Two-stage Linear Programming Model Research Articles

A Hybrid Heuristic Algorithm for Maximizing the Resilience of Underground Logistics Network Planning

In recent times, there has been a sharp increase in the congestion of ground transportation, the scarcity of land resources, and various disasters. Hence, there is an urgent need to find an effective and sustainable approach to transportation. The construction of an underground logistics network, where transportation activities occur beneath the surface of the ground, is anticipated to emerge as a future trend. This study aims to formulate a resilient-maximizing plan for the underground logistics network, ensuring optimal meeting of transportation demands in the aftermath of ground disasters. Accordingly, a two-stage linear programming model is established to determine the layout plan for the most resilient underground logistics network. The first phase of the model is designed to generate viable layouts for the underground logistics network, while the second phase is dedicated to evaluating the resilience of the proposed layout plan. During the evaluation of network resilience, Monte Carlo simulations are used to simulate disaster scenarios. Given the inherent complexity of the model, the traditional solver cannot efficiently solve the problem. Thus, a new hybrid heuristic algorithm is designed to obtain solutions that maximize network resilience. The results show the effectiveness of the designed algorithm and the significant improvement in network resilience achieved by numerical experiments. Moreover, sensitivity analyses are conducted to reveal the relationships between resilience and budget, as well as resilience and the capacity of underground pipelines. It has a significant impact on sustainability when making decisions regarding network planning.

Stochastic Programming For Order Allocation And Production Planning

Stochastic demand is an important factor that heavily affects production planning. It influences activities such as purchasing, manufacturing, and selling, and quick adaption is required. In production planning, for reasons such as reducing costs and obtaining supplier discounts, many decisions must be made in the initial stage when demand has not been realized. The effects of non-optimal decisions will propagate to later stages, which can lead to losses due to overstocks or out-of-stocks. To find the optimal solutions for the initial and later stage regarding demand realization, this study proposes a stochastic two-stage linear programming model for a multi-supplier, multi-material, and multi-product purchasing and production planning process. The objective function is the expected total cost after two stages, and the results include detailed plans for purchasing and production in each demand scenario. Small-scale problems are solved through a deterministic equivalent transformation technique. To solve the problems in the large scale, an algorithm combining metaheuristic and sample average approximation is suggested. This algorithm can be implemented in parallel to utilize the power of the solver. The algorithm based on the observation that if the remaining quantity of materials and number of units of products at the end of the initial stage are given, then the problems of the first and second stages can be decomposed.

A two-stage fuzzy optimization model for scarce drugs supply and ration planning under uncertainty: A case study

The scarce drugs rationing is a serious challenge in the public health system. This study proposes a two-stage linear programming model for the scarce drug rationing problem which reflects the conflicts of interest between supply chain members. The proposed model uses a rolling horizon planning mechanism along with an iterative procedure for supplying and rationing the scarce drugs. The maximization of minimum suppliers’ profit and the minimization of maximum shortage are considered as the first and second stage models’ objective functions, respectively. Furthermore, two need-based indicators including disability-adjusted life years (DALYs) and population are utilized to enhance the performance of the proposed model. Besides, human capital method is applied for calculating the shortage costs of demand zones. Due to the inherent epistemic uncertainty in some critical input parameters such as the exchange rate and demand, a credibility-based robust possibilistic programming approach is used to deal with imprecise parameters. Finally, the applicability and usefulness of the proposed approach are investigated by a real case study from Iranian food and drug administration. The computational results demonstrate the superiority of robust programming model against deterministic one.

Optimising Crop Selection for Small Urban Food Gardens in Dry Climates

The net value of urban agriculture has not been studied, especially accounting for the cost of water. This study has sought to remedy this gap in the literature by examining the varying price of water in different climates. A two-stage linear programming model has been used to maximise the net value of urban agriculture. The decision variables included the type and yield of crops; constraints included upper and lower bounds of dietary food groups, individual foods, protein and energy as well as area utilised per person. The results show optimal crop regimes are similar across different climates and water prices due to the selection of crops that have high profit margins. The results also showed that per capita garden size is critical with smaller gardens optimal in terms of water applied per unit area and net value returned as well as return per unit area due to the ability to select the highest value crops. Generally, the more high-value and low water-use crops that can be included, the higher the value in larger gardens. The results indicate that a modest food garden growing the right crops can be highly cost-effective, even with conservative crop yields and water use.

Group decision-making based on heterogeneous preference relations with self-confidence

Preference relations are very useful to express decision makers’ preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing preference relations. In this study, we define the preference relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the preference relation with self-confidence. Furthermore, we present a two-stage linear programming model for estimating the collective preference vector for the group decision-making based on heterogeneous preference relations with self-confidence. Finally, numerical examples are used to illustrate the two-stage linear programming model, and a comparative analysis is carried out to show how self-confidence levels influence on the group decision-making results.

An Inexact Mix-Integer Two-Stage Linear Programming Model for Supporting the Management of a Low-Carbon Energy System in China

In view of the great contribution of coal-fired units to CO2 emissions, the coupled coal and power system with consideration of CO2 mitigation is a typical sub-system of the highly emitting Chinese energy system for low-carbon studies. In this study, an inexact mix-integer two-stage programming (IMITSP) model for the management of low-carbon energy systems was developed based on the integration of multiple inexact programming techniques. Uncertainties and complexities related to the carbon mitigation issues in the coupled coal and power system can be effectively reflected and dealt with in this model. An optimal CO2 mitigation strategy associated with stochastic power-generation demand under specific CO2 mitigation targets could be obtained. Dynamic analysis of capacity expansion, facility improvement, coal selection, as well as coal blending within a multi-period and multi-option context could be facilitated. The developed IMITSP model was applied to a semi-hypothetical case of long-term coupled management of coal and power within a low-carbon energy system in north China. The generated decision alternatives could help decision makers identify desired strategies related to coal production and allocation, CO2 emission mitigation, as well as facility capacity upgrade and expansion under various social-economic, ecological, environmental and system-reliability constraints. It could also provide interval solutions with a minimized system cost, a maximized system reliability and a maximized power-generation demand security. Moreover, the developed model could provide an in-depth insight into various CO2 mitigation technologies and the associated environmental and economic implications under a given reduction target. Tradeoffs among system costs, energy security and CO2 emission reduction could be analyzed.

Dual Estimates of the Optimal Plan Model and Regional Market Costs: A Relationship

The relationship between linear programming dual estimates for the optimal production plan model and real regional market costs is studied. A two-stage linear programming model is necessary for exact approximation of cost allocation in analyzing with optimal plan estimates. A sign criterion is formulated for analyzing the reliability of the production planning model based on a comparison of the changes in the regional market costs and optimal plan estimates. An example is given to illustrate the analysis of reliability of the solution.