A randomized concave programming method for choice network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing froman offer set, have recently become popular in assortment optimization and revenue management.The dynamic program for these models is intractable and approximated by a deterministiclinear program called the CDLP which has an exponential number of columns. However, whenthe segment consideration sets overlap, the CDLP is difficult to solve. Column generationhas been proposed but finding an entering column has been shown to be NP-hard. In thispaper we propose a new approach called SDCP to solving CDLP based on segments and theirconsideration sets. SDCP is a relaxation of CDLP and hence forms a looser upper bound onthe dynamic program but coincides with CDLP for the case of non-overlapping segments. Ifthe number of elements in a consideration set for a segment is not very large (SDCP) can beapplied to any discrete-choice model of consumer behavior. We tighten the SDCP bound by(i) simulations, called the randomized concave programming (RCP) method, and (ii) by addingcuts to a recent compact formulation of the problem for a latent multinomial-choice model ofdemand (SBLP+). This latter approach turns out to be very effective, essentially obtainingCDLP value, and excellent revenue performance in simulations, even for overlapping segments.By formulating the problem as a separation problem, we give insight into why CDLP is easyfor the MNL with non-overlapping considerations sets and why generalizations of MNL posedifficulties. We perform numerical simulations to determine the revenue performance of all themethods on reference data sets in the literature.

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.

An intense form of homeostatic proliferation of naive CD8+ cells driven by IL-2.

In conditions of T lymphopenia, interleukin (IL) 7 levels rise and, via T cell receptor for antigen-self-major histocompatibility complex (MHC) interaction, induce residual naive T cells to proliferate. This pattern of lymphopenia-induced "homeostatic" proliferation is typically quite slow and causes a gradual increase in total T cell numbers and differentiation into cells with features of memory cells. In contrast, we describe a novel form of homeostatic proliferation that occurs when naive T cells encounter raised levels of IL-2 and IL-15 in vivo. In this situation, CD8(+) T cells undergo massive expansion and rapid differentiation into effector cells, thus closely resembling the T cell response to foreign antigens. However, the responses induced by IL-2/IL-15 are not seen in MHC-deficient hosts, implying that the responses are driven by self-ligands. Hence, homeostatic proliferation of naive T cells can be either slow or fast, with the quality of the response to self being dictated by the particular cytokine (IL-7 vs. IL-2/IL-15) concerned. The relevance of the data to the gradual transition of naive T cells into memory-phenotype (MP) cells with age is discussed.

Tomosyn-1 is involved in a post-docking event required for pancreatic beta-cell exocytosis.

Although the assembly of a ternary complex between the SNARE proteins syntaxin-1, SNAP25 and VAMP2 is known to be crucial for insulin exocytosis, the mechanisms controlling this key event are poorly understood. We found that pancreatic beta-cells express different isoforms of tomosyn-1, a syntaxin-1-binding protein possessing a SNARE-like motif. Using atomic force microscopy we show that the SNARE-like domain of tomosyn-1 can form a complex with syntaxin-1 and SNAP25 but displays binding forces that are weaker than those observed for VAMP2 (237+/-13 versus 279+/-3 pN). In pancreatic beta-cells tomosyn-1 was found to be concentrated in cellular compartments enriched in insulin-containing secretory granules. Silencing of tomosyn-1 in the rat beta-cell line INS-1E by RNA interference did not affect the number of secretory granules docked at the plasma membrane but led to a reduction in stimulus-induced exocytosis. Replacement of endogenous tomosyn-1 with mouse tomosyn-1, which differs in the nucleotide sequence from its rat homologue and escapes silencing, restored a normal secretory rate. Taken together, our data suggest that tomosyn-1 is involved in a post-docking event that prepares secretory granules for fusion and is necessary to sustain exocytosis of pancreatic beta-cells in response to insulin secretagogues.

