redundant inequalities and give the corresponding computational results for the same numerical examples used in Prékopa and Boros, Operat Res 39 (1991) 119–129. We also show how to improve the lower and upper bounds of the probability using the multitree and hypermultitree, respectively. Furthermore, we propose an exact solution approach based on the state space decomposition to compute the probability. We derive a feasible state from a state space and then decompose the space into several disjoint subspaces iteratively. The probability is equal to the sum of the probabilities in these subspaces. We use the 8‐node and 15‐node network examples in Prékopa and Boros, Operat Res 39 (1991) 119–129 and the Sioux‐Falls network with 24 nodes to show that the space decomposition algorithm can obtain the exact probability of these classical examples efficiently. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 479–491, 2016     

Pricing bridges to cross a river

We consider a pricing problem in directed, uncapacitated networks. Tariffs must be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs in the network are assumed to be given. There are n clients, the followers, and after the tariffs have been determined, the clients route their demands independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by applications in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX‐hard. Moreover, we analyze the effect of uniform pricing, proving that it yields both an m approximation and a (1 + lnD)‐approximation. Here, D is upper bounded by the total demand of all clients. In addition, we consider the problem under the additional restriction that the operator must not reject any of the clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless P = NP, and we prove the existence of an n‐approximation algorithm. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

We consider a multi‐stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118–138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system‐wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T²) algorithm for the single‐stage dynamic lot sizing problem; (2) an O(T³) algorithm for the case of a single‐warehouse single‐retailer system; and (3) a nested shortest‐path algorithm for the single‐warehouse multi‐retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single‐stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Minimal disconnecting sets in directed multi-commodity networks

The problem of finding minimal disconnecting sets for multi-commodity directed networks may be solved using an arc-path formulation and Gomory's all-integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.     

On the uncapacitated K‐commodity network design problem with zero flow‐costs

Extending Sastry's result on the uncapacitated two‐commodity network design problem, we completely characterize the optimal solution of the uncapacitated K‐commodity network design problem with zero flow costs for the case when K = 3. By solving a set of shortest‐path problems on related graphs, we show that the optimal solutions can be found in O(n³) time when K = 3, where n is the number of nodes in the network. The algorithm depends on identifying a list of “basic patterns”; the number of basic patterns grows exponentially with K. We also show that the uncapacitated K‐commodity network design problem can be solved in O(n³) time for general K if K is fixed; otherwise, the time for solving the problem is exponential. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A decomposable transshipment algorithm for a multiperiod transportation problem

A dynamic version of the transportation (Hitchcock) problem occurs when there are demands at each of n sinks for T periods which can be fulfilled by shipments from m sources. A requirement in period t₂ can be satisfied by a shipment in the same period (a linear shipping cost is incurred) or by a shipment in period t₁ < t₂ (in addition to the linear shipping cost a linear inventory cost is incurred for every period in which the commodity is stored). A well known method for solving this problem is to transform it into an equivalent single period transportation problem with mT sources and nT sinks. Our approach treats the model as a transshipment problem consisting of T, m source — n sink transportation problems linked together by inventory variables. Storage requirements are proportional to T² for the single period equivalent transportation algorithm, proportional to T, for our algorithm without decomposition, and independent of T for our algorithm with decomposition. This storage saving feature enables much larger problems to be solved than were previously possible. Futhermore, we can easily incorporate upper bounds on inventories. This is not possible in the single period transportation equivalent.     

An extension of the (szwarc) truck assignment problem

In this journal in 1967. Szware presented an algorithm for the optimal routing of a common vehicle fleet between m sources and n sinks with p different types of commodities. The main premise of the formulation is that a truck may carry only one commodity at a time and must deliver the entire load to one demand area. This eliminates the problem of routing vehicles between sources or between sinks and limits the problem to the routing of loaded trucks between sources and sinks and empty trucks making the return trip. Szwarc considered only the transportation aspect of the problem (i. e., no intermediate points) and presented a very efficient algorithm for solution of the case he described. If the total supply is greater than the total demand, Szwarc shows that the problem is equivalent to a (mp + n) by (np + m) Hitchcock transportation problem. Digital computer codes for this algorithm require rapid access storage for a matrix of size (mp + n) by (np + m); therefore, computer storage required grows proportionally to p². This paper offers an extension of his work to a more general form: a transshipment network with capacity constraints on all arcs and facilities. The problem is shown to be solvable directly by Fulkerson's out-of-kilter algorithm. Digital computer codes for this formulation require rapid access storage proportional to p instead of p². Computational results indicate that, in addition to handling the extensions, the out-of-kilter algorithm is more efficient in the solution of the original problem when there is a mad, rate number of commodities and a computer of limited storage capacity.     

