Multi-stage Stochastic Programming Method Research Articles

Liability-driven investment for pension funds: stochastic optimization with real assets

Using a multi-stage stochastic programming method, we suggest an optimal liability-driven investment (LDI) strategy for a closed defined-benefit pension fund including real assets. The objective is to jointly optimize contribution, funding ratio, and buyout cost, subject to a constraint on downside risk in terms of expected shortfall of assets relative to liabilities. Over a 10-year planning horizon, the optimal LDI strategy with a key-rate duration-matching bond portfolio outperforms the corresponding strategy with a duration-convexity matching bond portfolio as well as a strategy with an aggregate bond index-tracking portfolio. When real assets are introduced, the optimal LDI strategy includes significant investment in infrastructure and real estate, illiquidity notwithstanding. Nevertheless, delays in sales of real assets induced by illiquidity can increase downside risk.

Design of a Supply Chain-Based Production and Distribution System Based on Multi-Stage Stochastic Programming

Abstract Supply chains are one of the key tools in optimizing production and distribution simultaneously. However, information uncertainty is always a challenge in production and distribution management. The main purpose of this paper is to design a two-echelon supply chain in a multi-cycle state and in conditions of demand uncertainty. The task includes determining the number and location of distribution centers, planning capacity for active distribution centers, and determining the amount of shipments between different levels so that the total costs of the chain are minimized. Uncertainty is applied through discrete scenarios in the model and the problem is formulated by multi-stage stochastic programming method in the form of a mixed integer linear model. The results acquired using two indicators called VMS and VSS demonstrated that modeling the supply chain design problem with the multi-stage stochastic approach can result in significant costs reduction. Plus, utilizing mathematical expectation can generate misleading results, therefore resulting in the development of supply chain designs incapable of satisfying demand due to its overlooked limitations.

Lyapunov Optimization-Based Trade-Off Policy for Mobile Cloud Offloading in Heterogeneous Wireless Networks

In order to improve mobile users’ service experience, mobile cloud computing (MCC) is promoted. Although MCC can alleviate the burdens of Smart mobile devices (SMDs) by offloading computation-intensive applications to the cloud, it also aggravates computing and storage overheads in cloud centers and bandwidth overhead on wireless links for offloading workloads of mobile users. Therefore, we should carefully design the offloading policy to decrease these overheads while easing the burdens of SMDs. To this end, we investigate the offloading policy in heterogeneous wireless networks. In this paper, a queue model is built to formulate the mobile users’ workload offloading problem and Lyapunov optimization framework is proposed to make trade-off between system offloading utility and queue backlog. For deterministic WiFi connections, a Lagrangian optimization method is proposed to decide the optimal offloading workloads. Furthermore, considering random WiFi connection durations, a multi-stage stochastic programming method is proposed. The experimental results show effectiveness of the Lagrangian optimization offloading method for deterministic WiFi connection and the multi-stage stochastic programming method for random WiFi connection.

Liability-Driven Investment for Pension Funds: Stochastic Optimization with Real Assets

Using a multi-stage stochastic programming method, we suggest an optimal liability-driven investment (LDI) strategy for a closed defined-benefit pension fund including real assets. The objective is to minimize or stabilize contributions, funding ratio, buyout cost, and expected shortfall. Over a 10-year planning horizon, the optimal LDI strategy with a key-rate duration-matching bond portfolio outperforms one with a duration-convexity matching bond portfolio or an aggregate bond index-tracking portfolio in terms of the objective measures. When real assets are introduced, the optimal LDI strategy includes significant investment in infrastructure and real estate, illiquidity notwithstanding. Nevertheless, delays in sales of real assets induced by illiquidity can increase downside risk.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

We develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

Water resources management under multi-parameter interactions: A factorial multi-stage stochastic programming approach

The paper proposes a factorial multi-stage stochastic programming (FMSP) approach to support water resources management under uncertainty. This approach was developed based on the conventional inexact multi-stage stochastic programming method. Five alternative inexact multi-stage stochastic programming algorithms in addition to the conventional algorithm were introduced and bundled to offer multiple decision options that reflect decision makers' perspectives and the complexities in system uncertainties. More importantly, factorial analysis, a multivariate inference method, was introduced into the modeling framework to analyze the potential interrelationships among a variety of uncertain parameters and their impacts on system performance. The proposed approach was applied to a water resources management case. The desired water-allocation schemes were obtained to assist in maximizing the total net benefit of the system. Multiple uncertain parameters and their interactions were examined, and those that had significant influences on system performance were identified. For example, the medium flow in the third planning period was the system objective's most influential factor. Any variation of this factor would significantly influence the acquisition of the total net benefit in the community. The significant interactions were also identified, such as the interaction between the agricultural sector's penalty and the medium flow in the third planning period. Through the analysis of multi-parameter interactions, the interrelationships among the uncertain parameters could be further revealed.

Simulation-based optimization method for water resources management in Tarim River Basin, China

In this study, a simulation-based optimization method (SOM) is developed for supporting water resources planning and management under uncertainty in Tarim River Basin, China. The modeling system couples a lumped rainfall runoff model and an inexact multistage stochastic programming (IMSP) into the general framework. The SOM extends upon the existing multistage stochastic programming method by allowing uncertainties expressed as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. Its random parameter is provided by the statistical analysis of simulation outcomes of the rainfall runoff model. Moreover, it can also reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. The results indicate that reasonable solutions have been generated. The results are helpful for water resources managers in not only making decisions of water allocation but also gaining insight into the tradeoffs between environmental and economic objectives.

An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty

In this study, an interval-parameter multi-stage stochastic linear programming (IMSLP) method has been developed for water resources decision making under uncertainty. The IMSLP is a hybrid methodology of inexact optimization and multi-stage stochastic programming. It has three major advantages in comparison to the other optimization techniques. Firstly, it extends upon the existing multi-stage stochastic programming method by allowing uncertainties expressed as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. Secondly, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. Thirdly, it cannot only handle uncertainties through constructing a set of scenarios that is representative for the universe of possible outcomes, but also reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. The developed IMSLP method is applied to a hypothetical case study of water resources management. The results are helpful for water resources managers in not only making decisions of water allocation but also gaining insight into the tradeoffs between environmental and economic objectives.