Schedule design for liner services under vessel speed reduction incentive programs

Gas and particulate emissions from ship transportation have been increasing in recent years. In order to mitigate ship emissions near coastal areas, voluntary vessel speed reduction incentive programs (VSRIPs) were put in place by a number of ports. This paper studies a schedule design problem faced by liner shipping companies under VSRIPs. It proposes a mixed-integer nonlinear mathematical model for the minimization of the total cost, consisting of fuel cost, as well as operating cost, minus dockage refunds. The model balances three determinants, that is, the compliance of VSRIPs, the speed limit (the maximum physical speed of ships and the upper speed limit imposed by VSRIPs), and the limited number of ships. An enumerative algorithm and a piecewise-linear approximation algorithm are developed, based on some properties of the nonlinear model. The efficiency of the proposed algorithms is validated through extensive computational experiments.     

Vessel allocation by linear programming

This paper presents a linear programming model of a fleet of vessels which is required to transport quantities of cargo, such as coal, iron ore, limestone, and salt from certain producing ports to specific destination ports. This model has been implemented and is currently being used both for planning purposes and as an aid in scheduling the trips to be made by each vessel.     

On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles

Given a number of patrollers that are required to detect an intruder in a channel, the channel patrol problem consists of determining the periodic trajectories that the patrollers must trace out so as to maximized the probability of detection of the intruder. We formulate this problem as an optimal control problem. We assume that the patrollers' sensors are imperfect and that their motions are subject to turn‐rate constraints, and that the intruder travels straight down a channel with constant speed. Using discretization of time and space, we approximate the optimal control problem with a large‐scale nonlinear programming problem which we solve to obtain an approximately stationary solution and a corresponding optimized trajectory for each patroller. In numerical tests for one, two, and three underwater patrollers, an underwater intruder, different trajectory constraints, several intruder speeds and other specific parameter choices, we obtain new insight—not easily obtained using simply geometric calculations—into efficient patrol trajectory design under certain conditions for multiple patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Primal dual algorithms for the vehicle refueling problem

Mehrez, Stern, and Ronen have defined a vehicle refueling problem in which a fleet of vehicles travels on a round-trip, self-contained mission from a common origin, with the objective of maximizing the operational range of the fleet. They have defined a “pure refueling chain” strategy for transferring fuel between vehicles in the fleet, and have solved the problem in the special cases when all vehicles have the same fuel capacity or consumption rate. In this article we present algorithms for the general case, where vehicles have different capacities and consumption rates. Our approach is based on a new primal dual formulation of the problem. The exact algorithm was effective to find the optimal solution for a fleet size n ⩽13. For larger fleets, we present an approximation version of it, which very quickly found a solution within 1% of the maximum possible range for arbitrarily large (up to n = 200) fleets. We also show that a small number of the best vehicles can always reach almost the same range as a large fleet. © 1992 John Wiley & Sons, Inc.     

Allocation policies and cost approximations for multilocation inventory systems

Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty-cost/holding-cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem. Each approach provides both a near-optimal order policy and an approximation of the optimal cost of the original problem. In addition, simple but effective allocation policies are discussed.     

Modeling and solution for the ship stowage planning problem of coils in the steel industry

We consider a ship stowage planning problem where steel coils with known destination ports are to be loaded onto a ship. The coils are to be stowed on the ship in rows. Due to their heavy weight and cylindrical shape, coils can be stowed in at most two levels. Different from stowage problems in previous studies, in this problem there are no fixed positions on the ship for the coils due to their different sizes. At a destination port, if a coil to be unloaded is not at a top position, those blocking it need to be shuffled. In addition, the stability of ship has to be maintained after unloading at each destination port. The objective for the stowage planning problem is to minimize a combination of ship instability throughout the entire voyage, the shuffles needed for unloading at the destination ports, and the dispersion of coils to be unloaded at the same destination port. We formulate the problem as a novel mixed integer linear programming model. Several valid inequalities are derived to help reducing solution time. A tabu search (TS) algorithm is developed for the problem with the initial solution generated using a construction heuristic. To evaluate the proposed TS algorithm, numerical experiments are carried out on problem instances of three different scales by comparing it with a model‐based decomposition heuristic, the classic TS algorithm, the particle swarm optimization algorithm, and the manual method used in practice. The results show that for small problems, the proposed algorithm can generate optimal solutions. For medium and large practical problems, the proposed algorithm outperforms other methods. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 564–581, 2015     

Resource allocation with lumpy demand: To speed or not to speed?

