Designing robust liner shipping schedules: Optimizing recovery actions and buffer times

It is important for liner shipping companies to maintain cost efficient and robust liner shipping networks. Regularly, they set up pro-forma schedules, yet it is difficult to stay on time. We consider the problem of managing the delays. Therefore, we need to determine an optimal recovery policy and buffer time allocation to the ship route in order to minimize the total costs associated with delays and recovery actions, such as increasing sailing speed. We introduce a general framework consisting of a mixed integer programming formulation to solve discrete stochastic decision problems with short and long term decisions and apply this framework to the above described problem. Furthermore, we propose and test four heuristics for this problem. We compared the results of our method with an existing liner shipping route schedule and found a cost decrease of 28.9% after optimizing the buffer time distribution compared to the cost of sailing the current route schedule at constant speed.     

Proportion-based robust optimization and team orienteering problem with interval data

In this paper, a proportion-based robust optimization approach is developed to deal with uncertain combinatorial optimization problems. This approach assumes that a certain proportion of uncertain coefficients in each solution are allowed to change and optimizes a deterministic model so as to achieve a trade-off between optimality and feasibility when the coefficients change. We apply this approach on team orienteering problem with interval data (TOPID), a variant of vehicle routing problem, which has not yet been studied before. A branch and price algorithm is proposed to solve the robust counterpart by using two novel dominance relations. Finally, numerical study is performed. The results show the usefulness of the proposed robust optimization approach and the effectiveness of our algorithm.     

A note on issues of over-conservatism in robust optimization with cost uncertainty

We identify and discuss issues of hidden over-conservatism in robust linear optimization, when the uncertainty set is polyhedral with a budget of uncertainty constraint. The decision-maker selects the budget of uncertainty to reflect his degree of risk aversion, i.e. the maximum number of uncertain parameters that can take their worst-case value. In the first setting, the cost coefficients of the linear programming problem are uncertain, as is the case in portfolio management with random stock returns. We provide an example where, for moderate values of the budget, the optimal solution becomes independent of the nominal values of the parameters, i.e. is completely disconnected from its nominal counterpart, and discuss why this happens. The second setting focusses on linear optimization with uncertain upper bounds on the decision variables, which has applications in revenue management with uncertain demand and can be rewritten as a piecewise linear problem with cost uncertainty. We show in an example that it is possible to have more demand parameters equal their worst-case value than what is allowed by the budget of uncertainty, although the robust formulation is correct. We explain this apparent paradox.     

Support vector machine classifiers with uncertain knowledge sets via robust optimization

In this article we study support vector machine (SVM) classifiers in the face of uncertain knowledge sets and show how data uncertainty in knowledge sets can be treated in SVM classification by employing robust optimization. We present knowledge-based SVM classifiers with uncertain knowledge sets using convex quadratic optimization duality. We show that the knowledge-based SVM, where prior knowledge is in the form of uncertain linear constraints, results in an uncertain convex optimization problem with a set containment constraint. Using a new extension of Farkas' lemma, we reformulate the robust counterpart of the uncertain convex optimization problem in the case of interval uncertainty as a convex quadratic optimization problem. We then reformulate the resulting convex optimization problems as a simple quadratic optimization problem with non-negativity constraints using the Lagrange duality. We obtain the solution of the converted problem by a fixed point iterative algorithm and establish the convergence of the algorithm. We finally present some preliminary results of our computational experiments of the method.     

需求不确定下应急医疗服务站鲁棒配置模型与算法

大型突发事件发生后需要快速启动应急救灾网络,合理配置应急医疗服务站。本文考虑各应急医疗服务站选址节点需求的不确定性,引入三个不确定水平参数,构建四类不确定需求集合(box, ellipsoid, polyhedron和interval-polyhedron)对应的应急医疗服务站鲁棒配置模型,运用分支-切割算法求解,最后,进行需求扰动比例的灵敏度分析。算例结果表明,四类不确定需求集下的鲁棒配置模型中,ellipsoid不确定需求集合配置模型开放设施较少,总成本最小,鲁棒性较好。决策者还可以根据风险偏好选择不确定水平和需求扰动比例的组合,以使得总成本最小。     

A robust optimization model for dynamic market with uncertain production cost

This article presents a robust optimization formulation for dealing with production cost uncertainty in an oligopolistic market scenario. It is not uncommon that players in the market face an equilibrium selling price but uncertain production costs. We show that, based on a nominal problem, the robust optimization formulation can be derived as a variational inequality with control and state variables. This convenient approach may be applied for computing optimal solutions efficiently, which help manufacturers dramatically and rapidly reform production and distribution schedules such that they can compete in the market successfully.     

