## Journals

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JIMO

How to equitably distribute a common fixed cost among decision
making units (DMUs) of an organization is a typical problem in
organization management. Based on the data envelopment analysis
technique, this paper proposes a new proportional sharing model to
determine a unique fixed cost allocation under two assumptions:
efficiency invariance and zero slack. It is noteworthy that the
fixed cost allocation determined by our proportional sharing model
is a feasible solution to the model proposed by Cook and Zhu [Cook
and Zhu,

*Allocation of shared costs among decision making units: A DEA approach*, Computers & Operations Research,**32**(2005) 2171-2178]. To ensure the uniqueness of the fixed cost allocation, three algorithms are proposed under the new model. Different from current fixed cost allocation methods under the efficiency invariance assumption, our approach can generate a fixed cost allocation that is unique, partially dependent of DMUs' inputs and units-invariant, and thus is more effective. Numerical examples are used to illustrate the validity and superiorities of our approach.
JIMO

Due to the non-separability of the variance operator, the optimal
investment policy of the multi-period mean-variance model in
Markovian markets doesn't satisfy the time consistency. We propose a
new weak time consistency in stochastic markets and show that the
pre-commitment optimal policy satisfies the weak time consistency at
any intermediate period as long as the investor's wealth is no more
than a specific threshold. When the investor's wealth exceeds the
threshold, the weak time consistency no longer holds. In this case,
by modifying the pre-commitment optimal policy, we derive a wealth
interval, from which we determine a more efficient revised policy.
The terminal wealth obtained under this revised policy can achieve
the same mean as, but not greater variance than those of the
terminal wealth obtained under the pre-commitment optimal policy; a
series of superior investment policies can be obtained depending on
the degree the investor wants the conditional variance to decrease.
It is shown that, in the above revising process, a positive cash
flow can be taken out of the market. Finally, an empirical example
illustrates our theoretical results. Our results generalize existing
conclusions for the multi-period mean-variance model in
deterministic markets.

NACO

For two-stage stochastic programs with quadratic continuous recourse
where all the coefficients in the objective function and the
right-hand side vector in the second-stage constraints vary
simultaneously, we firstly show the locally Lipschtiz continuity of
the optimal value function of the recourse problem, then under
suitable probability metric, we derive the joint Lipschitz
continuity of the expected optimal value function with respect to
the first-stage variables and the probability distribution.
Furthermore, we establish the qualitative and quantitative stability
results of the optimal value function and the optimal solution set
with respect to the Fortet-Mourier probability metric, when the
underlying probability distribution is perturbed. Finally, we show
the exponential convergence rate of the optimal value sequence when
we solve two-stage quadratic stochastic programs by the sample
average approximation method.

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