Stochastic Demand Research Articles

Spectral incremental dynamic methodology for nonlinear structural systems endowed with fractional derivative elements subjected to fully non-stationary stochastic excitation

A novel spectral incremental dynamic analysis methodology for analysing structural response in nonlinear systems with fractional derivative elements is presented, aligning with modern seismic design codes, like Eurocode 8. Drawing inspiration from the concept of fully non-stationary stochastic processes, the vector of the imposed seismic excitations is characterised by time and frequency evolving power spectra stochastically compatible with elastic response spectra of specified damping ratio and ground acceleration. The proposed method efficiently determines the nonlinear system time-dependent probability density functions for the non-stationary system response amplitude by employing potent nonlinear stochastic dynamics concepts, such as stochastic averaging and statistical linearisation. Unlike traditional incremental dynamic analysis curves found in the literature, the herein proposed method introduces a three-dimensional alternative counterpart, that of stochastic engineering demand parameter surfaces, providing with higher-order statistics of the system response. An additional noteworthy aspect involves the derivation of response evolutionary power spectra as function of spectral acceleration, offering a deeper insight into the underlying system dynamics. Besides its capabilities, the method maintains the coveted element of a particularly low associated computational cost, increasing its attractiveness and practicality among diverse applications of engineering interest. Numerical examples comprising the bilinear hysteretic model endowed with fractional derivative elements subject to an Eurocode 8 elastic design spectrum demonstrate the capabilities and reliability of the proposed methodology. Its accuracy is assessed by juxtaposing the derived results with germane Monte Carlo Simulation data.

Dynamic tugboat deployment and scheduling with stochastic and time-varying service demands

Container ports serve as crucial logistics hubs in global supply chains, but navigating ships within such ports is complex due to restricted waterways. Tugboats play a critical role in ensuring safety and efficiency by escorting and towing ships under these conditions. However, the tugboat deployment and scheduling problem has received little attention. To fill the research gap, we propose a new research problem - the dynamic tugboat deployment and scheduling problem, in which not all requests are confirmed initially but dynamically confirmed over time and future tugging demands need to be anticipated when managing the utilization of tugboats. To formulate the problem, we propose an extended Markov decision process (MDP) that incorporates both reactive task assignment decisions and proactive tugboat waiting decisions, creating a reactive and proactive MDP. To solve the advanced MDP model efficiently for real-time decisions, we develop an anticipatory approximate dynamic programming method that incorporates appropriate task assignment and waiting strategies for deploying and scheduling a heterogeneous tugboat fleet and embed the method into an improved rollout algorithm to anticipate future scenarios. The effectiveness, efficiency, and performance sensitivity of the developed modeling and solution methods are demonstrated via extensive numerical experiments for the Singapore container port.

Bayesian optimization for battery electric vehicle charging station placement by agent-based demand simulation

The optimal placement of electric vehicle charging infrastructure (EVCI) is critical for meeting the charging demand of battery electric vehicles (BEVs). However, the questions of how to coordinate the stochastic charging demand and placement of charging infrastructure in an economically effective way and how to solve such a problem on a large real-world scale remain unanswered. This study addresses these questions by developing an agent-based charging station placement model (ACPM) that incorporates demand uncertainty by simulating the behaviors of BEV users. A solution algorithm based on random embedding Bayesian optimization (REMBO) is proposed and shown to significantly improve computational efficiency and solve the ACPM on a large real-world scale. The model and algorithm are applied to a case study of the Atlanta metropolitan area. In the study, the algorithm finds an optimal placement using only 2% of the runtime of existing benchmark methods. This enables the use of the algorithm on a more complex, real-world scale. Results from the case study indicate that the optimal placement of EVCI uses level-2 and direct-current fast charging (DCFC) roughly equally and distributes these relatively evenly throughout the region. This optimal EVCI placement has significant economic benefits because it can improve the expected net present value (NPV) by 50% to 100% relative to common benchmark charging placement practices, such as placing the EVCI uniform randomly or weighted by the number of parked vehicles. Finally, a sensitivity analysis demonstrates that factors such as the size of the BEV market, charging preferences, and charging price are shown to have significant impacts on the optimal placement and profitability of an EVCI project.

