A cross entropy-Lagrangean hybrid algorithm for the multi-item capacitated lot-sizing problem with setup times

The aim of this article is to introduce a hybrid algorithm for the multi-item multi-period capacitated lot-sizing problem with setups. In this problem, demands over a finite planning horizon must be met, where several items compete for space with limited resources in each period, and a portion of these resources is used by setups. The proposed scheme considers a Lagrangean relaxation of the problem and applies a cross entropy-based metaheuristic to the uncapacitated version of the original problem. A thorough experimental plan has been designed and implemented to test the effectiveness and the robustness of the algorithm: first, drawing inspiration from the response surface methodology, we calibrate the algorithm by identifying the optimal parameters value for any given instance size. Next, we carry out experiments on large scale instances, collecting information about solution quality and computational time, and comparing these results with those offered by a global optimizer.     

Analysis of a dynamic lot‐sizing problem with production capacity constraint

We study a capacitated dynamic lot‐sizing problem with special cost structure involving setup cost, freight cost, production cost, and inventory holding cost. We investigate two cases of the problem categorized by whether the maximal production capacity in one period is an integral multiple of the capacity of a container and reveal the special structure of an optimal solution for each case. In the case where the maximal production capacity is an integral multiple of a container's capacity, the T‐period problem is solved using polynomial effort by a network algorithm. For the other case, the problem is transformed into a shortest path problem, and a network‐based algorithm combining dynamic programming is proposed to solve it in polynomial time. Numerical examples are presented to illustrate application of the algorithms to solve the two cases of the problem.     

The capacitated dynamic lot size problem with variable technology

Traditionally, the technological coefficients in production models were assumed to be fixed. In recent years however, researchers have used the learning curve model to represent nonlinear technological coefficients, and the dynamic lot-sizing problem with learning in setups has received attention. This article extends the research to consider capacity restrictions in the single-level, multi-item case. The research has two goals, first, to analyze the effects of setup learning on a production schedule, and second, to investigate efficient ways of solving the resulting nonlinear integer model. Previously derived algorithms do not address the issue of capacity; thus a heuristic is developed and its solution is compared with the optimal solution, where possible, or to a lower bound solution.     

The multi-item capacitated lot-sizing problem with safety stocks and demand shortage costs

We address a multi-item capacitated lot-sizing problem with setup times, safety stock and demand shortages. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is np-hard. We propose a Lagrangian relaxation of the resource capacity constraints. We develop a dynamic programming algorithm to solve the induced sub-problems. An upper bound is also proposed using a Lagrangian heuristic with several smoothing algorithms. Some experimental results showing the effectiveness of the approach are reported.     

Vehicle routing under time-dependent travel times: The impact of congestion avoidance

Daily traffic congestion forms a major problem for businesses such as logistic service providers and distribution firms. It causes late arrivals at customers and additional costs for hiring the truck drivers. Such costs caused by traffic congestion can be reduced by taking into account and avoiding predictable traffic congestion within vehicle route plans. In the literature, various strategies are proposed to avoid traffic congestion, such as selecting alternative routes, changing the customer visit sequences, and changing the vehicle-customer assignments. We investigate the impact of these and other strategies in off-line vehicle routing on the performance of vehicle route plans in reality. For this purpose, we develop a set of vehicle routing problem instances on real road networks, and a speed model that reflects the key elements of peak hour traffic congestion. The instances are solved for different levels of congestion avoidance using a modified Dijkstra algorithm and a restricted dynamic programming heuristic. Computational experiments show that 99% of late arrivals at customers can be eliminated if traffic congestion is accounted for off-line. On top of that, about 87% of the extra duty time caused by traffic congestion can be eliminated by clever congestion avoidance strategies.     

