Inflation and the optimal inventory replenishment schedule within a finite planning horizon

The subject of this paper is the problem of finding the optimal replenishment schedule for an inventory, subject to time-dependent demand and deterioration, within a finite time planning horizon. It is shown that taking inflation into account has a profound effect on the solution of the problem. For instance, there is a critical number of replenishment periods, in excess of which the optimal schedule is characterized by the inclusion of token orders at the end of the planning horizon. This and other conclusions, obtained via a careful mathematical analysis of the problem, rectify those of earlier studies.     

Robust combinatorial optimization with variable cost uncertainty

We present in this paper a new model for robust combinatorial optimization with cost uncertainty that generalizes the classical budgeted uncertainty set. We suppose here that the budget of uncertainty is given by a function of the problem variables, yielding an uncertainty multifunction. The new model is less conservative than the classical model and approximates better Value-at-Risk objective functions, especially for vectors with few non-zero components. An example of budget function is constructed from the probabilistic bounds computed by Bertsimas and Sim. We provide an asymptotically tight bound for the cost reduction obtained with the new model. We turn then to the tractability of the resulting optimization problems. We show that when the budget function is affine, the resulting optimization problems can be solved by solving n+1$n+1$ deterministic problems. We propose combinatorial algorithms to handle problems with more general budget functions. We also adapt existing dynamic programming algorithms to solve faster the robust counterparts of optimization problems, which can be applied both to the traditional budgeted uncertainty model and to our new model. We evaluate numerically the reduction in the price of robustness obtained with the new model on the shortest path problem and on a survivable network design problem.     

Using possibilistic logic for modeling qualitative decision: Answer Set Programming algorithms

A qualitative approach to decision making under uncertainty has been proposed in the setting of possibility theory, which is based on the assumption that levels of certainty and levels of priority (for expressing preferences) are commensurate. In this setting, pessimistic and optimistic decision criteria have been formally justified. This approach has been transposed into possibilistic logic in which the available knowledge is described by formulas which are more or less certainly true and the goals are described in a separate prioritized base. This paper adapts the possibilistic logic handling of qualitative decision making under uncertainty in the Answer Set Programming (ASP) setting. We show how weighted beliefs and prioritized preferences belonging to two separate knowledge bases can be handled in ASP by modeling qualitative decision making in terms of abductive logic programming where (uncertain) knowledge about the world and prioritized preferences are encoded as possibilistic definite logic programs and possibilistic literals respectively. We provide ASP-based and possibilistic ASP-based algorithms for calculating optimal decisions and utility values according to the possibilistic decision criteria. We describe a prototype implementing the algorithms proposed on top of different ASP solvers and we discuss the complexity of the different implementations.     

Combining chain-ladder claims reserving with fuzzy numbers

In this paper we extend the classical chain-ladder claims reserving method using fuzzy methods. Therefore, we derive new estimators for the claims development factors as well as new predictors for the ultimate claims. The advantage in using fuzzy numbers lies in the fact that the model uncertainty is directly included in and can be controlled by the “new” fuzzy claims development factors. We also provide an estimator for the uncertainty of the ultimate claims for single accident years and for aggregated accident years.     

Some results on cooperative interval games

Uncertainty is a daily presence in the real world. It affects our decision-making and may have influence on cooperation. On many occasions, uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e. payoffs lie in some intervals. A suitable game theoretic model to support decision-making in collaborative situations with interval data is that of cooperative interval games. Solution concepts that associate with each cooperative interval game sets of interval allocations with appealing properties provide a natural way to capture the uncertainty of coalition values into the players’ payoffs. In this paper, the relations between some set-valued solution concepts using interval payoffs, namely the interval core, the interval dominance core, the square interval dominance core and the interval stable sets for cooperative interval games, are studied. It is shown that the interval core is the unique stable set on the class of convex interval games.     

市场需求不确定结构模型研究

在一个由原始设备制造商、合同制造商和原材料供应商组成的三级链中,简述了在市场需求不确定情况下存在成本信息不对称的整合外包模型,并对这个模型进行了分析.最后,运用MATLAB进行了实例分析,说明了市场需求不确定对模型的影响.     

Knight不确定下考虑保险和退休的最优消费-投资和遗产问题研究

研究在Knight不确定环境下,考虑投资者遗产和保险,在三种不同借款约束下的最优消费与投资问题.借助于倒向随机微分方程（BsDE）理论求出了投资者最优消费和投资策略的显式表达式.最后结合数值分析,给出含糊与含糊态度对最优消费和投资决策的影响.     

Multiresidue analysis of 83 pesticides and 12 dioxin-like polychlorinated biphenyls in wine by gas chromatography–time-of-flight mass spectrometry

A multiresidue method is described for simultaneous estimation of 83 pesticides and 12 dioxin-like polychlorinated biphenyls (PCBs) in red and white wines. The samples (20 mL wine, acidified with 20 mL 1% HCl) were extracted with 10 mL ethyl acetate (+20 g sodium sulphate) and cleaned by dispersive solid-phase extraction (DSPE) with anhydrous calcium chloride and Florisil successively. The final extract (5 mL) was solvent exchanged to 1 mL of cyclohexane:ethyl acetate (9:1), further cleaned by DSPE with 25 mg primary secondary amine sorbent and analyzed by gas chromatography–time-of-flight mass spectrometry (GC–TOF-MS) within 31 min run time. The limits of quantification of most analytes were ≤10–20 μg/L. Acidification of wine prior to extraction prevented hydrolysis of organophosphorous pesticides as well as dicofol, whereas treatment with CaCl₂ minimized the fatty acid co-extractives significantly. Solvent exchange to cyclohexane:ethyl acetate (9:1) further minimized the co-extractives. Recoveries at 5, 10 and 20 ng/mL were >80% for most analytes except cyprodinil, buprofezin and iprodione. The expanded uncertainties at 10 ng/mL were <20% for most analytes. Intra-laboratory precision in terms of Horwitz ratio of all the analytes was below 0.5, suggesting ruggedness of the method. Effectively, the method detection limit for most analytes was as low as up to 1 ng/mL in both red and white wine, except for cyfluthrin and cypermethrin.     

铬铁矿标准物质研制

根据我国铬铁矿标准物质的需求,制备了4个铬铁矿标准物质,Cr2O3含量范围为17.59%～57.80%。经检验,制备的标准物质具有良好的均匀性与稳定性。采用多家实验室协作定值方法,测试方法可靠,标准值与不确定度计算合理。该系列铬铁矿标准物质定值项目18项,其中16项成分给出标准值,FeO和CO2两项成分给出参考值。     

ASSESSING COMPONENTS OF UNCERTAINTY IN VPA ABUNDANCE AND MORTALITY ESTIMATES USING AN ALTERNATIVE EXPLOITATION RATE‐BASED ALGORITHM

Abstract Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope approximation to the original VPA equations, I show how to derive variance estimates for the key VPA outputs (recruitment, SSB, exploitation rates) given variance information on the key inputs (catch‐at‐age/terminal exploitation rates). Given the alternative VPA algorithm permits closed‐form solutions for the outputs in terms of the inputs, the delta method is employed to obtain the variance estimates, removing the need for complex simulation techniques. Using North Sea herring data as an example, the method’s utility is demonstrated by exploring the impact of aging error in the catch data and tuning error on the precision of estimates of SSB, recruitment and exploitation rates, and the parameters of the stock‐recruit relationship.