Production-allocation scheduling and capacity expansion using network flows under uncertainty

This paper extends Connors and Zangwill's work in network flows under uncertainty to the convex costs case. In this paper the extended network flow under uncertainty algorithm is applied to compute N-period production and delivery schedules of a single commodity in a two-echelon production-inventory system with convex costs and low demand items. Given an initial production capacity for N periods, the optimal production and delivery schedules for the entire N periods are characterized by the flows through paths of minimal expected discounted cost in the network As a by-product of this algorithm the multi-period stochastic version of the parametric budget problem for the two-echelon production-inventory system is solved.     

Decomposition algorithms for the maximum-weight connected graph problem

Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph problem (MCG) is to find a connected subgraph with R vertices that maximizes the sum of their weights. MCG has applications to communication network design and facility expansion. The constrained MCG (CMCG) is MCG with a constraint that one predetermined vertex must be included in the solution. In this paper, we introduce a class of decomposition algorithms for MCG. These algorithms decompose MCG into a number of small CMCGs by adding vertices one at a time and building a partial graph. They differ in the ordering of adding vertices. Proving that finding an ordering that gives the minimum number of CMCGs is NP-complete, we present three heuristic algorithms. Experimental results show that these heuristics are very effective in reducing computation and that different orderings can significantly affect the number of CMCGs to be solved. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 817–837, 1998     

高速SpaceFibre总线节点的系统设计

为了实现SpaceFibre总线节点的高效数据传输,针对网络协议中关键问题和技术提出了一种基于现场可编程门阵列(Field Programmable Gate Array,FPGA)的SpaceFibre总线节点系统设计方案。其中,采用了轮询仲裁算法,解决了多路虚拟通道中流量控制字的申请冲突;设计了基于服务质量机制的高效处理状态机,实现了多路虚拟通道的服务质量调度;提出了一种并行的分区存储架构和重发控制算法,实现了基于错误检测隔离恢复机制的错误恢复;采用了不同的数据并行处理方案,实现了多种数据格式的循环冗余校验和伪随机序列的计算。通过ModelSim仿真平台对节点系统进行功能仿真,并在Virtex-6 FPGA上完成了系统验证。结果表明,该设计实现了SpaceFibre总线节点的功能,串行传输速度可达3.125 Gbit/s,能够满足高速数据传输需求。     

Evaluating cost and reliability integrated performance of stochastic logistics systems

The significance of integrating reliability into logistics performance has been established [The Logistics Performance Index and Its Indicators, World Bank International Trade and Transport Departments, (2010)]. Hence, as a response to the work by the World Bank, the present article aims to evaluate the performance index R_b,d of logistics systems as the probability that a specified demand d can be distributed successfully through multistate arc capacities from the source to the destination under the constraint that the total distribution cost should not exceed the cost limitation b. This article provides a pioneering approach for a straightforward computation of the performance index R_b,d. The proposed algorithm is a hybrid between the polynomial time capacity‐scaling algorithm, which was presented by Edmonds and Karp [JACM 19 (1972)], and the decomposition algorithm, which was presented by Jane and Laih [IEEE (2008)]. Currently, the proposed approach is the only algorithm that can directly compute R_b,d. An illustration of the proposed algorithm is presented. The results of the computational experiments indicate that the presented algorithm outperforms existing algorithms. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

协同作战中信息分发算法研究

大规模协同作战中的高效通信问题为当前信息战的研究重点之一,但由于单独作战单元无法了解全局的信息内容及需求方,这给通信资源有限的参战兵力之间的态势共享带来了困难。为此提出了一个分布式协作信息分发算法,在理论上借鉴了复杂网络的小世界特性,即单元节点可以通过邻节点在较少跳数内完成信息的传输。在思路上利用了信息相关性概念,作战单元利用信息之间的关联性及信息与节点之间的收发关系建立控制信息发送的路由表。并通过仿真实验验证了不同网络拓扑下算法性能的变化情况,结果证明分发算法能较好地支持信息共享。     

