Multi-period Linear Programming Research Articles

Possible Pathways toward Carbon Neutrality in Thailand’s Electricity Sector by 2050 through the Introduction of H2 Blending in Natural Gas and Solar PV with BESS

To avoid the potential adverse impacts of climate change from global warming, it is suggested that the target of net zero emissions should be reached by this mid-century. Thailand is aiming to achieve carbon neutrality by 2050. Since electricity generation is one of the largest producers of carbon dioxide emission, the associated emissions must be greatly reduced to achieve the targets mentioned above. Thus, new generation expansion plans must be well developed. This paper discusses the development of generation expansion plans considering Thailand’s latest policies along with enhancement of the existing multi-period linear programming model, allowing new electricity generation technologies having low emissions, e.g., solar PV with battery and hydrogen blending in natural gas, to be integrated into generation expansion planning. Then, four generation expansion plans with different levels of hydrogen blending in natural gas are proposed and discussed. It is found that Thailand can achieve carbon neutrality by 2050 by promoting more use of renewable energy altogether with trade-off between land for solar PV installation and amount of hydrogen blended in natural gas. The lesson learned from this study provides crucial information about possible pathways to achieve carbon neutrality in the electricity sector for policy makers in other countries.

Analyses on ICU and non-ICU capacity of government hospitals during the COVID-19 outbreak via multi-objective linear programming: An evidence from Istanbul

The current infectious disease outbreak, a novel acute respiratory syndrome [SARS]-CoV-2, is one of the greatest public health concerns that the humanity has been struggling since the end of 2019. Although, dedicating the majority of hospital-based resources is an effective method to deal with the upsurge in the number of infected individuals, its drastic impact on routine healthcare services cannot be underestimated. In this study, the proposed multi-objective, multi-period linear programming model optimizes the distribution decision of infected patients and the evacuation rate of non-infected patients simultaneously. Moreover, the presented model determines the number of new COVID-19 intensive care units, which are established by using existing hospital-based resources. Three objectives are considered: (1) minimization of total distance travelled by infected patients, (2) minimization of the maximum evacuation rate of non-infected patients and (3) minimization of the infectious risk of healthcare professionals. A case study is performed for the European side of Istanbul, Turkey. The effect of the uncertain length of the stay of infected patients is demonstrated via sensitivity analyses.

A multi-period linear programming model for the natural gas distribution network of Thailand

ABSTRACT As a consequence of the impending gas shortages from sources in the Gulf of Thailand, the country will be obliged to switch to imports of LNG to achieve energy security. The gas system of Thailand is constructed as a mathematical model. In the simulation, the output shows that reserves gas of Thailand is insufficient to face the demand in 2015–2036, while the consumption of natural gas reserves continues at a rate that indicates that LNG imports will become the primary supply in the future to meet rising demand. The linear programming approach indicates patterns in the supply of gas which will see imports of LNG expanding at a rate lower than that predicted in the plan, thus undercutting the figures for the 2021 MMSCFD under the Gas Plan. The programming described in this study, however, may serve as the foundation for further examinations of Thailand’s situation regarding energy security.

Decision Planning in Agricultural Production to Achieve a Green Economy in Mae Faek Sub-District, Chiang Mai Province, Thailand

The research aims to study decision making using producing factors under the concept of green economy to enhance the community’s economic sustainability for 250 agricultural households who grow glutinous rice, animal feed maize and potato in an area of 2,500 Rai in Mae-Faek Mai Sub-District, Sansai District, Chiang Mai Province. The study employs the Fuzzy Analysis Hierarchical Process (FAHP) together with Multi-goal and Multi-Period Linear Programming. The results reveal that growing in-season glutinous rice alternating with potato is the most appropriate way to increase net revenue and to decrease the amount of greenhouse emission, followed by growing in-season glutinous rice alternating with animal feed maize as this helps income stability when drought occurs. In contrast, growing in-season glutinous rice alternating with off-season glutinous rice is not only affected by a lack of water resources, but also increases the amount of greenhouse gas from the growing process.