In the classical EPQ model with continuous and constant demand, holding and setup costs are minimized when the production rate is no larger than the demand rate. However, the situation may change when demand is lumpy. We consider a firm that produces multiple products, each having a unique lumpy demand pattern. The decision involves determining both the lot size for each product and the allocation of resources for production rate improvements among the products. We find that each product's optimal production policy will take on only one of two forms: either continuous production or lot‐for‐lot production. The problem is then formulated as a nonlinear nonsmooth knapsack problem among products determined to be candidates for resource allocation. A heuristic procedure is developed to determine allocation amounts. The procedure decomposes the problem into a mixed integer program and a nonlinear convex resource allocation problem. Numerical tests suggest that the heuristic performs very well on average compared to the optimal solution. Both the model and the heuristic procedure can be extended to allow the company to simultaneously alter both the production rates and the incoming demand lot sizes through quantity discounts. Extensions can also be made to address the case where a single investment increases the production rate of multiple products. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Location-allocation for distribution to a uniform demand with transshipments

This article analyzes the location-allocation problem for distribution from a single fixed origin via transshipment terminals to a continuous uniformly distributed demand. Distribution through terminals concentrates flows on the origin-to-terminal links and transportation economies of scale encourage the use of larger vehicles. Analytical expressions are derived for the optimal terminal locations, the optimal allocation of destinations to terminals, and the optimal transportation cost. Continuous analytic models assume either an allocation, by partitioning the service region into sectors, or terminal locations. This is unlikely to produce an optimal distribution system. The optimal cost is compared to the cost for suboptimal location-allocation combinations. Results indicate that the location decision is not too important if destinations are allocated optimally and that allocation to the nearest terminal may be poor, even with optimal locations. © 1992 John Wiley & Sons, Inc.     

Minimizing logistic costs in multistage supply chains

We consider the problem in which a set of products has to be shipped from a common origin to a common destination through one or several intermediate nodes with the objective of minimizing the sum of inventory and transportation costs when a set of possible shipping frequencies is given on each link. From the theoretical point of view, the main issue is the computation of the inventory cost in the intermediate nodes. From the computational point of view, given that the simpler single link problem is known to be NP-hard, we present four classes of heuristic algorithms. The first two classes are based on the decomposition of the sequence in links, the third class on the adaptation of the EOQ-type solution known for the continuous case, and the fourth on the optimal solution of a simpler problem through dynamic programming techniques. Finally, we compare them on a set of randomly generated problem instances. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 399–417, 1999     

软件构件可靠性与费用分配最优模型

针对软件构件可靠性和费用分配问题,给出一种可靠性和费用分配最优模型。文中将软件系统可靠性定义为软件构件失效密度、操作剖面、构件使用矩阵以及软件无失效运行时间的函数,描述了费用最优模型的建立和利用非线性规划理论求解模型的步骤,有效地处理了带有复杂计算的目标函数和约束条件的可靠性和费用最优分配问题。计算实例表明,利用该模型进行可靠性和费用分配是可行的。     

Determination of the optimal investment in end products and repair resources

This paper demonstrates how to determine the minimal cost combination of end products and repair service capability in order to maintain a given level of operating end products. It is shown that the general rule for optimal resource allocation requires simply that the absolute value of the marginal factor cost of repair services divided by the marginal factor cost of end products be equal to the arrival rate of end products to repair. The model is applied to the problem of determining the resources required to support an operating level of Navy F-4 aircraft.     

基于非对称balls-into-bins的高效平衡负载分配模型

在大规模数据中心和P2P覆盖网络等复杂网络负载平衡分配中,前人提出了多种多样的负载分配方法,但许多方法为了达到更好的平衡负载指标,追求越来越复杂的算法,使得时间复杂度和算法复杂度很难控制在合理的范围之内。本文在研究了经典balls-into-bins、Azar balls-into-bins和balls into non-uniformbins等模型的基础上,提出了一种新颖高效的非对称balls-into-bins平衡负载分配模型,该模型具有异构的balls、异构的bins,以及不同的bin选择概率,能以很高的概率将最大负载均衡地控制在合理的范围内,通信负载很小,且具有很好的可扩展性,通过拓展,该模型在负载平衡的诸多领域都将有广阔的应用空间。     

A multifaceted heuristic for the orienteering problem

The orienteering problem involves the selection of a path between an origin and a destination which maximizes total score subject to a time restriction. In previous work we presented an effective heuristic for this NP-hard problem that outperformed other heuristics from the literature. In this article we describe and test a significantly improved procedure. The new procedure is based on four concepts—center of gravity, randomness, subgravity, and learning. These concepts combine to yield a procedure which is much faster and which results in more nearly optimal solutions than previous procedures.     

