An approximate dynamic programming approach for network capacity control problem with origin-destination demands

We consider a canonical quantity-based network revenue management problem where a firm accepts or rejects incoming customer requests irrevocably in order to maximize expected revenue given limited resources. Because of the curse of dimensionality, the exact solution to this problem by dynamic programming is intractable when the number of resources is large. We study a family of re-solving heuristics that periodically re-optimize an approximation to the original problem known as the deterministic linear program (DLP), where random customer arrivals are replaced by their expectations. We find that, in general, frequently re-solving the DLP produces the same order of revenue loss as one would get without re-solving, which scales as the square root of the time horizon length and resource capacities. By re-solving the DLP at a few selected points in time and applying thresholds to the customer acceptance probabilities, we design a new re-solving heuristic with revenue loss that is uniformly bounded by a constant that is independent of the time horizon and resource capacities. This paper was accepted by Kalyan Talluri, revenue management and market analytics.

This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the established dynamic programming model for solving linear programming problems in a crisp environment. The mentioned approach is upgraded to address the problem in an uncertain environment. Dynamic programming model can either be passing forward or backward. In the proposed approach backward dynamic programming approach is adopted to address the problem. It is then followed by implementing the proposed method on the education system of Pakistan. The education system of Pakistan comprises of the Primary, Middle, Secondary, and Tertiary education stages. The problem is to maximize the efficiency of the education system while achieving the targets with minimum usage of the constrained resources. Likewise the model tries to maximize the enrollment in the Primary, Middle, Secondary and Tertiary educational categories, subject to the total available resources in a fuzzy uncertain environment. The solution proposes that the enrollment can be increased by an amount 9997130, by increasing the enrollment in the Middle and Tertiary educational categories. Thus the proposed method contributes to increase the objective function value by 30%. Moreover, the proposed solutions violate none of the constraints. In other words, the problem of resources allocation in education system is efficiently managed to increase efficiency while remaining in the available constrained resources. The motivation behind using the dynamic programming methodology is that it always possesses a numerical solution, unlike the other approaches having no solution at certain times. The proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.

<p class="MsoNormal" style="text-justify: inter-ideograph; text-align: justify; margin: 0in 36.1pt 0pt 0.5in; layout-grid-mode: char;"><span style="mso-bidi-font-style: italic;"><span style="font-size: x-small;"><span style="font-family: Times New Roman;">Seat inventory control is an important problem in revenue management which is to decide whether to accept or reject a booking request during the booking horizon in airlines. The problem can be modeled as dynamic stochastic programs, which are computationally intractable in network settings. Various researches have been tried to solve it effectively. Even though dynamic (and stochastic) programming (DP) models can be solved it optimally, they are computationally intractable even for small sized networks. Therefore, in practice, DP models are approximated by various mathematical programming models. In this paper, we propose an approximation model for solving airline seat inventory control problem in network environments. Using Linear Approximation technique, we will transform our problem into a concave piecewise LP model. Based on the optimal solution of ours, we suggest how to implement it for airline inventory control policies such as booking limits, bid-price controls and virtual nesting controls.</span></span></span></p>

Estimating multi-year [formula omitted] origin-destination demand using high-granular multi-source traffic data

Rail ticket allocation is a typical technique of revenue management that the operators determine the quantity of each train tickets allocated to each OD (Origin-Destination) pair. For increasing ticket allocation scheme flexibility and selling more tickets under stochastic demand, rail operators propose OD-shared tickets that are shared by all OD passengers. For avoiding OD-shared tickets are cut off by short-distance OD at early stage which causes long-distance passengers fail to purchase tickets, we integrate OD-shared ticket sales strategy into ticket allocation problem to further utilize OD-shared tickets. We formulate the model to jointly optimize both OD ticket and OD-shared ticket scheme and OD-shared ticket sales strategy. We simulate passenger purchasing process to calculate the ticket sold quantity and nest it in PSO algorithm to solve the model. Numerical experiment results show that considering OD-shared ticket sales strategy effectively improves OD-shared ticket and total ticket revenue by 9.55% and 2.26% respectively.