Feeding Models to Optimize Dairy Feed Rations in View of Feed Availability, Feed Prices and Milk Production Scenarios

In the global dairy production sector, feed ingredient price and availability are highly volatile; they may shape the composition of the feed ration and, in consequence, impact feed cost and enteric methane (CH4) emissions. The objective of this study is to explore the impact of changes in feed ingredients’ prices and feed ingredients’ availability on dairy ration composition, feed cost and predicted methane yield under different levels of milk production. To meet the research aim, a series of multi-period linear programming models were developed. The models were then used to simulate 14 feed rations formulations, each covering 162 months and three dairy production levels of 10, 25 and 35 kg milk/d, representing a total of 6804 feed rations altogether. Across milk production levels, the inclusion of alfalfa hay into the feed rations declined from 55% to 38% when daily milk production increased from 10 to 35 kg, reflecting the cows’ increased energy requirements. At a daily milk production level of 35 kg, CH4 production (per kg milk) was 21% and 53% lower than in average and low milk producing cows, respectively, whereas at 10 kg of milk production the potential to reduce CH4 production varied between 0.6% and 5.5% (average = 3.9%). At all production levels, a reduction in CH4 output was associated with an increase in feed costs. Overall, and considering feeding scenarios in low milk producing cows, feed cost per kg milk was 30% and 37% higher compared to that of average and high milk production, respectively. The feed ration modeling approach allows us to account for the interaction between feed ingredients over time, taking into consideration volatile global feed prices. Overall, the model provides a decision-making tool to improve the use of feed resources in the dairy sector.

A multimodal, multicommodity, and multiperiod planning problem for coal distribution to poor families

Tackling poverty has been one of the greatest global challenges and a prerequisite to sustainable development of countries. Countries implement nationally appropriate social protection systems and measures to address poverty. This paper addresses an aid system adopted by the government in Turkey where significant amounts of coal is distributed to poor families each year. The objective of the coal aid system is to complete the delivery of coal to poor families by the start of winter. However, an analysis of the data from previous years indicates that the distribution to many families cannot be completed on time. This results from the fact that planning is done manually and by trial-and-error as there is no system that can be used for distribution planning. This paper describes the planning problem encountered and develops a mathematical model to solve it. The proposed model is a multimodal, multicommodity, and multiperiod linear programming (LP) model. The model can be used to develop and update a distribution plan as well as to answer several what-if questions with regard to capacities, time constraints, and so forth. The model is solved using CPLEX for several problem instances obtained under different scenarios using data for the year 2012. The results show that at least 9% cost savings and about 40% decrease in distribution completion time can be achieved when the model is used. We analyze scenario results qualitatively and quantitatively and provide several insights to the decision makers. As a part of quantitative analysis, we develop regression models to predict optimal costs based on several factors. Our main contribution is to provide an efficient and effective tool to handle a large-scale real-world problem. The model has also helped to prove that the organization responsible for distribution planning may move from the current planning practice to an all-encompassing top-down approach.

A novel framework for development and optimisation of future electricity scenarios with high penetration of renewables and storage