A robust counterpart approach to the bi-objective emergency medical service design problem

The paper presents a bi-objective robust program to design a cost-responsiveness efficient emergency medical services (EMS) system under uncertainty. The proposed model simultaneously determines the location of EMS stations, the assignment of demand areas to EMS stations, and the number of EMS vehicles at each station to balance cost and responsiveness. We develop a robust counterpart approach to cope with the uncertain parameters in the EMS system. Extensive numerical studies are performed to demonstrate the benefits of our robust optimization approach.     

Semiconductor lot allocation using robust optimization

In this work, the problem of allocating a set of production lots to satisfy customer orders is considered. This research is of relevance to lot-to-order matching problems in semiconductor supply chain settings. We consider that lot-splitting is not allowed during the allocation process due to standard practices. Furthermore, lot-sizes are regarded as uncertain planning data when making the allocation decisions due to potential yield loss. In order to minimize the total penalties of demand un-fulfillment and over-fulfillment, a robust mixed-integer optimization approach is adopted to model is proposed the problem of allocating a set of work-in-process lots to customer orders, where lot-sizes are modeled using ellipsoidal uncertainty sets. To solve the optimization problem efficiently we apply the techniques of branch-and-price and Benders decomposition. The advantages of our model are that it can represent uncertainty in a straightforward manner with little distributional assumptions, and it can produce solutions that effectively hedge against the uncertainty in the lot-sizes using very reasonable amounts of computational effort.     

Computing robust basestock levels

This paper considers how to optimally set the basestock level for a single buffer when demand is uncertain, in a robust framework. We present a family of algorithms based on decomposition that scale well to problems with hundreds of time periods, and theoretical results on more general models.     

Capacity planning and warehouse location in supply chains with uncertain demands

We discuss the strategic capacity planning and warehouse location problem in supply chains operating under uncertainty. In particular, we consider situations in which demand variability is the only source of uncertainty. We first propose a deterministic model for the problem when all relevant parameters are known with certainty, and discuss related tractability and computational issues. We then present a robust optimization model for the problem when the demand is uncertain, and demonstrate how robust solutions may be determined with an efficient decomposition algorithm using a special Lagrangian relaxation method in which the multipliers are constructed from dual variables of a linear program.     

Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon’s vehicle routing problem with time windows (VRPTW) benchmark problems.     

Two-stage workforce planning under demand fluctuations and uncertainty

We address a multi-category workforce planning problem for functional areas located at different service centres, each having office-space and recruitment capacity constraints, and facing fluctuating and uncertain workforce demand. A deterministic model is initially developed to deal with workforce fluctuations based on an expected demand profile over the horizon. To hedge against the demand uncertainty, we also propose a two-stage stochastic program, in which the first stage makes personnel recruiting and allocation decisions, while the second stage reassigns workforce demand among all units. A Benders’ decomposition-based algorithm is designed to solve this two-stage stochastic mixed-integer program. Computational results based on some practical numerical experiments are presented to provide insights on applying the deterministic versus the stochastic programming approach, and to demonstrate the efficacy of the proposed algorithm as compared with directly solving the model using its deterministic equivalent.     

Minmax regret location–allocation problem on a network under uncertainty

We consider a robust location–allocation problem with uncertainty in demand coefficients. Specifically, for each demand point, only an interval estimate of its demand is known and we consider the problem of determining where to locate a new service when a given fraction of these demand points must be served by the utility. The optimal solution of this problem is determined by the “minimax regret” location, i.e., the point that minimizes the worst-case loss in the objective function that may occur because a decision is made without knowing which state of nature will take place. For the case where the demand points are vertices of a network we show that the robust location–allocation problem can be solved in O(min{p, n − p}n³m) time, where n is the number of demand points, p (p < n) is the fixed number of demand points that must be served by the new service and m is the number of edges of the network.     

Stochastic multi-site capacity planning of TFT-LCD manufacturing using expected shadow-price based decomposition

This paper presents a stochastic optimization model and efficient decomposition algorithm for multi-site capacity planning under the uncertainty of the TFT-LCD industry. The objective of the stochastic capacity planning is to determine a robust capacity allocation and expansion policy hedged against demand uncertainties because the demand forecasts faced by TFT-LCD manufacturers are usually inaccurate and vary rapidly over time. A two-stage scenario-based stochastic mixed integer programming model that extends the deterministic multi-site capacity planning model proposed by Chen et al. (2010) [1] is developed to discuss the multi-site capacity planning problem in the face of uncertain demands. In addition a three-step methodology is proposed to generate discrete demand scenarios within the stochastic optimization model by approximating the stochastic continuous demand process fitted from the historical data. An expected shadow-price based decomposition, a novel algorithm for the stage decomposition approach, is developed to obtain a near-optimal solution efficiently through iterative procedures and parallel computing. Preliminary computational study shows that the proposed decomposition algorithm successfully addresses the large-scale stochastic capacity planning model in terms of solution quality and computation time. The proposed algorithm also outperforms the plain use of the CPLEX MIP solver as the problem size becomes larger and the number of demand scenarios increases.     

