A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Proving the performance of a new revenue management system

Revenue management (RM) is a complicated business process that can best be described ascontrol of sales (using prices, restrictions, or capacity), usually using software as a tool to aiddecisions. RM software can play a mere informative role, supplying analysts with formatted andsummarized data who use it to make control decisions (setting a price or allocating capacity fora price point), or, play a deeper role, automating the decisions process completely, at the otherextreme. The RM models and algorithms in the academic literature by and large concentrateon the latter, completely automated, level of functionality.A firm considering using a new RM model or RM system needs to evaluate its performance.Academic papers justify the performance of their models using simulations, where customerbooking requests are simulated according to some process and model, and the revenue perfor-mance of the algorithm compared to an alternate set of algorithms. Such simulations, whilean accepted part of the academic literature, and indeed providing research insight, often lackcredibility with management. Even methodologically, they are usually awed, as the simula-tions only test \within-model" performance, and say nothing as to the appropriateness of themodel in the first place. Even simulations that test against alternate models or competition arelimited by their inherent necessity on fixing some model as the universe for their testing. Theseproblems are exacerbated with RM models that attempt to model customer purchase behav-ior or competition, as the right models for competitive actions or customer purchases remainsomewhat of a mystery, or at least with no consensus on their validity.How then to validate a model? Putting it another way, we want to show that a particularmodel or algorithm is the cause of a certain improvement to the RM process compared to theexisting process. We take care to emphasize that we want to prove the said model as the causeof performance, and to compare against a (incumbent) process rather than against an alternatemodel.In this paper we describe a \live" testing experiment that we conducted at Iberia Airlineson a set of flights. A set of competing algorithms control a set of flights during adjacentweeks, and their behavior and results are observed over a relatively long period of time (9months). In parallel, a group of control flights were managed using the traditional mix of manualand algorithmic control (incumbent system). Such \sandbox" testing, while common at manylarge internet search and e-commerce companies is relatively rare in the revenue managementarea. Sandbox testing has an undisputable model of customer behavior but the experimentaldesign and analysis of results is less clear. In this paper we describe the philosophy behind theexperiment, the organizational challenges, the design and setup of the experiment, and outlinethe analysis of the results. This paper is a complement to a (more technical) related paper thatdescribes the econometrics and statistical analysis of the results.

Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case

We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, andthe firm decides the best subset to offer at any given moment to maximize expected revenue. The resultingdynamic program for the firm is intractable and approximated by a deterministic linear programcalled the CDLP which has an exponential number of columns. However, under the choice-set paradigmwhen the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has beenproposed but finding an entering column has been shown to be NP-hard. In this paper, starting with aconcave program formulation based on segment-level consideration sets called SDCP, we add a class ofconstraints called product constraints, that project onto subsets of intersections. In addition we proposea natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methodson the benchmark data sets in the literature. Both the product constraints and the ?SDCP method arevery simple and easy to implement and are applicable to the case of overlapping segment considerationsets. In our computational testing on the benchmark data sets in the literature, SDCP with productconstraints achieves the CDLP value at a fraction of the CPU time taken by column generation and webelieve is a very promising approach for quickly approximating CDLP when segment consideration setsoverlap and the consideration sets themselves are relatively small.

Optimization of multiclass queueing networks with changeover times via the achievable region method: Part II, the multi-station case

We address the problem of scheduling a multi-station multiclassqueueing network (MQNET) with server changeover times to minimizesteady-state mean job holding costs. We present new lower boundson the best achievable cost that emerge as the values ofmathematical programming problems (linear, semidefinite, andconvex) over relaxed formulations of the system's achievableperformance region. The constraints on achievable performancedefining these formulations are obtained by formulatingsystem's equilibrium relations. Our contributions include: (1) aflow conservation interpretation and closed formulae for theconstraints previously derived by the potential function method;(2) new work decomposition laws for MQNETs; (3) new constraints(linear, convex, and semidefinite) on the performance region offirst and second moments of queue lengths for MQNETs; (4) a fastbound for a MQNET with N customer classes computed in N steps; (5)two heuristic scheduling policies: a priority-index policy, anda policy extracted from the solution of a linear programmingrelaxation.

Thermal modeling and management in ultrathin chip stack technology

This paper presents a thermal modeling for power management of a new three-dimensional (3-D) thinned dies stacking process. Besides the high concentration of power dissipating sources, which is the direct consequence of the very interesting integration efficiency increase, this new ultra-compact packaging technology can suffer of the poor thermal conductivity (about 700 times smaller than silicon one) of the benzocyclobutene (BCB) used as both adhesive and planarization layers in each level of the stack. Thermal simulation was conducted using three-dimensional (3-D) FEM tool to analyze the specific behaviors in such stacked structure and to optimize the design rules. This study first describes the heat transfer limitation through the vertical path by examining particularly the case of the high dissipating sources under small area. First results of characterization in transient regime by means of dedicated test device mounted in single level structure are presented. For the design optimization, the thermal draining capabilities of a copper grid or full copper plate embedded in the intermediate layer of stacked structure are evaluated as a function of the technological parameters and the physical properties. It is shown an interest for the transverse heat extraction under the buffer devices dissipating most the power and generally localized in the peripheral zone, and for the temperature uniformization, by heat spreading mechanism, in the localized regions where the attachment of the thin die is altered. Finally, all conclusions of this analysis are used for the quantitative projections of the thermal performance of a first demonstrator based on a three-levels stacking structure for space application.

Impact of quality improvement tools on the performance of firms using different quality management systems

This study compares the impact of quality management tools on the performance of organisations utilising the ISO 9001:2000 standard as a basis for a quality-management system band those utilising the EFQM model for this purpose. A survey is conducted among 107 experienced and independent quality-management assessors. The study finds that organisations with qualitymanagement systems based on the ISO 9001:2000 standard tend to use general-purpose qualitative tools, and that these do have a relatively positive impact on their general performance. In contrast, organisations adopting the EFQM model tend to use more specialised quantitative tools, which produce significant improvements in specific aspects of their performance. The findings of the study will enable organisations to choose the most effective quality-improvement tools for their particular quality strategy