Although electricity supply is still dominated by fossil fuels, it is expected that renewable sources will have a much larger contribution in the future due to the need to mitigate climate change. Therefore, this paper presents a new framework for developing Future Electricity Scenarios (FuturES) with high penetration of renewables. A multi-period linear programming model has been created for power-system expansion planning. This has been coupled with an economic dispatch model, PowerGAMA, to evaluate the technical and economic feasibility of the developed scenarios while matching supply and demand. Application of FuturES is demonstrated through the case of Chile which has ambitious plans to supply electricity using only renewable sources. Four cost-optimal scenarios have been developed for the year 2050 using FuturES: two Business as usual (BAU) and two Renewable electricity (RE) scenarios. The BAU scenarios are unconstrained in terms of the technology type and can include all 11 options considered. The RE scenarios aim to have only renewables in the mix, including storage. The results show that both BAU scenarios have a levelised cost of electricity (LCOE) lower than, or equal to, today’s costs ($72.7–77.3 vs $77.6/MWh) and include 81–90% of renewables. The RE scenarios are slightly more expensive than today’s costs ($81–87/MWh). The cumulative investment for the BAU scenarios is $123-$145 bn, compared to $147-$157 bn for the RE. The annual investment across the scenarios is estimated at $4.0 ± 0.4 bn. Both RE scenarios show sufficient flexibility in matching supply and demand, despite solar photovoltaics and wind power contributing around half of the total supply. Therefore, the FuturES framework is a powerful tool for aiding the design of cost-efficient power systems with high penetration of renewables.

Optimal dairy feed input selection under alternative feeds availability and relative prices

Feed formulation is essential in the dairy production chain from economic, nutritional, and environmental perspectives. Optimizing the feed formulation across those three domains – given uncertainty of input prices, input availability, and regional climatic conditions – is a challenge for those in the industry. The diet formulation method that is widely used by trading firms and feed production facilities employs a static linear programming (LP) approach. This approach does not allow for intertemporal feed formulations and switches between dietary feed commodities under feed availability conditions, which result in foregone economic gains for feed producers.The current study develops a multi-period LP feed model that uses historical data to capture ration switch opportunities between available feed resources for dairy cows and demonstrates the potential use of the method in different commodity feed availability situations. We apply 14 diet formulations, each covering 150 months, representing a total of 2100 diets. The diet formulation considers a specific milk production level for a “model cow”, alternative feed formulations available, and volatility in feed prices. The results demonstrate that there is an opportunity for efficiency gains in the dairy industry with respect to feed formulation.Based on dietary feed inclusion and price spreads, barley can be an important dairy feed grain which completely replaces wheat, corn, and sorghum at price spreads of less than 94%, less than 78%, and less than 67%, respectively. Grain-based feed scenarios represent the lowest nutrient variation while multiple meal feeds had the lowest costs. Furthermore, and on average, multiple meal feed scenarios provided 10% higher dietary crude protein contents compared to grain based feed scenarios (i.e. 163 vs 179 g/kg DM formulated feed). Meanwhile, multiple meal feeding cost was 11% lower than that in the grain based feeding scenarios. Additionally, the use of multiple meals reduces alfalfa dietary inclusion by 7% on dry matter basis. Our analysis shows a strong reduction in feed cost associated with dietary crude protein reduction equivalent to 7.6 USD/tonne per 1% reduction in dietary crude protein level.The modeling approach allows for the interaction between feed components over time taking into consideration volatile global feed prices, thereby improving feed availability and feed formulation. Overall, the model provides a decision making tool to improve the use of feed resources in the dairy sector.

Integrated model for renewable energy planning in Turkey

ABSTRACTAll economic sectors are associated with energy use; therefore, government organizations aim to supply sustainable energy for human needs and economic growth. In particular, increased environmental concerns of the public in Turkey have impacted policymaking for renewable energy (RE) management in Turkey. The primary objective for RE sources of the Turkish Ministry of Energy is to ensure that 30% of the share of electricity production is from RE resources in 2023. In this paper, the integrated multi-objective, multi-period linear programming model is presented to determine effective allocation of RE supply for seven different geographical regions in Turkey for the period of 2017 to 2024. The integrated model consists of two different stages. The first stage involves qualitative evaluations of RE sources for seven geographical regions. Analytical Hierarchy Process (AHP) is applied to determine criteria priorities and overall ratings of geographical regions across determined criteria for RE sources are computed. The second stage of the integrated model consists of a multi-objective, multi-period linear programming model. The proposed multi-objective linear programming model is coded in MPL (Mathematical Programming Language) and solved using the GUROBI 5.1.0 solver. The output of the integrated model presents the total supply amount of RE sources for geographical regions in planning period. The ε-constraints method is applied to compute the total supply amount of RE from geographical regions for the period of 2017 to 2024. In this study, a systematic decision-making model is generated to allocate renewable energy sources to the geographical regions. The presented model integrates qualitative evaluations and quantitative parameters of different geographical regions to determine the optimal supply amount of RE. The obtained results are consistent with the potential quantities of RE alternatives in geographical regions, regional specifications, and social requirements.