Evaluating planning and operational policies for urban public electric vehicle charging infrastructure

It is expected that public electric vehicle charging demands will gradually increase in Korea. In this study, we propose a macroscopic indicator of the level of service (LOS) of urban public fast charging infrastructure to quantitively evaluate the joint impacts of possible planning and operational policies on it. The indicator is defined as the reliability-based capacity, the number of electric vehicles that can be charged within the maximum targeted weighted delay between wait and detour. We consider three combinable policies: changing the distribution of chargers in the planning stage; assigning the optimal charging station to each charging event in real-time and evenly distributing daily charging demands in the operational phase. For multiple policy combinations and various demand cases, we compare their LOS levels, calculated by Monte Carlo simulations that can efficiently address the complex joint impact of stochastic demands. The simulation experiments are designed to explicitly discover the impacts of policies along with varying charging demands. The results show that certain combinations of proposed policies can effectively and efficiently improve LOS.

Behavioral Efficiency and Residential Electricity Consumption: A Microdata Study

Sustainability requires that policy makers be able to use market signals to implement energy and environmental policy and that energy consumers respond rationally to these signals. Therefore, it is essential to understand how consumers’ responses to market signals are formed. We propose a new model to measure behavioral efficiency in residential electricity consumption derived from the individual householder indirect utility function. This leads to a pair of simultaneous stochastic demand frontiers for electricity consumption (kWh) and power demand (kVA). Each is a function of power demand (standing) charges and energy demand (running) charges together with the net income after demand charges, the stock of appliances and household characteristics. We estimate the model using two samples of household responses, each of which represents around one percent of the total national population available, and we also pool these samples using pseudo-panel data procedures. We demonstrate how the resulting elasticity and efficiency estimates are related to the theory of behavioral agents from recent developments in behavioral economics. These developments also use the individual indirect utility function to derive propositions based on internality and hyperbolic discounting. The econometric estimates permit the calibration of the individual welfare effects of policy initiatives using carbon tax and price incentives with behavioral agents.

Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction

In order to support a low-carbon economy and manage market competition, location–inventory–routing logistics management must play a crucial role to minimize carbon emissions while maximizing customer satisfaction. This paper proposes a bi-objective mixed-integer nonlinear programming model with time window constraints that satisfies the normal distribution of stochastic customer demand. The proposed model aims to find Pareto optimal solutions for total cost minimization and customer satisfaction maximization. An improved non-dominated sorting genetic algorithm II (IMNSGA-II) with an elite strategy is developed to solve the model. The model considers cost factors, ensuring that out-of-stock inventory is not allowed. Factors such as a carbon trading mechanism and random variables to address customer needs are also included. An entropy weight method is used to derive the total cost, which is comprised of fixed costs, transportation costs, inventory costs, punishment costs, and the weight of carbon emissions costs. The IMNSGA-II produces the Pareto optimal solution set, and an entropy–TOPSIS method is used to generate an objective ranking of the solution set for decision-makers. Additionally, a sensitivity analysis is performed to evaluate the influence of carbon pricing on carbon emissions and customer satisfaction.

Research on Dynamic Subsidy Based on Deep Reinforcement Learning for Non-Stationary Stochastic Demand in Ride-Hailing

The ride-hailing market often experiences significant fluctuations in traffic demand, resulting in supply-demand imbalances. In this regard, the dynamic subsidy strategy is frequently employed by ride-hailing platforms to incentivize drivers to relocate to zones with high demand. However, determining the appropriate amount of subsidy at the appropriate time remains challenging. First, traffic demand exhibits high non-stationarity, characterized by multi-context patterns with time-varying statistical features. Second, high-dimensional state/action spaces contain multiple spatiotemporal dimensions and context patterns. Third, decision-making should satisfy real-time requirements. To address the above challenges, we first construct a Non-Stationary Markov Decision Process (NSMDP) based on the assumption of ride-hailing service systems dynamics. Then, we develop a solution framework for the NSMDP. A change point detection method based on feature-enhanced LSTM within the framework can identify the changepoints and time-varying context patterns of stochastic demand. Moreover, the framework also includes a deterministic policy deep reinforcement learning algorithm to optimize. Finally, through simulated experiments with real-world historical data, we demonstrate the effectiveness of the proposed approach. It performs well in improving the platform’s profits and alleviating supply-demand imbalances under the dynamic subsidy strategy. The results also prove that a scientific dynamic subsidy strategy is particularly effective in the high-demand context pattern with more drastic fluctuations. Additionally, the profitability of dynamic subsidy strategy will increase with the increase of the non-stationary level.