Optimal replacement of military aircraft: an economic approach

A nonlinear optimization model is developed in this paper to identify the optimal replacement strategy for military aircraft. In the model, the aircraft operating and maintenance (O&M) costs per available year are estimated as a function of age during the aircraft life cycle. After determining the optimal replacement policy, the model is applied to the CF Long-Range Patrol CP-140A Arcturus fleet. A sensitivity analysis is also carried out to assess the impact of some key model parameters on the result.     

A branch and bound algorithm for allocation problems in which constraint coefficients depend upon decision variables

A branch and bound algorithm is developed for a class of allocation problems in which some constraint coefficients depend on the values of certain of the decision variables. Were it not for these dependencies, the problems could be solved by linear programming. The algorithm is developed in terms of a strategic deployment problem in which it is desired to find a least-cost transportation fleet, subject to constraints on men/materiel requirements in the event of certain hypothesized contingencies. Among the transportation vehicles available for selection are aircraft which exhibit the characteristic that the amount of goods deliverable by an aircraft on a particular route in a given time period (called aircraft productivity and measured in kilotons/aircraft/month) depends on the ratio of type 1 to type 2 aircraft used on that particular route. A model is formulated in which these relationships are first approximated by piecewise linear functions. A branch and bound algorithm for solving the resultant nonlinear problem is then presented; the algorithm solves a sequence of linear programming problems. The algorithm is illustrated by a sample problem and comments concerning its practicality are made.     

Optimal strategies for problems of simultaneous attack against an area defense without impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker. The defense has no impact-point prediction; that is, it has no knowledge of any attacker's destination prior to allocation of area interceptors. For a given attack, the defense wishes to allocate its interceptors to maximize the total expected survival value of the targets. For a given attack size, the offense seeks a strategy to minimize total expected surviving value against best defense. We determine an optimal defensive strategy directly and develop an algorithm to determine an optimal attack and the optimal value of the min-max problem. A dynamic programming technique is used to obtain integer solutions, and illustrative computational results are provided.     

Lagrangian relaxation approach to the targeting problem

In this paper, we consider a new weapon–target allocation problem with the objective of minimizing the overall firing cost. The problem is formulated as a nonlinear integer programming model. We applied Lagrangian relaxation and a branch‐and‐bound method to the problem after transforming the nonlinear constraints into linear ones. An efficient primal heuristic is developed to find a feasible solution to the problem to facilitate the procedure. In the branch‐and‐bound method, three different branching rules are considered and the performances are evaluated. Computational results using randomly generated data are presented. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 640–653, 1999     

防空监视网络传感器资源分配的最优化

针对防空监视网络的传感器管理问题,讨论了传感器资源分配的最优化方法。提出了把传感器资源分配问题映射为多代理系统分布约束最优化问题的解决策略,设计了基于约束代价下界搜索的异步分枝定界最优化算法,实现了传感器资源分配问题最优解的异步并行搜索,给出的仿真实例说明了传感器资源分配最优化方法的有效性。     

An interactive optimization system for bulk-cargo ship scheduling

This article considers the efficient scheduling of a fleet of ships engaged in pickup and delivery of bulk cargoes. Our optimization system begins by generating a menu of candidate schedules for each ship. This menu can contain all feasible solutions, which guarantees we will find an optimal solution or can be heuristically limited to contain only those schedules likely to be in an optimal solution. The problem of choosing from this menu an optimal schedule for the fleet is formulated as a set-packing problem and solved with a dual algorithm. Computational experience is presented based on real data obtained from the Military Sealift Command of the U. S. Navy. Run times for this data were reasonable and solutions were generated with the potential of saving up to about $30 million per year over the manual system currently in place. We also describe a color-graphics interface developed to facilitate interaction with the optimization system.     

On the manipulation of transfer prices in a static environment

In a static environment, J. Hirschleifer's marginal cost solution to the transfer pricing problem is commonly accepted as analytically correct. However, actual pricing practice within Western corporations and socialist-planned economies generally deviates from marginal cost pricing. Some form of average cost pricing is more commonly chosen. Recently in this journal, H. Enzer has claimed to show that some form of average cost pricing is indeed the analytically correct solution to the transfer pricing problem when choice of technique and manipulation are allowed. Enzer claims that optimal decisions made by each of two divisions according to their individual self-interests are made compatible with overall firm optimization when the transfer price assigned to the internally-transferred commodity is any form of average cost. We show that the marginal cost solution is correct for Enzer's problem in the absence of manipulation by either division. Indeed, this was all that Hirschleifer claimed. In the process, we uncover a fundamental mathematical error in Enzer's argument. When manipulation of the transfer price by divisions is allowed, we demonstrate the faults with Enzer's average cost solution and conclude Hirschleifer's original statements on manipulation to be correct even in Enzer's environment. A final section briefly indicates the importance to the transfer pricing problem of a growing body of economic literature on incentive structures.