Unconstraining methods for revenue management systems under small demand

Sales data often only represents a part of the demand for a service product owing to constraints such as capacity or booking limits. Unconstraining methods are concerned with estimating the true demand from such constrained sales data. This paper addresses the frequently encountered situation of observing only a few sales events at the individual product level and proposes variants of small demand forecasting methods to be used for unconstraining. The usual procedure is to aggregate data; however, in that case we lose information on when restrictions were imposed or lifted within a given booking profile. Our proposed methods exploit this information and are able to approximate convex, concave or homogeneous booking curves. Furthermore, they are numerically robust due to our proposed group-based parameter optimization. Empirical results on accuracy and revenue performance based on data from a major car rental company indicate revenue improvements over a best practice benchmark by statistically significant 0.5%–1.4% in typical scenarios

Ride-matching and routing optimisation: Models and a large neighbourhood search heuristic

This paper considers a ridesharing problem on how to match riders to drivers and how to choose the best routes for vehicles. Unlike the others in the literature, we are concerned with the maximization of the average loading ratio of the entire system. Moreover, we develop a flow-dependent version of the model to characterize the impact of pick-up and drop-off congestion. In another extended model we take into account the riders’ individual evaluation on different transportation modes. Due to the large size of the resulting models, we develop a large neighbourhood search algorithm and demonstrate its efficiency

When to switch? Index policies for resource scheduling in emergency response

This paper considers the scheduling of limited resources to a large number of jobs (e.g., medical treatment) with uncertain lifetimes and service times, in the aftermath of a mass casualty incident. Jobs are subject to triage at time zero, and placed into a number of classes. Our goal is to maximise the expected number of job completions. We propose an effective yet simple index policy based on Whittle’s restless bandits approach. The problem concerned features a finite and uncertain time horizon that is dependent upon the service policy, which also determines the decision epochs. Moreover, the number of job classes still competing for service diminishes over time. To the best of our knowledge, this is the first application of Whittle’s index policies to such problems. Two versions of Lagrangian relaxation are proposed in order to decompose the problem. The first is a direct extension of the standard Whittle’s restless bandits approach, while in the second the total number of job classes still competing for service is taken into account; the latter is shown to generalise the former. We prove the indexability of all job classes in the Markovian case, and develop closed-form indices. Extensive numerical experiments show that the second proposal outperforms the first one (that fails to capture the dynamics in the number of surviving job classes, or bandits) and produces more robust and consistent results as compared to alternative heuristics suggested from the literature, even in non-Markovian settings

A dynamic programming approach to a multi-objective disassembly line balancing problem

This paper concerns a disassembly line balancing problem (DLBP) in remanufacturing that aims to allocate a set of tasks to workstations to disassemble a product. We consider two objectives in the same time, i.e., minimising the number of workstations required and minimising the operating costs. A common approach to such problems is to covert the multiple objectives into a single one and solve the resulting problem with either exact or heuristic methods. However, the appropriate weights must be determined a priori, yet the results provide little insight on the trade-off between competing objectives. Moreover, DLBP problems are proven NP-complete and thus the solvable instances by exact methods are limited. To this end, we formulate the problem into a multi-objective dynamic program and prove the monotonicity property of both objective functions. A backward recursive algorithm is developed to efficiently generate all the non-dominated solutions. The numerical results show that our proposal is more efficient than alternative exact algorithms proposed in the literature and can handle much larger problem instances

Partial disassembly line balancing under uncertainty: robust optimisation models and an improved migrating birds optimisation algorithm

A partial disassembly line balancing problem under uncertainty is studied in this paper, which concerns the allocation of a sequence of tasks to workstations such that the overall profit is maximised. We consider the processing time uncertainty and develop robust solutions to accommodate it. The problem is formulated as a non-linear robust integer program, which is then converted into an equivalent linear program. Due to the intractability of such problems, the exact algorithms are only applicable to small-scale instances. We develop an improved migrating birds optimisation algorithm. Two enhancement techniques are proposed. The first one finds the optimal number of tasks to be performed for each sequence rather than random selection used in the literature; while the second one exploits the specific problem structure to construct effective neighbourhoods. The numerical results show the strong performance of our proposal compared to CPLEX and the improved gravitational search algorithm (IGSA), especially for large-scale problems. Moreover, the enhancement due to the proposed techniques is obvious across all instances considered.</div

Bid price controls for car rental network revenue management

We consider a car rental network revenue management (RM) problem, accounting for the key operational characteristics of car rental services such as the varying length of rentals and mobility of inventories which imply the inter-temporal and spatial correlations of rental demands for inventories across different locations and days. The problem is formulated as an infinite-horizon cyclic stochastic dynamic program to account for the time-varying and cyclic nature of car rental businesses. To tackle the curse of dimensionality, we propose a Lagrangian relaxation (LR) approach with product- and time-dependent Lagrangian multipliers to decomposing the dynamic network problem into multiple singlestation single-day sub-problems. We show that the Lagrangian dual problem is a convex program and then develop a subgradient-based algorithm to solve the dual problem and derive an LR-based bid price policy. To improve the scalability of the LR approach, we further propose three simpler LR-based bid price policy variants with either location-dependent or leadtime-dependent Lagrangian multipliers, or both. Our numerical study indicates that the LR-based bid price policies can outperform some commonly used heuristics. Using a set of real-world booking data, we provide a case study in which we empirically demonstrate the operational characteristics of car rental services, calibrate the arrival process of booking requests using a Poisson regression model and demonstrate that the LR-based bid price policies indeed outperform other heuristics consistently in both in-sample and out-of-sample horizons.</p

