Multi-stage Programming Model Research Articles

A multi-stage stochastic programming model for sustainable closed-loop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain

This paperproposes a multi-objective, multi-stage programming model to design a sustainable closed-loop supply chain network considering financial decisions. A multi-product, sustainable closed-loop plastic supply chain network design problem which encompasses economic, environmental and social objectives is modeled in a mathematical manner. The decisions to be made are concerned with location of facilities; the flow of products, loans to take and investments to make. Uncertainty issue is about demand of customers and investment's rate of return. The decision making model is formulated as a multi-objective, multi-stage mixed integer linear programming problem and is solved by implementing path formulation and augmented Ɛ-constraint methods. Computational analysis, is provided based on the subject company to determine the significance of the proposed model and the efficiency regarding integrating financial decisions with supply chain network design decisions.

Optimal Policy Mechanism Design for Cross-Sector and Multi-Stage Pollution Control with a Bilevel Model: Application to SO2 Emission in China

In this paper, we construct a multi-stage coordinated programming model under tax system to control SO2 emission. The model is based on an explicitly formulated SO2 abatement cost function created under Chinese condition. Analysis of the effectiveness and impact on the economy of the model is carried out with consideration of game theory. By solving the model, theoretical results show that the volume-based multi-stage SO2 tax system has two properties: effectiveness and equal-rate. Based on these theoretical results, empirical study is also performed using Chinese historical data. Compared with yearly single-stage programming model, the tax rate generated by the coordinated multi-stage programming model is time-invariant and rather moderate in scale. The total abatement cost among planning years in our model is 21.03 % less than the actual number and 6.68 % less than that in the single-stage situation. The tax payment suggested by our model is 10.62 % less than by the single-stage model. In general, a coordinated multi-stage programming model helps reduce the overall costs of environmental protection while achieving the same emission control target with less burden added to the economy.

Optimal Scheduling of Logistical Support for Medical Resource with Demand Information Updating

This paper presents a discrete time-space network model for a dynamic resource allocation problem following an epidemic outbreak in a region. It couples a forecasting mechanism for dynamic demand of medical resource based on an epidemic diffusion model and a multistage programming model for optimal allocation and transport of such resource. At each stage, the linear programming solves for a cost minimizing resource allocation solution subject to a time-varying demand that is forecasted by a recursion model. The rationale that the medical resource allocated in early periods will take effect in subduing the spread of epidemic and thus impact the demand in later periods has been incorporated in such recursion model. A custom genetic algorithm is adopted to solve the proposed model, and a numerical example is presented for sensitivity analysis of the parameters. We compare the proposed medical resource allocation mode with two traditional operation modes in practice and find that our model is superior to any of them in less waste of resource and less logistic cost. The results may provide some practical guidelines for a decision-maker who is in charge of medical resource allocation in an epidemics control effort.

A Method of Drawing up a Recursive Farming Plan by Use of a Multistage Programming Model

A Method of Drawing up a Recursive Farming Plan by Use of a Multistage Programming Model