A new approach for allocating fixed costs among decision making units
Ruiyue Lin Zhiping Chen Zongxin Li
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.
keywords: units-invariance. efficiency invariance Data envelopment analysis fixed cost allocation uniqueness
Time consistent policy of multi-period mean-variance problem in stochastic markets
Zhiping Chen Jia Liu Gang Li
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.
keywords: policy revision. Markovian markets Bellman's optimality principle mean-variance Time inconsistency
Continuity and stability of two-stage stochastic programs with quadratic continuous recourse
Zhiping Chen Youpan Han
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.
keywords: Stochastic quadratic programming stability sample average approximation. probability metric Lipschitz continuity

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