Mathematical optimization models for fuelwood production

Forests are among the most sensitive systems in nature. This is attributed to the fact that, forests are directly affected by fluctuations in price of fossil fuels. Wood products and especially forest fuel products are accessible by anyone, without any prior processing. As forest fuel is a subsidy for fossil fuels (oil) for heating purposes, households turn to forest fuel especially in countries that are heavily impacted by economic recession. The over-exploitation of this natural resource leads the forest to abnormal situation and eventually to deforestation. The exhaust of the natural resource capital has negative impact not only on the local economy, where fuelwood market contributes especially in mountainous regions, but also on the environmental stability of ecosystems. In this paper, two multi-period Linear Programming models are proposed for management of coppice forests. The aim of these models is to maximize the Net Present Value, which is constructed as a function of the revenue from trading fuelwood (price times the logged quantities) minus the transportation cost from the forest to merchants. Two aspects have been investigated in this paper; sustainability and maximum yield. The sustainability aspect is guaranteed by imposing constraints for equalization of non-logged areas at the end of the planning horizon. With maximum yield aspect, the maximization of the logged quantities (and therefore the maximization of the objective function) is guaranteed. The model is solved for various scenarios regarding transportation cost. The applicability of the model is demonstrated through a real-world case study of an even coppice forest in Achladochori–Aggistro–Sidirokastro. The proposed model is easy to be implemented, since it uses only the initial conditions of the forest (area) and can be applied to even and uneven aged forests.

Sustainable intensification of Brazilian livestock production through optimized pasture restoration

Grassland degradation compromises the profitability of Brazilian livestock production, and pasture recovery is a promising strategy for sustainable intensification of agriculture (SAI). Recovery increases carbon sequestration into the soil and can potentially avoid deforestation; thereby reducing emissions intensity (EI), but only at increased investment cost per unit of area. We develop a multi-period linear programming (LP) model for grazing beef production planning to represent a typical Cerrado stocking and finishing beef farm. We compare economic and environmental performance of two alternative optimized pasture management approaches relative to the traditional practice (TRP), which is based on restoring pasture after a full degradation cycle of 8years. The scenarios considered the difference made by access to subsidized credit through the Low Carbon Agriculture program (“Programa ABC”). The model estimates EI using upstream life cycle assessment (LCA), and dynamically estimates soil organic carbon (SOC) changes as a function of pasture management. The results show net present values (NPV) ranging from −67 Brazilian reals per hectare-year (R$·ha−1·yr−1) to around 300 R$·ha−1·yr−1, respectively for traditional and optimized pasture management strategies. Estimated EI of the TRP is 9.26 kgCO2 equivalent per kg of carcass weight equivalent (kgCO2e/kg CWE) relative to 3.59kgCO2e/kg CWE for optimized management. Highest emission abatement results from improved SOC sequestration, while access to credit could further reduce EI by around 20%. We consider the effects of alternative credit interest on both NPV and EI. The results provide evidence to inform the design of Brazil's key domestic policy incentive for low carbon agriculture, which is an important component of the country's Intended Nationally Determined Contributions (INDC) on emissions mitigation. The results also contribute to the global debate on the interpretation of SAI.