A gradient-descent-based framework for solving a stochastic two-echelon delivery problem with cargo-bikes

In this paper, we examine a stochastic two-echelon vehicle routing problem (2e-VRP) using cargo bikes within hyperconnected networks. The focus is on the integration of both delivery and pickup of reusable containers, incorporating transshipment operations, time windows, and stochastic demand constraints. The model also considers the flow consolidation for empty and full containers at the satellites and allows for load splitting. Moreover, this study introduces an innovative gradient-descent-based optimization framework to handle the combinatorial complexity of the proposed model, opening new avenues in stochastic programming. Furthermore, the performance of this novel method is compared against the sample average approximation method, evaluating both solution quality and computational efficiency. Experimental results demonstrate the model’s advanced integration and flexibility, significantly enhancing urban delivery systems and advancing logistics and transportation optimization research.

Hardness of Pricing Routes for Two-Stage Stochastic Vehicle Routing Problems with Scenarios

On the Difficulty of Pricing Routes for Stochastic Vehicle Routing Problems Many approaches exist for dealing with the uncertainty in the vehicle routing problem with stochastic demands (VRPSD), but the most popular approach models the VRPSD as a two-stage stochastic program where a recourse policy prescribes actions that handle when the realized demands exceed the vehicle capacity. Similarly to other VRP variants, some state-of-the-art algorithms for the VRPSD use set-partitioning formulations that generate variables (routes) via a pricing problem. All of these algorithms, however, have strong assumptions on the probability distribution of customer demands, a simplification that might not be realistic in some applications. In “Hardness of Pricing Routes for Two-Stage Stochastic Vehicle Routing Problems with Scenarios,” Ota and Fukasawa examine the challenges associated with solving the pricing problem of the VRPSD when the customer demands are given by scenarios. They demonstrate that the VRPSD pricing problem is strongly NP-hard for a wide variety of recourse policies and route relaxations. This highlights the difficulty of developing efficient pricing algorithms for the VRPSD with scenario-based demand models.

Modelling and Optimization of Residential Electricity Load under Stochastic Demand

The paper considers a modelling framework for a set of households in residential areas; using electricity as a form of energy for domestic consumption. Considering the demand and availability of units for electricity consumption, optimal decisions for electricity load allocation are paramount to sustain energy management. We formulate this problem as a stochastic decision-making process model where electricity demand is characterized by Markovian demand. The loading and operational framework is governed by the demand and supply phenomena; where shortage costs are realized when demand exceeds supply. Empirical data for electricity consumption was collected from fifty households in two residential areas within the suburbs of Kampala in Uganda. Data collection was made at hourly intervals over a period of four months. The major problem focussed on determining an optimal electricity loading decision in order to minimize consumption costs as demand changes from one state to another. Considering a multi-period planning horizon, an optimal decision was determined for loading or not loading additional electricity units using Markov decision process approach. The model was tested; whose results demonstrated the existence of an optimal state-dependent decision and consumption costs considering the case study used in this study. The proposed model can be cost-effective for managers in the electricity industry. Improved efficiency and utilization of resources for the distribution systems of electricity to residential areas was realised; with subsequent enhanced reliability of service to essential customers of the energy market.

Supply chain model having stochastic lead time demand with variable production rate and demand dependent on price and advertisement

In this present study, a single-manufacturer and single-retailer supply chain management model are formulated for a single product. This study specifically looks at a supply chain with variable production rate, stochastic lead time demand, and price- and advertisement-dependent demand. By incorporating these complex aspects into a model, which enables to examine their combined effects on supply chain performance, this study adds to the body of knowledge. The study reveals unique insights into the complex interplay between pricing tactics, advertising efforts, production dynamics, and the variability brought on by stochastic lead times through meticulous study and modelling. Finally, the total system profit is calculated and optimized with all the decision variables. A classical approach is performed to obtain the optimized solution of the joint profit function along with the decision variables. Two models are discussed in the study: (1) the model with normally distributed lead time demand and (2) the model with distribution-free lead time demand. The joint profit of the supply chain is found to be lesser by 1% for the normally distributed lead time demand than the distribution free pattern. The comparison of the shipment policies and the safety factors for the different distribution patterns of the lead time demand are shown. Though the huge increment in the safety factor for unknown leadtime demand distribution may help in reducing the uncertainity factor and disruptions in the supply chain, but also it may unnecessarily tie up more capital which can be invested in other sectors of the supply chain.