A note on combined job selection and sequencing problems

We investigate the solvability of two single‐machine scheduling problems when the objective is to identify among all job subsets with cardinality k,1≤k≤n, the one that has the minimum objective function value. For the single‐machine minimum maximum lateness problem, we conclude that the problem is solvable in O(n²) time using the proposed REMOVE algorithm. This algorithm can also be used as an alternative to Moore's algorithm to solve the minimum number of tardy jobs problem by actually solving the hierarchical problem in which the objective is to minimize the maximum lateness subject to the minimum number of tardy jobs. We then show that the REMOVE algorithm cannot be used to solve the general case of the single‐machine total‐weighted completion time problem; we derive sufficient conditions among the job parameters so that the total weighted completion time problem becomes solvable in O(n²) time. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 449–453, 2013     

The procurement problem: An integer programming problem well suited to a solution using duality

A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.     

An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

A single server is faced with a collection of jobs of varying duration and urgency. Each job has a random lifetime during which it is available for nonpreemptive service. Should a job's lifetime expire before its service begins then it is lost from the system unserved. The goal is to schedule the jobs for service to maximize the expected number served to completion. Two heuristics have been proposed in the literature. One (labeled π^S) operates a static priority among the job classes and works well in a “no premature job loss” limit, whereas the second (π^M) is a myopic heuristic which works well when lifetimes are short. Both can exhibit poor performance for problems at some distance from the regimes for which they were designed. We develop a robustly good heuristic by an approximative approach to the application of a policy improvement step to the asymptotically optimal heuristic π^S, in which we use a fluid model to obtain an approximation for the value function of π^S. The performance of the proposed heuristic is investigated in an extensive numerical study. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

一种面向节点定位的移动信标动态路径规划方法

针对基于移动信标的传感器节点定位问题,提出一种基于在线决策的移动信标动态路径规划方法.针对以往算法大都只适用于节点均匀分布的局限,该方法用移动信标不断获取两跳范围内的未定位节点数目,并向最大覆盖未定位节点方向移动,不需要网络先验信息,即可实现路径的优化.仿真结果表明:与传统方法相比,该方法无需网络的先验信息,在移动路径长度上具有明显优越性,减少了信标的能量消耗,更适用于户外部署的大规模传感器网络.     

合作定位节点选择策略

合作定位是指接收机之间通过合作网络交换关键定位信息实现协同定位的新技术,接收机进行合作定位过程中可供使用的辅助节点包括可视卫星和已定位邻居接收机。接收机之间的合作增加定位过程中的可用辅助节点数量,进而增加位置估计的计算量和计算时间,在可用辅助节点较多时,定位实时性很难得到保证。提出改进次优节点选择算法,计算备选节点之间单位向量差作为节点价值,选择拥有最大价值的节点作为辅助节点。将新算法与4种典型的节点选择算法进行了对比,仿真实验证明该算法能够在较短时间内选择出接近最优算法得到的组合,综合性能优于现有节点选择算法。     

Machine sequencing: Disjunctive graphs and degree-constrained subgraphs

In two earlier papers, we proposed algorithms for finding an optimal sequence of processing m items on q machines, by finding a minimaximal path in a disjunctive network. In a third paper, this latter model was generalized (from 2-state to 3-state disjunctive graphs) so as to accommodate project scheduling with resource constraints. In this paper, we discuss another algorithm for the (2-state) disjunctive network problem, closely related to those mentioned above. To make the paper self-contained, section 2 briefly describes the problem. Section 3 introduces a class of constraints which forms the basis of the algorithm discussed in section 4. The constraints have only 1, ?1, or 0 as coefficients on the left-hand side, integers on the right-hand side. The whole procedure of generating these constraints and finding a feasible solution whenever a new constraint is added, can be interpreted (section 5) as a process of generating a graph with degree-constraints on its nodes, and then finding a subgraph satisfying the degree-constraints. The nodes of the graph are generated by solving a critical-path-problem, the feasible subgraphs are found by implicit enumeration.