The Cardinality Constrained Multi-Period Linear Programming Knapsack Problem

The Cardinality Constrained Multi-Period Linear Programming Knapsack Problem

An integrated stochastic multi-regional long-term energy planning model incorporating autonomous power systems and demand response

The power sector faces a rapid transformation worldwide from a dominant fossil-fueled towards a low carbon electricity generation mix. Renewable energy technologies (RES) are steadily becoming a greater part of the global energy mix, in particular in regions that have put in place policies and measures to promote their utilization. This paper presents an optimization-based approach to address the generation expansion planning (GEP) problem of a large-scale, central power system in a highly uncertain and volatile electricity industry environment. A multi-regional, multi-period linear mixed-integer linear programming (MILP) model is presented, combining optimization techniques with a Monte Carlo (MCA) method and demand response concepts. The optimization goal concerns the minimization of the total discounted cost by determining optimal power capacity additions per time interval and region, and the power generation mix per technology and time period. The model is evaluated on the Greek power system (GPS), taking also into consideration the scheduled interconnection of the mainland power system with those of selected autonomous islands (Cyclades and Crete), and aims at providing full insight into the composition of the long-term energy roadmap at a national level.

Optimal operation of a distributed energy generation system for a sustainable palm oil-based eco-community

The palm oil industry potentially can be environmentally sustainable through utilizing the vast availability of biomass residues from palm oil mills as renewable energy sources. This work addresses the optimal operation of a combined bioenergy and solar PV distributed energy generation system to meet the electricity and heat demands of an eco-community comprising a palm oil mill and its surrounding residential community. A multiperiod mixed-integer linear programming planning and scheduling model is formulated on an hourly basis that optimally selects the power generation mix from among available biomass, biogas, and solar energy resources with consideration for energy storage and load shifting. A multiscenario approach is employed that considers scenarios in the form of many possible weather conditions and various energy profiles under varying mill operation modes and residential electricity consumption. The proposed approach is demonstrated on a realistic case study for a palm oil mill in the Iskandar Malaysia economic development region. The computational results indicate that biomass-based resource is the preferred renewable energy to be implemented due to the high cost associated with solar PV. As well, load shifting and energy storage can be feasibly deployed for demand peak shaving particularly for solar PV systems.

An efficient algorithm for bi-objective combined heat and power production planning under the emission trading scheme

The growing environmental awareness and the apparent conflicts between economic and environmental objectives turn energy planning problems naturally into multi-objective optimization problems. In the current study, mixed fuel combustion is considered as an option to achieve tradeoff between economic objective (associated with fuel cost) and emission objective (measured in CO2 emission cost according to fuels and emission allowance price) because a fuel with higher emissions is usually cheaper than one with lower emissions. Combined heat and power (CHP) production is an important high-efficiency technology to promote under the emission trading scheme. In CHP production, the production planning of both commodities must be done in coordination. A long-term planning problem decomposes into thousands of hourly subproblems. In this paper, a bi-objective multi-period linear programming CHP planning model is presented first. Then, an efficient specialized merging algorithm for constructing the exact Pareto frontier (PF) of the problem is presented. The algorithm is theoretically and empirically compared against a modified dichotomic search algorithm. The efficiency and effectiveness of the algorithm is justified.

Economic Analysis Determining the Optimal Replanting Age of Date Palm

Two alternative analytical models were used to estimate the economically optimal age of replanting date palm, namely; Comparison of Equivalent Annual Net Revenue (CEAN) and Multi-Period Linear Programming Model (MPLP). Solution procedures of both models are based on the theory of optimal replacement of capital assets. Data on date palm age-yield relationship and other socioeconomic variables were gleaned through a farm survey of 34 large commercial farms, in Izki, Bahla, and Al-Hamra wilayats in the Al- Dakhilya governorate of the Sultanate of Oman. The study estimated the optimal age of replanting date palms as 50-55 years. Both models, CEAN and MPLP gave consistent estimates. The optimal age to replant date palms was sensitive only to changes in the interest rates. Low interest rates shortened the optimal age of date palm replanting. Changes in date price, yield and variable production costs did not change the optimal age of replanting date palms. The incremental revenue that could be accrued to the Sultanate of Oman through replanting date palms was estimated as 7 million OR/ year.