Exploring Green Inventory Management through Periodic Review Inventory Systems—A Comprehensive Literature Review and Directions for Future Research

With the increasing environmental concerns and legislative pressures, the focus on incorporating ecologically sustainable practices into inventory management systems has grown, leading to the emergence of green inventory management. However, this field is not without its challenges, with numerous conflicting real-world constraints and goals. A comprehensive literature review targeting green inventory management operating under a periodic review inventory system was conducted to identify research gaps and potential directions for future research. Despite the growing interest in the field, this review highlighted the scarcity of relevant studies. Out of the 1272 papers reviewed, only 16 studies, or 1.3%, met the criteria for exploring periodic review inventory systems while simultaneously considering environmental and economic aspects. These studies were further analyzed in detail and categorized according to key classification criteria. The future research directions highlighted the need for additional studies on periodic review inventory systems operating under stochastic market demand in the context of green supply chain management. The standardization of emission calculation methodologies was also emphasized as a crucial step towards aligning inventory management practices with the aim of increasing inventory management efficiency and the related improvement in the environmental performance of supply chains.

Pricing strategy based on a stochastic problem with barter exchange under variable promotional effort for a retail channel

Barter exchange platform gains popularity as an effective trade exchange strategy to minimize the vast use of paper money. In retail management, the application of the barter platform is growing because of cashless trade. It allows a retail enterprise to trade unused products in exchange for other assets purchased by reducing the actual purchase of assets. In this context, the study analyzes a stochastic model of a barter exchange problem under a retail channel. It investigates the barter exchange policy in three different models: conventional newsvendor model without barter exchange, with barter exchange, and with barter exchange with promotional effort and emissions level. The market demand for products is considered random and random with deterministic variables for three types of models. Stochastic models are solved in two different ways: with and without probability distribution functions of the random market demand. For maximization of the retailer's profit, the proposed framework obtains optimal decisions on ordered quantity, retail price, promotional effort, and emissions level. Five examples are tested and numerical results show that the barter exchange policy is more profitable than a traditional newsvendor model. A combination of stochastic and deterministic variable demand provides 34.31% more profit than a stochastic demand. Sensitivity analysis, discussions, and managerial insights are provided in detail on optimal decisions.

Mathematical Model for Multi Depot Simultaneously Pick Up and Delivery Vehicle Routing Problem with Stochastic Pick Up Demand

In classical vehicle routing problem (VRP), customer demands are known with certainty. On the other hand, in real life problems, customer demands may change over time. Therefore, in the classical VRP, the assumption that customer demands are stochastic should be taken into account. In order to meet the demands of the customers faster and to reduce the fuel consumption and carbon emissions, the companies meet the distribution and collection demands of the customers simultaneously. Customers' distribution requirements can be predicted, but it is impossible to predict in advance the product requirements they will send for recycling. Hence in this study, a mathematical programming model is developed for the multi-depot simultaneously pick up and delivery vehicle routing problem, under the assumption that customers' picking demands are stochastic. However, There are non-linear constraints in the developed model. Thereby firstly the stochastic model is linearized, and then the effectiveness of the model is analyzed. The efficiency of the linearized model is determined by creating test problems.

Deep reinforcement learning algorithms for dynamic pricing and inventory management of perishable products

A perishable product has a limited shelf life, and inefficient management often leads to waste. This paper focuses on dynamic pricing and inventory management strategies for perishable products. By implementing effective inventory control and the right pricing policy, it is possible to maximize expected revenue. However, the exponential growth of the problem size due to the shelf life of the products makes it impractical to use methods that guarantee optimal solutions, such as Dynamic Programming (DP). Therefore, approximate solution algorithms become necessary. We use Deep Reinforcement Learning (DRL) algorithms to address the dynamic pricing and ordering problem for perishable products, considering price and age-dependent stochastic demand. We investigate Deep Q Learning (DQL) solutions for discrete action spaces and Soft Actor-Critic (SAC) solutions for continuous action spaces. To mitigate the negative impact of the stochastic environment inherent in the problem, we propose two different DQL approaches. Our results show that the proposed DQL and SAC algorithms effectively address inventory control and dynamic pricing for perishable products, even when products of different ages are offered simultaneously. Compared to dynamic programming, our proposed DQL approaches achieve an average approximation of 95.5 % and 96.6 %, and reduce solution times by 71.5 % and 79.9 %, respectively, for the largest problem. In addition, the SAC algorithm achieves on average 4.6 % and 1.7 % better results and completes the task 56.1 % and 48.2 % faster than the proposed DQL algorithms.