A family of multi-path congestion control algorithms with global stability and delay robustness

The goal of traffic management is to efficiently allocate network resources via adjustment of source transmission rates and routes selection. Mathematically, it aims to solve a traditional utility maximization problem in a fair and distributed manner. In this paper, we first develop a generalized multi-path utility maximization problem which features a weighted average of the classical Kelly’s formulation and the Voice’s model. Next, we design from this broader framework a family of multi-path dual congestion control algorithms whose equilibrium point can both achieve a desired bandwidth utilization and preserve a notion of fairness among competing users. Global stability can be guaranteed for the proposed schemes in the absence of delays by use of a totally novel Lyapunov function. Moreover, when heterogeneous propagation delays are taken into account, we establish decentralized and scalable sufficient conditions for robust global stability by constructing a reasonable Lyapunov–Krasovskii functional candidate. These conditions give estimates for the maximum admissible delays that the controller can tolerate without losing stability. Finally, we verify the results through simulation.     

Heuristic approaches for the multiperiod location-transportation problem with reuse of vehicles in emergency logistics

The coordination among the different actors in relief chains is crucial to provide effective and efficient response in emergency logistics. By recognizing this fact, we have developed two stochastic mixed-integer programming models to integrate and coordinate facility location, transportation and fleet sizing decisions in a multi-period, multi-commodity, and multi-modal context under uncertainty. One model even considers the option of reusing vehicles to cover extra routes within the same time period in an attempt to save overall resources and improve service levels. Typical uncertainty in victims׳ needs, incoming supply, inventory conditions, and roads availability are modeled through a set of scenarios representing plausible disaster impacts. To solve instances of practical size, we have devised relax-and-fix and fix-and-optimize heuristics based on decompositions by time, scenario, and stage. The proposed instances entail characteristics of the megadisaster in the Mountain Region of Rio de Janeiro State in Brazil. The results suggest that the integration of decisions in a multiperiod context and the option of reusing vehicles reduce total costs, thus improving the overall performance of the relief operations. Also, the time-decomposition fix-and-optimize heuristic outperforms the CPLEX solver in terms of elapsed times and optimality gaps, mainly in moderate-size instances. Finally, we show the importance to explicitly consider randomness instead of using simpler worst-case scenario approaches.     

The value of modeling with reference effects in stochastic inventory and pricing problems

We analyze a periodic review inventory system in which the random demand is contingent on the current price and the reference price. The reference price captures the price history and acts as a benchmark against which the current price is compared. The randomness is due to additive and multiplicative random terms. The objective is to maximize the discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We study three key issues using numerical computation and simulation. First, we study the effects of reference price mechanism on the total expected profit. It is shown that high dependence on a good history increases the profit. Second, we investigate the value of dynamic programming and show that the firm that ignores the dynamic structure suffers from the revenue. Third, we analyze the value of estimating the correct demand model with reference effects. We observe that this value is significant when the inventory related costs are low.     

An investigation of mating and population maintenance strategies in hybrid genetic heuristics for product line designs

This research builds on prior work on developing near optimal solutions to the product line design problems within the conjoint analysis framework. In this research, we investigate and compare different genetic algorithm operators; in particular, we examine systematically the impact of employing alternative population maintenance strategies and mutation techniques within our problem context. Two alternative population maintenance methods, that we term “Emigration” and “Malthusian” strategies, are deployed to govern how individual product lines in one generation are carried over to the next generation. We also allow for two different types of reproduction methods termed “Equal Opportunity” in which the parents to be paired for mating are selected with equal opportunity and a second based on always choosing the best string in the current generation as one of the parents which is referred to as the “Queen bee”, while the other parent is randomly selected from the set of parent strings. We also look at the impact of integrating the artificial intelligence approach with a traditional optimization approach by seeding the GA with solutions obtained from a Dynamic Programming heuristic proposed by others. A detailed statistical analysis is also carried out to determine the impact of various problem and technique aspects on multiple measures of performance through means of a Monte Carlo simulation study. Our results indicate that such proposed procedures are able to provide multiple “good” solutions. This provides more flexibility for the decision makers as they now have the opportunity to select from a number of very good product lines. The results obtained using our approaches are encouraging, with statistically significant improvements averaging 5% or more, when compared to the traditional benchmark of the heuristic dynamic programming technique.     