Contributors

The natural flow regime can sustain the ecological integrity of riverine ecosystems. Different reservoir operation polices differ in their effects on the degree of alteration of natural flow regimes. Dynamic programming plays an important role in developing operation policies. When using dynamic programming models to develop operation policies, the discrete number of storage states (DNSS), which is a key factor affecting the reservoirs operation policies, is always been determined based on computational efficiency and economic benefits. Little consideration has been given to the ecological disturbance caused by different DNSS‐based operation policies. To analyze the impact of DNSS, we built a deterministic dynamic programming model to explore the relationship among DNSS, the flow regime alteration (ecological disturbance), and the cumulative annual power generation (economic benefits) by setting a range of DNSS scenarios. We used three reservoirs with different storage coefficients (ratios of usable storage to annual average runoff) as examples and used the range of variability approach to assess the ecological disturbance under these scenarios. We compared the results with those of a stochastic dynamic programming (SDP) model and a Bayesian SDP (BSDP) model. We found that when DNSS is low, increasing DNSS improves economic benefits but causes a more severe ecological disturbance; when DNSS is high, increasing DNSS improves the economic benefits only slightly, without exacerbating the ecological disturbance; for a given DNSS, the BSDP model provides higher economic benefits than the SDP model and a similar disturbance of the riverine ecosystem; and larger reservoirs more often cause more severe disturbance of riverine ecosystems because monthly mean flows and annual extreme flows change more drastically. Our results will help to protect the riverine ecosystems and improve economic benefits if reservoir operation managers consider DNSS using dynamic programming models.

The problem of designing fibre-optic networks for local-access telecommunications generates (at least) three non-trivial subproblems. In the first of these subproblems one must determine how many fibre-optic cables (fibres) are required at either end of a street. In the next subproblem a minimum-cost network must be designed to support the fibres. The network must also provide distinct paths from either end of the street to the central exchange(s). Finally, the fibre-optic cables must be placed in protective covers. These covers are available in a number of different sizes, allowing some flexibility when covering each section of the network. In this paper we describe a dynamic programming (DP) formulation for finding a minimum-cost (protective) covering for the network (the third of the subproblems). This problem is a generalised set covering problem with side constraints and is further complicated by the introduction of fixed and variable welding costs. The DP formulation selects covers along each arc (in the network), but cannot exactly model the fixed costs and so does not guarantee optimality. We also describe an integer programming (IP) formulation for assessing the quality of the DP solutions. The cost of the networks constructed by the IP model is less than those designed using the DP model, but the saving is not significant for the problems examined (less than 0.1%). This indicates that the DP model will generally give very good solutions. Furthermore, as the problem dimensions grow, DP gives significantly better solution times than IP.

CARE: Heuristics for two-stage multi-product inventory routing problems with replenishments

A linear programming-based method for the network revenue management problem of air cargo

Standardized cargo network revenue management with dual channels under stochastic and time-dependent demand

Automated extraction of origin-destination demand for public transportation from smartcard data with pattern recognition

SummaryThe estimation of finite‐horizon discrete‐choice dynamic programming (DCDP) models is computationally expensive. This limits their realism and impedes verification and validation efforts. Keane and Wolpin (Review of Economics and Statistics, 1994, 76(4), 648–672) propose an interpolation method that ameliorates the computational burden but introduces approximation error. I describe their approach in detail, successfully recompute their original quality diagnostics, and provide some additional insights that underscore the trade‐off between computation time and the accuracy of estimation results.

This paper deals with the capacitated single-stage production lot sizing and scheduling problem with multiple items, setup time, stochastic demand and unrelated parallel machines. A stochastic mixed-integer linear programming model is proposed to formulate the problem. Based on the uncertain constraints, the chance constrained programming approach is used to transform them into equivalent deterministic constraints and then obtain an optimal solution by deterministic mixed-integer linear programming model. Due to the complexity of problem, the mixed-integer programming (MIP) of the equivalence deterministic model of the capacitated single-stage production lot sizing problem with multiple items, setup time, stochastic demand and unrelated parallel machines is reformulated as a shortest path reformulation problem. The proposed algorithm is evaluated through a numerical example. Computational results show that the proposed method gives optimal or near optimal solution and have good-quality result for the test problem.

Existing work has tackled the problem of estimating Origin-Destination (OD) demands and recovering travel latency functions in transportation networks under the Wardropian assumption. The ultimate objective is to derive an accurate predictive model of the network to enable optimization and control. However, these two problems are typically treated separately and estimation is based on parametric models. In this paper, we propose a method to jointly recover nonparametric travel latency cost functions and estimate OD demands using traffic flow data. We formulate the problem as a bilevel optimization problem and develop an iterative first-order optimization algorithm to solve it. A numerical example using the Braess Network is presented to demonstrate the effectiveness of our method.