A genetic algorithm for robust schedules in a one-machine environment with ready times and due dates

Computing a schedule for a single machine problem is often difficult, but when the data are uncertain, the problem is much more complicated. In this paper, we modify a genetic algorithm to compute robust schedules when release dates are subject to small variations. Two types of robustness are distinguished: quality robustness or robustness in the objective function space and solution robustness or robustness in the solution space. We show that the modified genetic algorithm can find solutions that are robust with respect to both types of robustness. Moreover, the risk associated with a specific solution can be easily evaluated. The modified genetic algorithm is applied to a just-in-time scheduling problem, a common problem in many industries.     

多目标应急物流中心选址的鲁棒优化模型

针对重大突发事件的应急物资救援,研究了应急物流中心的选址及应急物资的调运问题。利用离散的情景集合描述受灾点应急物资需求的不确定性以及应急物资运输成本和运输时间的不确定性,同时考虑应急救援成本和应急救援时间两个目标,建立了多目标应急物流中心选址的确定型模型和鲁棒优化模型。为将多目标问题转化为单目标问题,利用成本单目标和时间单目标的最优结果将多目标转化为相对值再加权处理,该方法既可消除多个目标之间的单位及数量级差异,还可以根据问题的数据变化进行动态调整。以提供应急物资救援服务的设施作为编码,设计了一种通用的混合蛙跳算法。为检验模型和算法的有效性,设计了一个多情景的算例,结果表明两个模型和算法具备良好的可行性和有效性,且鲁棒优化模型能较好地保持对各种不确定性的抗干扰能力;最后,讨论分析了成本偏好权重和鲁棒约束系数的影响,结果表明可根据成本偏好权重的取值范围来区分各种应急救援阶段,体现不同救援阶段的救援要求及特征,并给出了成本偏好权重和鲁棒约束系数的取值建议。     

Decentralized Dual-Based Algorithm for Computing Optimal Flows in a General Supply Chain

This paper addresses the issue of the optimal flow allocation in general supply chains. Our basic observation is that a distribution channel involving several reselling steps for a particular product can be viewed as a route in a supply chain network. The flow of goods or services along each route is influenced by the customer's demand, described by the corresponding utility functions, and prices charged at each node. We develop an optimization algorithm based on the primal-dual framework and the Newton's step that computes optimal prices at each node (dual problem) and then computes the optimal flow allocation (primal problem) based on these prices. Our main contribution is a discovery that the Newton's step leads to a partially decentralized algorithm which is a first step toward a decentralization schema for computing optimal prices.     

A branch-and-bound algorithm for the resource-constrained project scheduling problem

We describe a time-oriented branch-and-bound algorithm for the resource-constrained project scheduling problem which explores the set of active schedules by enumerating possible activity start times. The algorithm uses constraint-propagation techniques that exploit the temporal and resource constraints of the problem in order to reduce the search space. Computational experiments with large, systematically generated benchmark test sets, ranging in size from thirty to one hundred and twenty activities per problem instance, show that the algorithm scales well and is competitive with other exact solution approaches. The computational results show that the most difficult problems occur when scarce resource supply and the structure of the resource demand cause a problem to be highly disjunctive.     

一种求解柔性资源约束前摄性项目调度问题的启发式算法

在不确定环境中,一个具有较高鲁棒性的进度计划可以保证项目的稳定实施。考虑到现实中资源可能具有多种技能,会对制定鲁棒性较高进度计划的过程产生影响,因此本文研究了柔性资源约束下前摄性项目调度优化问题。首先界定研究问题;然后从鲁棒性最大化的视角出发,构建了研究问题的优化模型,在对模型进行分析的基础上将其分解为经典鲁棒优化和资源技能分配两个子模型;随后设计了求解问题的基于削峰算法的启发式算法;最后用一个实际案例验证了算法有效性,并分析了关键参数对进度计划鲁棒性的影响,得到如下结论:项目进度计划鲁棒性随着项目工期的延长、资源可用量的增加或资源柔性的提高而增大。     

Medium Term Production Management for Cyclic Deliveries

The growing quality and delay requirements have catalyzed the emergence of new commercial paradigms, which have strongly modified the customer–supplier relationship. Customers and suppliers become more and more linked with contracts or global orders spanned over a relatively important period. This paper, examines a type of contract which specifies a fixed and cyclic delivery dates with delivery quantities varying between a min and a max values. The exact delivery quantities are usually known only few days before the delivery. A company which produces n items on a bottleneck facility is considered; each item is confronted to a cyclic demand and has an important holding cost in comparison to set-up costs. We propose heuristic approaches, to build, in a medium term level, cyclic production schedules. These schedules face the demand and minimize a total cost function composed of holding and set-up costs. An experiment is proposed in order to prove the effectiveness of our approaches.