Economic Risks of Cheatgrass Invasion on a Simulated Eastern Oregon Ranch

The potential of invasive plants to alter fuel properties over time has implications for the ranchers of semiarid rangelands throughout the world. A prime example of this phenomenon is the cheatgrass (Bromus tectorum L.) invasion of the native shrub-steppe lands in Great Basin of the western United States. The purpose of this study is to develop a bioeconomic model that optimizes simulated ranch behavior given the beginning stages of cheatgrass invasion on a public forage allotment. The bioeconomic model is applied to a typical eastern Oregon 300 cow-calf ranch. Livestock production decisions are simulated over a 40-yr planning horizon using a multiperiod linear programming model. Results showed changes in profit-maximizing ranch management strategies in the form of decreased optimal stocking rates and forage substitution. The net present value of the simulated ranch’s income stream declined, and the probability that the ranch cannot meet its full costs of livestock production and would exit the industry increased as a result. These economic impacts were more pronounced with decreased sale price. Sensitivity analysis showed that overall results in terms of ranch behavior were specific neither to the assumed discount rate nor to the assumed percentage of cheatgrass cover (as long as this percentage is within the reference state) on the public grazing allotment. This study introduces a method for managers to quantify impacts on ranches from fuel-altering invasive plants on public lands, emphasizing the importance of including information about native and invasive forage production characteristics and wildfire frequency as a function of the state of invasion.

Closed-Loop Supply Chain Network Design with Recovery of Glass Containers

Reverse logistics (RL) and closed-loop supply chains (CLSC) have recently received enormous attention due to growing environmental concerns and legislations coupled with the lucrative business potential. The main purpose of this paper is to develop a closed-loop supply chain network design model capable of recovering glass containers. A multi-period multi-product mixed-integer linear programming model is proposed to maximize profit. The strategic design of the supply chain is dealt simultaneously with the tactical planning of its operation, which covers procurement, production, storage, distribution, take-back, reprocessing, reuse, and recycling. To illustrate the efficiency and practicability of the model, it is applied to a real-world case of beverage supply chain where the glass containers are either re-used or recycled into their original form, as raw materials. Finally, sensitivity analyses, from a financial perspective, have been conducted to reveal the determinants of profitable product recovery and grasp their managerial implications. The analyses showed that return rate and return acquisition cost have determinant impact on the economic viability of product recovery practice.

A mathematical programming approach to crop mix problem

Problems normally faced by farmers include what to plant, how much to plant and when to plant. In this study, a linear programming crop mix model for a finite-time planning horizon was proposed. Given limited available resources such as budget and land acreage, the crop-mix planning model was formulated and transformed into a multi-period linear programming problem. The objective was the maximization of the total returns at the end of the planning horizon. The model was applied to selected single-harvest crops and solved by LINDO, a linear programming package. The results were analyzed and discussed. Key words: Crop mix, single-harvest, linear programming.

Study on energy strategy of Chinese capital region under the new national policy of reducing carbon dioxide emissions

Chinese government committed to reducing carbon dioxide emissions per unit of GDP by 40% to 45% by 2020. As the capital and one of the biggest cites, Beijing expected to both keep higher GDP growth than average and cut unit GDP carbon emission, and has to adjust the relevant energy strategy in near future. The paper analysis the characteristics of energy supply and energy consumption in Beijing, and setups the economic-energy-environment-oriented reference energy system (RES), selects MARKAL as the optimal model and constructs districted multi-period linear programming matrix, which including 15 energy carriers, 4 energy processes, 17 energy conversions, and 18 energy end-use sets. Furthermore, the paper designs 11 scenarios in various pollute emission restrictions, and establishes the total economic cost as the optimize target, the low-carbon emission as main restriction, to obtain the suitable energy supply structure and end-use technology structure. At last, we have the conclusion that Beijing can attach the demands of cutting carbon emissions per unit of GDP by 45% under the scheduled GDP growth.