Supplementary information files for Bid price controls for car rental network revenue management

Supplementary files for article Bid price controls for car rental network revenue management We consider a car rental network revenue management (RM) problem, accounting for the key operational characteristics of car rental services such as the varying length of rentals and mobility of inventories which imply the inter-temporal and spatial correlations of rental demands for inventories across different locations and days. The problem is formulated as an infinite-horizon cyclic stochastic dynamic program to account for the time-varying and cyclic nature of car rental businesses. To tackle the curse of dimensionality, we propose a Lagrangian relaxation (LR) approach with product- and time-dependent Lagrangian multipliers to decomposing the dynamic network problem into multiple singlestation single-day sub-problems. We show that the Lagrangian dual problem is a convex program and then develop a subgradient-based algorithm to solve the dual problem and derive an LR-based bid price policy. To improve the scalability of the LR approach, we further propose three simpler LR-based bid price policy variants with either location-dependent or leadtime-dependent Lagrangian multipliers, or both. Our numerical study indicates that the LR-based bid price policies can outperform some commonly used heuristics. Using a set of real-world booking data, we provide a case study in which we empirically demonstrate the operational characteristics of car rental services, calibrate the arrival process of booking requests using a Poisson regression model and demonstrate that the LR-based bid price policies indeed outperform other heuristics consistently in both in-sample and out-of-sample horizons. </p

The multi-visit drone routing problem for pickup and delivery services

Unmanned aerial vehicles, commonly known as drones, have gained wide attention in recent years due to their potential of revolutionizing logistics and transportation. In this paper, we consider a variant of the combined truck-drone routing problem, which allows drones to serve multiple customers and provide both pickup and delivery services in each flight. The problem concerns the deployment and routing of a fleet of trucks, each equipped with a supporting drone, to serve all the pickup and delivery demands of a set of customers with minimal total cost. We explicitly model the energy consumption of drones by their travel distance, curb weight and the carrying weight of parcels, develop a mixed-integer linear programming model (MILP) with problem-customized inequalities, and show a sufficient condition for the benefit of the combined truck-drone mode over the truck-only mode. Considering the complexity of the MILP model, we propose a novel two-stage heuristic algorithm in which a maximum payload method is developed to construct the initial solutions, followed by an improved simulated annealing algorithm with problem-specific neighborhood operators and tailored acceleration strategies. Furthermore, two methods are developed to test the feasibility for both trucks and drones in each solution. The proposed algorithm outperforms two benchmark heuristics in our numerical experiments, which also demonstrate the considerable benefit of allowing multiple visits and both pickup and delivery operations in each drone flight.</p

A vehicle routing problem with distribution uncertainty in deadlines

This article considers a stochastic vehicle routing problem with probability constraints. The probability that customers are served before their (uncertain) deadlines must be higher than a pre-specified target. It is unrealistic to expect that the perfect knowledge on the probability distributions of deadlines is always available. To this end, we propose a distributionally robust optimisation framework to study worst bounds of the problem, which exploits the moment information of the historical observations. This framework includes two steps. We first use Conditional Value-at-Risk (CVaR) as a risk approximation to the probability of missing customer deadlines. The resulting nonlinear model is then transformed into a semi-infinite mixed integer program, using the dual form of the CVaR approximation. A sample approximation approach is then used to address the computational challenges. As the standard CVaR approximation to probability constraints is rather conservative, we suggest a relaxation to the approximation and develop an iterative algorithm to find the right value of the parameter that is introduced to the relaxed CVaR constraints. The extensive numerical experiments show that the routing policies developed by the proposed solution framework are robust and able to achieve the required target, regardless of deadline distributions

Carbon-efficient deployment of electric rubber-tyred gantry cranes in container terminals with workload uncertainty

Rubber-tyred gantry cranes are one of the major sources of carbon dioxide emissions in container terminals. In a move to green transportation, the traditional diesel powered cranes are being converted to electric ones. In this paper, we study the deployment of electric powered gantry cranes (ERTGs) in container terminal yards. Cranes always move in-between blocks to serve different workload. ERTGs use electricity for most movements but switch to diesel engines to allow inter-block transfers between unaligned blocks. We exploit this feature and propose to consider simultaneously the CO2 emissions and workload delays to develop carbon-efficient deployment strategies. Moreover, unlike previous works we consider the workload uncertainty, and model the problem as a two-stage stochastic program. A sample average approximation framework with Benders decomposition is employed to solve the problem. Multiple acceleration techniques are proposed, including a tailored regularised decomposition approach and valid inequalities. A case study with sample data from a major port in East China show that our proposal could reduce significantly CO2 emissions with only a marginal compromise in workload delays. Our numerical experiments also highlight the significance of the stochastic model and the efficiency of the Benders algorithms