Motion planning in uncertain environments with vision-like sensors

In this work we present a methodology for intelligent path planning in an uncertain environment using vision-like sensors, i.e., sensors that allow the sensing of the environment non-locally. Examples would include a mobile robot exploring an unknown terrain or a micro-UAV navigating in a cluttered urban environment. We show that the problem of path planning in an uncertain environment, under certain assumptions, can be posed as the adaptive optimal control of an uncertain Markov decision process, characterized by a known, control-dependent system, and an unknown, control-independent environment. The strategy for path planning then reduces to computing the control policy based on the current estimate of the environment, also known as the “certainty-equivalence” principle in the adaptive control literature. Our methodology allows the inclusion of vision-like sensors into the problem formulation, which, as empirical evidence suggests, accelerates the convergence of the planning algorithms. Further we show that the path planning and estimation problems, as formulated in this paper, possess special structure which can be exploited to significantly reduce the computational burden of the associated algorithms. We apply this methodology to the problem of path planning of a mobile rover in a completely unknown terrain.     

Convergence of best-response dynamics in games with conflicting congestion effects

We study the model of resource allocation games with conflicting congestion effects that was introduced by Feldman and Tamir [9]. In this model, an agent's cost consists of its resource's load (which increases with congestion) and its share in the resource's activation cost (which decreases with congestion). The current work studies the convergence rate of best-response dynamics (BRD) in the case of homogeneous agents. Even within this simple setting, interesting phenomena arise. We show that, in contrast to standard congestion games with identical jobs and resources, the convergence rate of BRD under conflicting congestion effects might be super-linear in the number of jobs. Nevertheless, a specific form of BRD is proposed, which is guaranteed to converge in linear time.     

Solving single-product economic lot-sizing problem with non-increasing setup cost,constant capacity and convex inventory cost in O(N log N) time

This paper considers an economic lot sizing model with constant capacity, non-increasing setup cost, and convex inventory cost function. Algorithms with computational time of O(N×TD_N)have been developed for solving the model, where N is the number of planning periods and TD_N is the total demand. This study partially characterizes the optimal planning structure of the model. A new efficient algorithm with computational time of O(N log N) has also been developed based on the partial optimal structure. Moreover, computational study demonstrates that the new algorithm is efficient.     

ATM网络拥塞预防的动态负载平衡策略

讨论了拥塞预防在ＡＴＭ网络中的必要性以及拥塞预防的关键性要素,并利用公式系统中并行计算的动态负载平衡的思想,提出了ＡＴＭ网络中负载的概念,给出了ＡＴＭ网络拥塞预防的算法。     

非线性动态优化仿真在间歇过程中的应用

为实现求解大规模非线性系统最优控制问题的自动设计及算法自动生成问题,开发基于非线性规划的动态优化软件集成系统.首先自定义基于XML的标准化非线性动态优化标记语言NDOML,采用NDOML模型设计模型编辑器;结合联立法和多点打靶法对NDOML模型进行自动离散化处理;最后利用内点算法解题器IPOPT设计了解题器接口程序生成器,实现模型录入通用化、模型离散自动化及优化控制算法代码的自动生成等多种应用功能.最后通过一个间歇反应过程实例验证动态优化软件系统的有效性,结果显示,系统能够实现最优控制算法的自动生成,仿真结果为大型非线性系统求解优化提供了依据.     