On the throughput-WIP trade-off in queueing systems, diminishing returns and the threshold property: A linear programming approach

We present a new unifying framework for investigating throughput-WIP(Work-in-Process) optimal control problems in queueing systems,based on reformulating them as linear programming (LP) problems withspecial structure: We show that if a throughput-WIP performance pairin a stochastic system satisfies the Threshold Property we introducein this paper, then we can reformulate the problem of optimizing alinear objective of throughput-WIP performance as a (semi-infinite)LP problem over a polygon with special structure (a thresholdpolygon). The strong structural properties of such polygones explainthe optimality of threshold policies for optimizing linearperformance objectives: their vertices correspond to the performancepairs of threshold policies. We analyze in this framework theversatile input-output queueing intensity control model introduced byChen and Yao (1990), obtaining a variety of new results, including (a)an exact reformulation of the control problem as an LP problem over athreshold polygon; (b) an analytical characterization of the Min WIPfunction (giving the minimum WIP level required to attain a targetthroughput level); (c) an LP Value Decomposition Theorem that relatesthe objective value under an arbitrary policy with that of a giventhreshold policy (thus revealing the LP interpretation of Chen andYao's optimality conditions); (d) diminishing returns and invarianceproperties of throughput-WIP performance, which underlie thresholdoptimality; (e) a unified treatment of the time-discounted andtime-average cases.

Implementing interactive computing in an object-oriented environment

Statistical computing when input/output is driven by a Graphical User Interface is considered. A proposal is made for automatic control ofcomputational flow to ensure that only strictly required computationsare actually carried on. The computational flow is modeled by a directed graph for implementation in any object-oriented programming language with symbolic manipulation capabilities. A complete implementation example is presented to compute and display frequency based piecewise linear density estimators such as histograms or frequency polygons.

Implementing TURF analysis through binary linear programming

This paper introduces the approach of using Total Unduplicated Reach and Frequency analysis (TURF) to design a product line through a binary linear programming model. This improves the efficiency of the search for the solution to the problem compared to the algorithms that have been used to date. The results obtained through our exact algorithm are presented, and this method shows to be extremely efficient both in obtaining optimal solutions and in computing time for very large instances of the problem at hand. Furthermore, the proposed technique enables the model to be improved in order to overcome the main drawbacks presented by TURF analysis in practice.

Restless bandits, linear programming relaxations and a primal-dual index heuristic

We develop a mathematical programming approach for the classicalPSPACE - hard restless bandit problem in stochastic optimization.We introduce a hierarchy of n (where n is the number of bandits)increasingly stronger linear programming relaxations, the lastof which is exact and corresponds to the (exponential size)formulation of the problem as a Markov decision chain, while theother relaxations provide bounds and are efficiently computed. Wealso propose a priority-index heuristic scheduling policy fromthe solution to the first-order relaxation, where the indices aredefined in terms of optimal dual variables. In this way wepropose a policy and a suboptimality guarantee. We report resultsof computational experiments that suggest that the proposedheuristic policy is nearly optimal. Moreover, the second-orderrelaxation is found to provide strong bounds on the optimalvalue.

Proposta de Implementação do Time-Driven Activity - Based Costing numa Empresa Industrial

O presente trabalho tem como objectivo a apresentação do processo de concepção e implementação de um projecto-piloto de um sistema de custeio baseado em actividades e tempo – TDABC, numa empresa industrial de conserva de pescado, Frescomar, S.A. Mais especificamente o trabalho desenvolveu-se na apuração do custo da área de produção da empresa objecto de estudo. O sistema de custeio Time-Driven Activity-Based Costing (TDABC) representa um modelo alternativo aos sistemas tradicionais da contabilidade de custos, e é uma evolução do Activity-Based Costing (ABC). O sistema ABC surgiu durante a década de 1980 e tem vindo a evoluir desde então. Muitas empresas abandonaram o ABC, pois este método de custeio, além de não conseguir captar a complexidade das suas operações, a sua implementação é demorado, e é muito dispendioso de aplicar e manter. Com o método TDABC encontra-se uma alternativa para dirimir estes problemas. Observou-se a necessidade do desenvolvimento de apenas algumas equações de tempo (time equations) para representar as principais actividades da área de produção. Foram observadas, durante a realização do estudo, vários dos benefícios do TDABC como: a facilidade em modelar actividades complexas por meio das equações de tempo, obtenção rigorosa de gastos e o baixo tempo de desenvolvimento do modelo. Contudo, também foram identificadas algumas limitações como subjectividade no cálculo do tempo de execução das actividades e dificuldade em se estimar as equações de tempo para actividades pouco estruturadas.