On Policies for Single-leg Revenue Management with Limited Demand Information

In this paper we study the single-item revenue management problem, with no information given about the demand trajectory over time. When the item is sold through accepting/rejecting different fare classes, Ball and Queyranne (2009) have established the tight competitive ratio for this problem using booking limit policies, which raise the acceptance threshold as the remaining inventory dwindles. However, when the item is sold through dynamic pricing instead, there is the additional challenge that offering a low price may entice high-paying customers to substitute down. We show that despite this challenge, the same competitive ratio can still be achieved using a randomized dynamic pricing policy. Our policy incorporates the price-skimming technique from Eren and Maglaras (2010), but importantly we show how the randomized price distribution should be stochastically-increased as the remaining inventory dwindles. A key technical ingredient in our policy is a new "valuation tracking" subroutine, which tracks the possible values for the optimum, and follows the most "inventory-conservative" control which maintains the desired competitive ratio. Finally, we demonstrate the empirical effectiveness of our policy in simulations, where its average-case performance surpasses all naive modifications of the existing policies

Limousine Service Management: Capacity Planning with Predictive Analytics and Optimization

The limousine service in luxury hotels is an integral component of the whole customer journey in the hospitality industry. One of the largest hotels in Singapore manages a fleet of both in-house and outsourced vehicles around the clock, serving 9000 trips per month on average. The need for vehicles may scale up rapidly, especially during special events and festive periods in the country. The excess demand is met by having additional outsourced vehicles on standby, incurring millions of dollars of additional expenses per year for the hotel. Determining the required number of limousines by hour of the day is a challenging service capacity planning problem. In this paper, a recent transformational journey to manage this problem in the hotel is introduced, driving up to S\$3.2 million of savings per year with improved service level. The approach builds on widely available open-source statistical and spreadsheet optimization tools, along with robotic process automation, to optimize the schedule of its fleet of limousines and drivers, and to support decision-making for planners/controllers to drive sustained business value

Aerodynamic Shape Design of Transonic Airfoils Using Hybrid Optimization Techniques and CFD

This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to demonstrate an oscillatory behavior in the vicinity of a local optima. To overcome this tendency, a hybrid method designed to take full advantage of SPSA’s high rate of reduction of the objective function at the inception of the design process to drive the design cycles towards the optimal zone at first, and then combining with other methods to perform the final stages of the convergence towards the optimal solutions is considered. SPSA method has been combined with the gradient-based Broydon-Fletcher-Goldfarb-Shanno (BFGS) method as well as Simulated Annealing method for the transonic inverse airfoil design problem that is concerned with the specification of a target airfoil surface pressure distribution and starting from an initial guess of an airfoil shape, the target airfoil shape is reached by way of minimization of a quantity that depends on the difference between the target and current airfoil surface pressure distribution. For a typical transonic flow test case, the effects of using hybrid optimization techniques such as SPSA+BFGS and SPSA+SA as opposed to using SPSA alone can be seen in Figure 1. After 800 design cycles using SPSA, the hybrid SPSA+SA method took 2521 function evaluations of SA while the SPSA+BFGS method took 271 function evaluations to reach similar values which are much better than that reached by using SPSA alone in the entire minimization process. Results indicate that both of the two hybrid methods have capability to find a global optimum more efficiently than the SPSA method. The paper will address issues related to hybridization and its impact on the optimal airfoil shape designs in various contexts.Singapore-MIT Alliance (SMA

Applications of Semidefinite Optimization in Stochastic Project Scheduling

We propose a new method, based on semidefinite optimization, to find tight upper bounds on the expected project completion time and expected project tardiness in a stochastic project scheduling environment, when only limited information in the form of first and second (joint) moments of the durations of individual activities in the project is available. Our computational experiments suggest that the bounds provided by the new method are stronger and often significant compared to the bounds found by alternative methods.Singapore-MIT Alliance (SMA

On Optimizing PSA Berth Planning System

Competition among container ports continues to increase as the differentiation of hub ports and feeder ports progresses. Managers in many container terminals are trying to attract carriers by automating handling equipment, providing and speeding up various services, and furnishing the most current information on the flow of containers. At the same time, however, they are trying to reduce costs by utilizing resources efficiently, including human resources, berths, container yards, quay cranes, and various yard equipment. When planning berth usage, the berthing time and the exact position of each vessel at the wharf, as well as various quay side resources are usually determined in the process. Several variables must be considered, including the length overall (LOA) and arrival time of each vessel, the number of containers for discharging and loading, and the storage location of outbound/inbound containers to be loaded onto/discharged from the corresponding vessel. Furthermore, we aim to propose berthing plan that will be "robust", since the actual arrival time of each vessel can vary substantially from forecast. This is particular important for vessels from priority customers (called priority vessels hereon), who have been promised berth-on-arrival (i.e. within two hours of arriving) service guarantee in their contract with PSA. A robust plan will also helps to minimize the frequent updates (changes) to berthing plan that have repercussion in resource and sta deployment within the terminal. Thus, the problem reduces to one of finding a berthing plan, so that priority vessels can be berthed-on-arrival with high probability, and the vessels can be berthed as close to their preferred locations as possible, to reduce the cost of transporting the containers within the terminal. In this paper, we described an approach to address this problem.Singapore-MIT Alliance (SMA

Stochastic Transportation-Inventory Network Design Problem

In this paper, we study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand. Due to this uncertainty, some amount of safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers (and therefore inventory storage locations) for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. Shen et al. (2000) and Daskin et al. (2001) formulated this problem as a set-covering integer-programming model. The pricing subproblem that arises from the column generation algorithm gives rise to a new class of submodular function minimization problem. They only provided efficient algorithms for two special cases, and assort to ellipsoid method to solve the general pricing problem, which run in O(n⁷ log(n)) time, where n is the number of retailers. In this paper, we show that by exploiting the special structures of the pricing problem, we can solve it in O(n² log n) time. Our approach implicitly utilizes the fact that the set of all lines in 2-D plane has low VC-dimension. Computational results show that moderate size transportation-inventory network design problem can be solved efficiently via this approach.Singapore-MIT Alliance (SMA

A New Method to Solve Zero-Sum Games under Moment Conditions

When only the moments (mean, variance or t-th moment) of the underline distribution are known, numerous max-min optimization models can be interpreted as a zero-sum game, in which the decision maker (DM) chooses actions to maximize her expected profit while Adverse Nature chooses a distribution subject to the moments conditions to minimize DM’s expected profit. We propose a new method to efficiently solve this class of zero-sum games under moment conditions. By applying the min-max inequality, our method reformulates the zero-sum game as a robust moral hazard model, in which Adverse Nature chooses both the distribution and actions to minimize DM’s expected profit subject to incentive compatibility (IC) constraints. Under quasi-concavity, these IC constraints are replaced by the first-order conditions, which give rise to extra moment constraints. Interestingly, these extra moment constraints drastically reduce the number of corner points to be considered in the corresponding semi-infinite programming models. We show that in the equilibrium, these moment constraints are binding but have zero Lagrangian multipliers and thus facilitate closed-form solutions in several application examples with different levels of complexity. The high efficiency of the method enables us to solve a large class of zero-sum games and the corresponding max-min robust optimization models