A Mathematical Model for the Capacity Expansion Problem of Inter-regional Water Supply Facilities

This paper concerns the capacity expansion problem of inter-regional water supply facilities, and presents a mathematical model to analyze the problem. The model postulates such an inter-regional water supply system that is managed by a body which is independent of municipalites ; and provides water to municipalities by conveying purified water to distribution reserviors in the municipalities through conduits laid between them. The formulated model, which belongs to a nonlinear programming, is solved by both an enumeration method and dynamic programming. A case study was conducted by applying the model to the capacity expansion problem in the region consisting of Takasago, Kakogawa and Akashi Cities in Hyogo Prefecture The calculated results show that such a management system as is presumed in the model, is economically effective mainly because joint expansion for the increased supply in several municipalities will save associated costs, provided that unnecessarily excessive expansion is avoided

A unifying view on the irreversible investment exercise boundary in a stochastic, time-inhomogeneous capacity expansion problem

This paper studies the investment exercise boundary erasing in a stochastic, continuous time capacity expansion problem with irreversible investment on the finite time interval $[0, T]$ and a state dependent scrap value associated with the production facility at the finite horizon $T$. The capacity process is a time-inhomogeneous diffusion in which a monotone nondecreasing, possibly singular, process representing the cumulative investment enters additively. The levels of capacity, employment and operating capital contribute to the firm's production and are optimally chosen in order to maximize the expected total discounted profits. Two different approaches are employed to study and characterize the boundary. From one side, some first order condition are solved by using the Bank and El Karoui Representation Theorem, and that sheds further light on the connection between the threshold which the optimal policy of the singular stochastic control problem activates at and the optional solution of Representation Theorem. Its application in the presence of the scrap value is new. It is accomplished by a suitable devise to overcome the difficulties due to the presence of a non integral term in the maximizing functional. The optimal investment process is shown to become active at the so-called "base capacity" level, given as the unique solution of an integral equation. On the other hand, when the coefficients of the uncontrolled capacity process are deterministic, the optimal stopping problem classically associated to the original capacity problem is resumed and some essential properties of the investment exercise boundary are obtained. The optimal investment process is proved to be continuous. Unifying approaches and views, the exercise boundary is shown to coincide with the base capacity, hence it is characterized by an integral equation not requiring any a priori regularity

A Multistage Stochastic Mixed-Integer Model for Perishable Capacity Expansion Problem

We study a multi-stage capacity expansion problem under demand uncertainty. We consider the problem where there are multiple resources to be expanded at each stage. Moreover, the resources have limited life time after acquisition. Our goal is to determine the time and size of each resource to be expanded so that the expected expansion cost of capacities is minimized. Therefore, we formulate the problem as a multi-stage stochastic mixed-integer program. Capacity shortage and excess are allowed subject to a joint chance constraint. We apply the multi-stage stochastic mixed-integer model to formulate vaccine vial opening decisions in the health clinics. This formulation enables us to find the optimal combination of vial sizes to be opened. Additionally, a trade off between vaccine wastage and shortage can be addressed using the chance constraint. We provide a branch and price algorithm based on a nodal decomposition to solve the model. In addition, a heuristic algorithm is proposed to solve the subproblems where the life time of the resources is limited to one period. We implement the branch and price algorithm assuming continuous capacity expansion decisions. Computational results are presented for the vaccine vial opening problem with three vial sizes; 1-, 5-, and 10-doses. The primary results indicate the strength of the proposed algorithm in solving problems with large dimensions. Moreover we report results that indicate the usage of 10-dose vials and the portion of 10-dose vials in the total vaccine usage increases with the arrival rate. Although the total usage of 1- and 5- dose vials increase with the arrival rate, their portion in the total vaccine usage decreases. This implies that vaccination wastage or shortage can be managed by keeping moderate amount of smaller size vials while supplying most of the demand using larger vial sizes to benefit from the economies of scale

Urban Rapid Transit Network Capacity Expansion

This paper examines a multi-period capacity expansion problem for rapid transit network design. The capacity expansion is realized through the location of train alignments and stations in an urban traffic context by selecting the time periods. The model maximizes the public transportation demand using a limited budget and designing lines for each period. The location problem incorporates the user decisions about mode and route. The network capacity expansion is a long-term planning problem because the network is built over several periods, in which the data (demand, resource price, etc.) are changing like the real problem changes. This complex problem cannot be solved by branch and bound, and for this reason, a heuristic approach has been defined in order to solve it. Both methods have been experimented in test networks

Non-Wire Alternatives to Capacity Expansion

Distributed energy resources (DERs) can serve as non-wire alternatives to capacity expansion by managing peak load to avoid or defer traditional expansion projects. In this paper, we study a planning problem that co-optimizes DERs investment and operation (e.g., energy efficiency, energy storage, demand response, solar photovoltaic) and the timing of capacity expansion. We formulate the problem as a large scale (in the order of millions of variables because we model the operation of DERs over a period of decades) non-convex optimization problem. Despite its non-convexities, we find its optimal solution by decomposing it using the Dantzig-Wolfe Decomposition Algorithm and solving a series of small linear problems. Finally, we present a real planning problem at the University of Washington Seattle Campus.Comment: This document is an online supplement for a paper submitted to the 2018 Power and Energy Society General Meetin

Renewable fuel regulation: Implications for e-fuel production infrastructure in energy hubs

Renewable fuels of non-biological origin (RFNBOs) are needed to decarbonize hard-to-electrify sectors that rely on liquid or gaseous fuels, such as long-haul shipping. The EU's Delegated Act on RFNBOs defines renewable hydrogen by considering rules on additionality as well as temporal and geographical correlation of the electricity used. For a Danish case study, we examine the impact on the capacity expansion problem of an energy hub producing renewable hydrogen, e-methanol, and e-ammonia using a mixed-integer linear problem formulation. We analyze the investments in production capacity, storage assets, and Power Purchase Agreement (PPA) volume under different fuel price assumptions for 2030. We find that e-methanol (combined with limited storage to secure hydrogen supply to the synthesizer) provides the best business case with a PPA volume based on the maximum allowed electrolyzer size.Comment: Accepted versio

An Efficient Approach to Distributionally Robust Network Capacity Planning

In this paper, we consider a network capacity expansion problem in the context of telecommunication networks, where there is uncertainty associated with the expected traffic demand. We employ a distributionally robust stochastic optimization (DRSO) framework where the ambiguity set of the uncertain demand distribution is constructed using the moments information, the mean and variance. The resulting DRSO problem is formulated as a bilevel optimization problem. We develop an efficient solution algorithm for this problem by characterizing the resulting worst-case two-point distribution, which allows us to reformulate the original problem as a convex optimization problem. In computational experiments the performance of this approach is compared to that of the robust optimization approach with a discrete uncertainty set. The results show that solutions from the DRSO model outperform the robust optimization approach on highly risk-averse performance metrics, whereas the robust solution is better on the less risk-averse metric