In the paper, we minimize the holding cost of the safety stock held in a supply chain modeled as a general network. By our assumption, the demand is bounded by a concave function. This fact allows us to formulate the problem as a deterministic optimization. We minimize a concave function over a discrete polyhedron. The main goal of the paper is to describe an algorithm to solve the problem without assuming any particular structure of the underlying supply chain. The algorithm is a branch and bound algorithm. / Singapore-MIT Alliance (SMA)

Planning for Ontario’s future energy supply mix is a very challenging undertaking which requires consideration of various drivers and decision criteria. From the literature review conducted, no published work has been found addressing the multi-period energy planning problem with CO2 emission constraints and the option of carbon capture and storage (CCS). The objective of this project was to develop a novel multi-period mixed-integer non-linear programming (MINLP) model that is able to realize the optimal mix of energy supply sources which will meet current and future electricity demand, CO2 emission targets, and lower the overall cost of electricity. This model was implemented in GAMS (General Algebraic Modeling System). The model was formulated using an objective function that minimizes the net present value of the cost of electricity (COE) over a time horizon of 14 years. The formulation incorporates several time dependent parameters such as forecasted energy demand, fuel price variability, construction lead time, conservation initiatives, and increase in fixed operational and maintenance costs over time. The model was applied to two case studies in order to examine the economical, structural, and environmental effects that would result if Ontario’s electricity sector was required to reduce its CO2 emissions to a specific limit. The first case study examined a base case scenario in which no CO2 limits were imposed. The second case study examined a scenario in which Ontario’s electricity sector must comply with CO2 emission limits similar to the Kyoto target of 6% below 1990 levels. The results indicate that in order to meet the CO2 targets of 6% below 1990 levels, Nanticoke, Atikokan, and Thunder Bay coal-fired power plants must be fuel-switched, and Lambton coal-fired power plant must be retrofitted with a CCS system. Furthermore, a total CO2 reduction of approximately 32% was achieved when compared to the base case. The total cost associated with reducing the CO2 emissions to 6% below 1990 levels, per ton of CO2, was $48.79 / ton CO2 reduced. The total expenditure for Case Study II (CO2 limit of 6% below 1990 levels) was approximately 10.1% higher than for the base case. This model offers many potential benefits to Ontario’s energy sector. In addition to providing an optimal solution for meeting future electricity demand, it can help Ontario meet its emissions targets while minimizing the overall cost of electricity. Furthermore, although this project was aimed at Ontario’s future energy supply mix, it could also be readily applied to other regions or even countries as a whole.

Planning for Ontario’s future energy supply mix is a very challenging undertaking which requires consideration of various drivers and decision criteria. From the literature review conducted, no published work has been found addressing the multi-period energy planning problem with CO2 emission constraints and the option of carbon capture and storage (CCS). The objective of this project was to develop a novel multi-period mixed-integer non-linear programming (MINLP) model that is able to realize the optimal mix of energy supply sources which will meet current and future electricity demand, CO2 emission targets, and lower the overall cost of electricity. This model was implemented in GAMS (General Algebraic Modeling System). The model was formulated using an objective function that minimizes the net present value of the cost of electricity (COE) over a time horizon of 14 years. The formulation incorporates several time dependent parameters such as forecasted energy demand, fuel price variability, construction lead time, conservation initiatives, and increase in fixed operational and maintenance costs over time. The model was applied to two case studies in order to examine the economical, structural, and environmental effects that would result if Ontario’s electricity sector was required to reduce its CO2 emissions to a specific limit. The first case study examined a base case scenario in which no CO2 limits were imposed. The second case study examined a scenario in which Ontario’s electricity sector must comply with CO2 emission limits similar to the Kyoto target of 6% below 1990 levels. The results indicate that in order to meet the CO2 targets of 6% below 1990 levels, Nanticoke, Atikokan, and Thunder Bay coal-fired power plants must be fuel-switched, and Lambton coal-fired power plant must be retrofitted with a CCS system. Furthermore, a total CO2 reduction of approximately 32% was achieved when compared to the base case. The total cost associated with reducing the CO2 emissions to 6% below 1990 levels, per ton of CO2, was $48.79 / ton CO2 reduced. The total expenditure for Case Study II (CO2 limit of 6% below 1990 levels) was approximately 10.1% higher than for the base case. This model offers many potential benefits to Ontario’s energy sector. In addition to providing an optimal solution for meeting future electricity demand, it can help Ontario meet its emissions targets while minimizing the overall cost of electricity. Furthermore, although this project was aimed at Ontario’s future energy supply mix, it could also be readily applied to other regions or even countries as a whole.