Models Markowitz

The first approach adopts the classical Markowitz s MV model to handle randomness in the objective function coefficients of prices, in which the expected profit is maximized while an appended term representing the magnitude of operational risk due to variability or dispersion in price, as measured by variance, is minimized (Eppen, Martin, and Schrage, 1989). The model can be formulated as minimizing risk (i.e., variance) subject to a lower bound constraint on the target profit (i.e., the mean return). 

Konno and Yamazaki (1991) proposed a large-scale portfolio optimization model based on mean-absolute deviation (MAD). This serves as an alternative measure of risk to the standard Markowitz s MV approach, which models risk by the variance of the rate of return of a portfolio, leading to a nonlinear convex quadratic programming (QP) problem. Although both measures are almost equivalent from a mathematical point-of-view, they are substantially different computationally in a few perspectives, as highlighted by Konno and Wijayanayake (2002) and Konno and Koshizuka (2005). In practice, MAD is used due to its computationally-attractive linear property. 

In stochastic optimization, Cv can be purposefully employed to investigate, denote, and compare the relative uncertainty in models being studied. In a risk minimization model, as the expected value is reduced, the variability in the expected value (for example, as measured by variance or standard deviation) is reduced. The ratio of this change can be captured and described by Cv. Consequently, a comparison of the relative merit of models in terms of their robustness can be represented by their respective values of Cv, in the sense that a model with a lower Cv is favored since there is less uncertainty associated with it. In fact, Markowitz (1952) advocates that the use of Cy as a measure of risk would equally ensure that the outcome of a decisionmaking process still lies in the set of efficient portfolios for the case of operational investments. 

Fein D, Pennington B, Markowitz P, Braveman M, Waterhouse L (1986) Toward a neuropsychological model of infantUe autism are the social deficits primary J Am Acad Child Adolesc Psychiatry 25 198-212. 

Markowitz and Rosner, Deceit and Denial, p. 35 D. Davis, Secret History of the War on Cancer (Basic Books, New York, 2007), pp. 79, 94-95 J. O. Nriagu, Clair Patterson and Robert Kehoe s Paradigm of Show Me the Data on Environmental Lead Poisoning, Environmental Research, vol. A78, pp. 71—78 (1998) A. P. Loeb, Paradigms Lost A Case Study Analysis of Models of Corporate Responsibility for... 

CACI Products Company provides SIMSCRIPT II.5. Developed by Kiviat, Villanueva, and Markowitz, it is an event-oriented discrete-event simulation language (Eiviat et al. 1969 RusseU 1983). SIMSCRIPT II.5 consists of features for developing time-driven simulation models. It includes both... 

Chelatable lead is widely accepted as representing removal from soft tissue (e.g., Chisolm and Barltrop, 1979), but some mobilizable compartment for lead storage in bone must also be providing a sizeable contribution. Evidence for the bone source includes (1) the age dependency of chelatable lead in non-occupationally exposed subjects, whereas lead in soft tissue is rather invariant with age (Araki, 1973 Araki and Ushio, 1982) (2) experimental animal (Hammond, 1971, 1973) and in vitro bone culture data (Rosen and Markowitz, 1980) showing removal of lead from bone and (3) the tracer modelling data of Rabinowitz et al (1977), which define a bone compartment for lead which is kinetically well mixed with those for blood and soft tissue. 

We propose an integer quadratic programming model for partner selection that tries to minimize the overall cost impact from the deviation in supplier costs. Such a model will be very useftil to supply chain owners and channel masters. The model is an adaptation of the Markowitz model for financial portfolio management, for the purpose of managing a portfolio of suppliers. For this model, we define the impact in terms of the risk as given by the deviation of the total supply ehain cost from its expected mean value. Given the expected costs and the variability of costs for all suppliers and manufacturers the objective is to ehoose a set of suppliers and manufacturers that minimize the expected cost of operating the entire supply chain and at the same time minimize the risk of variations in the total supply chain cost. The selection of these partners also considers the allocation of orders between these selected partners. 

---