Note on the article: Maximum entropy analysis of the M/M/1 queueing system with multiple vacations and server breakdowns

Wang et al. [Wang, K. H., Chan, M. C., & Ke, J. C. (2007). Maximum entropy analysis of the M^[x]/M/1 queueing system with multiple vacations and server breakdowns. Computers & Industrial Engineering, 52, 192–202] elaborate on an interesting approach to estimate the equilibrium distribution for the number of customers in the M^[x]/M/1 queueing model with multiple vacations and server breakdowns. Their approach consists of maximizing an entropy function subject to constraints, where the constraints are formed by some known exact results. By a comparison between the exact expression for the expected delay time and an approximate expected delay time based on the maximum entropy estimate, they argue that their maximum entropy estimate is sufficiently accurate for practical purposes. In this note, we show that their maximum entropy estimate is easily rejected by simulation. We propose a minor modification of their maximum entropy method that significantly improves the quality of the estimate.     

The impact of estimation error on the dynamic order admission policy in B2B MTO environments

When swarming demands cause stringent capacity situations, order promising becomes a challenging job. However, a dynamic order admission policy by utilizing the concept of revenue management may find a good way to solve the problem. Unfortunately, the expected profit under different dynamic order admission policies is sensitive to the estimation error of order forecasts. In this paper, the impact of estimation error is investigated under various order structures. The post analysis is performed and shows significant statistical difference among the optimal unbiased DSKP policy, biased DSKP policy, and FCFS policy. The results reveal the robustness and superiority of DSKP policy in most scenarios.     

The distribution of network states during residence times in product form queueing networks

Product form queueing networks are so named because their equilibrium state probabilities have a simple product form. This simple form has lead to computationally efficient techniques for obtaining solutions of these networks. Recent work on the probability of network states at those instants when a customer completes service at a service center (departure instants) or arrives at a service center (arrival instants) has revealed a similar product form. The arrival instant result provides a simple, intuitive explanation of the Mean Value Analysis solution technique for product form networks with First-Come-First-Served service centers.In this paper we derive the distribution of network states seen by a particular customer while resident at a particular service center. This distribution too has a relatively simple product form. We use this information to explain in an intuitive way the MVA solution technique for a more general class of network, those containing load independent Processor Sharing and last-Come-First-Served-Preemptive-Resume service centers. It is hoped that, just as the intuitive explanation of the response time formula for FCFS centers has led to approximation techniques for non-separable FCFS centers, this new information may provide approximation techniques for non-separable centers with other scheduling disciplines such as preemptive and non-preemptive priority.     

虚拟场景中多面体浮力算法研究

随着仿真技术的不断发展,游戏玩家们对与流体有关的场景中的仿真效果的要求也不断提升.应此要求,在对虚拟场景中的多面体浮力算法进行研究基础上,提出了新的、并更加行之有效的计算多面体浮力的方法.采用分割多边形的途径,将组成多面体的各多边形的水下部分分割成若干三角形,之后再计算水下部分多边形的体积,进而求出浮力.同时,考虑到阻力因素的作用,计算出相关的阻力和阻力力矩后,便可精确显示出多面体在场景中的力作用情况.算法采用以仿真能量损耗和水流耦合,更简单于全动态水体仿真,并且不需要额外的创建步骤.方法效率高,易实现,且便于集成到物理引擎中.     

The integration of the output controllability index within the dynamic operability framework in process system design

This paper presents the integration of the output controllability index within the dynamic operability framework to facilitate controllability and economic assessment of process system design for regulatory cases. The framework utilises the geometric representation of feasible operating region as well as input, output and disturbance spaces, in terms of their convex hulls. The geometric operations amongst these convex hulls replace most of the inequalities on the original framework. In addition to the best feasible operating conditions, which are the original outcome, the framework also provides a controllability index involving all of the output variables (generalised integral absolute error, GIAE) and the expected variation of profit on disturbance rejection dynamics. The applicability of the proposed framework is demonstrated on a nonlinear chemical process system with a fixed control structure.     

The impact of supply contracts on supply chain product-flow management

One of the performance issues faced by the supply chain (SC) is the competitive production and delivery of products to all partners of the SC. The supply contract linking the Original Equipment Manufacturer (OEM) with its suppliers currently represents an important decision tool influencing the production and delivery of final products.