We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We introduce a new decision rule, called Global Stochastic Assessment (GSA) rule for the DS-VRPTW, and we compare it with existing decision rules, such as MSA. In particular, we show that GSA fully integrates nonanticipativity constraints so that it leads to better decisions in our stochastic context. We describe a new heuristic approach for efficiently approximating our GSA rule. We introduce a new waiting strategy. Experiments on dynamic and stochastic benchmarks, which include instances of different degrees of dynamism, show that not only our approach is competitive with state-of-the-art methods, but also enables to compute meaningful offline solutions to fully dynamic problems where absolutely no a priori customer request is provided.
@cite_24 studies the DS-VRPTW and introduces the Multiple Scenario Approach (MSA). A key element of MSA is an adaptive memory that stores a pool of solutions. Each solution is computed by considering a particular scenario which is optimized for a few seconds. The pool is continuously populated and filtered such that all solutions are consistent with the current system state. Another important element of MSA is the used to make operational decisions involving idle vehicles. The authors designed 3 algorithms for that purpose: @cite_4 @cite_29 samples a set of scenarios and selects the next request to be serviced by considering its average cost on the sampled set of scenarios. Algorithm @cite_2 depicts how it chooses the next action @math to perform. It requires an optimization for each action @math and each scenario @math (lines 3-4), which is computationally very expensive, even with a heuristic approach.
@cite_24 @cite_29 @cite_4 @cite_2
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In this paper, we combine ideas from machine learning (ML) and operations research and management science (OR MS) in developing a framework, along with specific methods, for using data to prescribe decisions in OR MS problems. In a departure from other work on data-driven optimization and reflecting our practical experience with the data available in applications of OR MS, we consider data consisting, not only of observations of quantities with direct effect on costs revenues, such as demand or returns, but predominantly of observations of associated auxiliary quantities. The main problem of interest is a conditional stochastic optimization problem, given imperfect observations, where the joint probability distributions that specify the problem are unknown. We demonstrate that our proposed solution methods are generally applicable to a wide range of decision problems. We prove that they are computationally tractable and asymptotically optimal under mild conditions even when data is not independent and identically distributed (iid) and even for censored observations. As an analogue to the coefficient of determination @math , we develop a metric @math termed the coefficient of prescriptiveness to measure the prescriptive content of data and the efficacy of a policy from an operations perspective. To demonstrate the power of our approach in a real-world setting we study an inventory management problem faced by the distribution arm of an international media conglomerate, which ships an average of 1 billion units per year. We leverage both internal data and public online data harvested from IMDb, Rotten Tomatoes, and Google to prescribe operational decisions that outperform baseline measures. Specifically, the data we collect, leveraged by our methods, accounts for an 88 improvement as measured by our coefficient of prescriptiveness. We present an adaptive memory programming (AMP) metaheuristic to address the robust capacitated vehicle routing problem under demand uncertainty. Contrary to its deterministic counterpart, the robust formulation allows for uncertain customer demands, and the objective is to determine a minimum cost delivery plan that is feasible for all demand realizations within a prespecified uncertainty set. A crucial step in our heuristic is to verify the robust feasibility of a candidate route. For generic uncertainty sets, this step requires the solution of a convex optimization problem, which becomes computationally prohibitive for large instances. We present two classes of uncertainty sets for which route feasibility can be established much more efficiently. Although we discuss our implementation in the context of the AMP framework, our techniques readily extend to other metaheuristics. Computational studies on standard literature benchmarks with up to 483 customers and 38 vehicles demonstrate that the proposed approach is able to quickly provide high-quality solutions. In the process, we obtain new best solutions for a total of 123 benchmark instances. We consider the problem of resource allocation in downlink OFDMA systems for multi service and unknown environment. Due to users' mobility and intercell interference, the base station cannot predict neither the Signal to Noise Ratio (SNR) of each user in future time slots nor their probability distribution functions. In addition, the traffic is bursty in general with unknown arrival. The probability distribution functions of the SNR, channel state and traffic arrival density are then unknown. Achieving a multi service Quality of Service (QoS) while optimizing the performance of the system (e.g. total throughput) is a hard and interesting task since it depends on the unknown future traffic and SNR values. In this paper we solve this problem by modeling the multiuser queuing system as a discrete time linear dynamic system. We develop a robust H∞ controller to regulate the queues of different users. The queues and Packet Drop Rates (PDR) are controlled by proposing a minimum data rate according to the demanded service type of each user. The data rate vector proposed by the controller is then fed as a constraint to an instantaneous resource allocation framework. This instantaneous problem is formulated as a convex optimization problem for instantaneous subcarrier and power allocation decisions. Simulation results show small delays and better fairness among users. In this paper, an estimation of distribution algorithm (EDA)-based memetic algorithm (MA) is proposed for solving the distributed assembly permutation flow-shop scheduling problem (DAPFSP) with the objective to minimize the maximum completion time. A novel bi-vector-based method is proposed to represent a solution for the DAPFSP. In the searching phase of the EDA-based MA (EDAMA), the EDA-based exploration and the local-search-based exploitation are incorporated within the MA framework. For the EDA-based exploration phase, a probability model is built to describe the probability distribution of superior solutions. Besides, a novel selective-enhancing sampling mechanism is proposed for generating new solutions by sampling the probability model. For the local-search-based exploitation phase, the critical path of the DAPFSP is analyzed to avoid invalid searching operators. Based on the analysis, a critical-path-based local search strategy is proposed to further improve the potential solutions obtained in the EDA-based searching phase. Moreover, the effect of parameter setting is investigated based on the Taguchi method of design-of-experiment. Suitable parameter values are suggested for instances with different scales. Finally, numerical simulations based on 1710 benchmark instances are carried out. The experimental results and comparisons with existing algorithms show the effectiveness of the EDAMA in solving the DAPFSP. In addition, the best-known solutions of 181 instances are updated by the EDAMA.