Development of N-Period Dynamic Programming Model for Determining EOQ under Stochastic Demand

Development of N-Period Dynamic Programming Model for Determining EOQ under Stochastic Demand

Offline planning and online operation of zonal-based flexible transit service under demand uncertainties and dynamic cancellations

This paper introduces a comprehensive framework for planning and operating a zonal-based flexible transit (FT) service, a public transit mode designed to accommodate uncertain demand patterns. The framework addresses both offline planning based on stochastic demand distributions and cancellations, as well as online routing considering real-time orders and cancellation behaviour. Offline interzonal route planning is formulated as a two-stage recourse problem, while the intrazonal routing problem is modelled using a Markov decision process (MDP) that incorporates online information. To solve the problem, a service reliability-based decomposition method is employed to divide the problem into three mixed-integer subproblems. The first subproblem focuses on designing interzonal routes up to a specific demand level, taking into account a designated cancellation probability as determined by reliability measures. An insertion heuristic is developed for this subproblem to improve the solution efficiency. The second subproblem allocates passengers from certain categories to vehicles based on the passenger volume designated by reliability measures. Lastly, the third subproblem refines the vehicle intrazonal route according to the passenger assignment from the previous subproblem. The reliability measures are optimised iteratively until no further improvements are observed in consecutive iterations. The proposed FT service’s performance is evaluated using numerical simulations based on real New York City (NYC) taxi demand data, illustrating the effectiveness of the integrated planning and operational approach in accommodating uncertainties in on-demand transit systems.

Climate change adaptation projects of transport facilities: is a demonstrator necessary?

AbstractTransport facilities are increasingly threatened by the climate-change related natural disasters in recent years. In order to incentivize the transport facility operators to engage in climate change adaptation, governments may provide subsidies to the adaptation investment. Due to the substantial uncertainties in the outcomes of the adaptation projects, the government can set up an “experiment” project, which can be used as a demonstrator. In this paper, we develop real-option game models to investigate the transport facility operators’ adaptation investment under static stochastic demand and time-varying stochastic demand. Meanwhile, the government’s optimal decisions on whether to set up a demonstrator and the related subsidy policies are also examined. We find that under static stochastic demand, the government prefers to set up a demonstrator if the marginal benefit of the adaptation capacity is larger than its marginal cost, or the demonstration effect is high enough. Under time-varying stochastic demand, the government prefers to set up a demonstrator when the demand volatility is low. Moreover, increasing demand volatility requires less (or more) subsidy, when the demonstrator is (or is not) set up. Increasing demand volatility leads to postponement of the adaptation timing and more adaptation investment, irrespective of whether there is a demonstrator.

Collecting and Delivering Fattened Pigs to the Abattoir.

In the context of pig farming, this paper addresses the optimization problem of collecting fattened pigs from farms to deliver them to the abattoir. Assuming that the pig sector is organized as a competitive supply chain with narrow profit margins, our aim is to apply analytics to cope with the uncertainty in production costs and revenues. Motivated by a real-life case, the paper analyzes a rich Team Orienteering Problem (TOP) with a homogeneous fleet, stochastic demands, and maximum workload. After describing the problem and reviewing the related literature, we introduce the PJS heuristic. Our approach is first compared with exact methods, which are revealed as computationally unfeasible. Later, a scenario analysis based on a real instance was performed to gain insight into the practical aspects. Our findings demonstrate a positive correlation between the number of alternative routes explored, the number of trips, the transportation cost, and the maximum reward. Regarding the variability in the number of pigs to collect, when a truck can visit more than one farm, better solutions can be found with higher variability since the load can be combined more efficiently.

A benchmark dataset for the retail multiskilled personnel planning under uncertain demand

In this data article, we present and describe datasets designed to address multiskilled personnel assignment problems (MPAP) under uncertain demand. The data article introduces simulated datasets and a real dataset obtained from a retail store in Chile. The real dataset provides details on the structure of the store, including the number of departments and workers, the type of labor contract, the cost parameter values, and the average demand across all store departments. The simulated datasets, consisting of 18 categorized text files, were generated through Monte Carlo simulation to encapsulate information about the stochastic demand for store departments. These text files are classified based on: (i) type of sample (in-sample or out-of-sample), (ii) type of truncation method (zero-truncated or percentile-truncated), and (iii) demand coefficient of variation (5%, 10%, 20%, 30%, 40%, 50%). This categorization allows academics and practitioners to select the scenarios that meet with their specific research or application needs, increasing the flexibility and applicability of the datasets. In addition, researchers and practitioners can use these comprehensive real and simulated datasets to benchmark the performance of diverse optimization methods under uncertain demand, thereby ensuring robust multiskilling levels for similar MPAPs. Furthermore, we offer an Excel workbook with the capability to generate up to 10,000 demand scenarios for varying coefficients of variation in demand.