Takayuki Shiina

Unit Commitment by Column Generation

The unit commitment problem is to determine the schedule of power generating units and the generating level of each unit. The decisions involve which units to commit at each time period and at what level to generate power to meet the electricity demand. We consider the heuristic column generation algorithm to solve this problem. Previous methods used the approach in which each column corresponds to the start–stop schedule and output level. Since power output is a continuous quantity, it takes time to generate the required columns efficiently. In our proposed approach, the problem to be solved is not a simple set partitioning problem, because the columns generated contain only a schedule specified by 0–1 value. It is shown that the proposed heuristic approach is effective to solve the problem.

Market Risk Control in Flexible Investment Decisions

This chapter introduces models for risk control in investment decisions when the exit time of an investment is flexible, and the methods for solving these investment models.

Market Risk Measures for Flexible Investments

This chapter aims at introducing risk indices for the investments where investment timings are not fixed. Investment timings are the time at which an investment is made and the time investors liquidate their investments.

Reorganization of Logistics Network

In Chap. 8, the stochastic programming model for the logistics network design and the efficient solution method are shown. The traditional expected cost model and the Conditional Value at Risk (CVaR) model are compared in numerical experiments. Selection of facilities to be used in logistics network design is a very important decision item with regard to the supply chain. Facilities maintenance, sale, and relocation must be taken into consideration in a logistics network reorganization problem concerning the use of existing facilities and new facilities. Reorganization of the network requires considerable capital investment. It is necessary to make the optimal decision from a long-term view. However, as customer demand is not predictable, it is difficult to optimize the network. Decision-making on relocation of a facility takes place at a strategic level. This decision drives other operational decisions according to the standards, and thus, careful discussions are required. According to Ballou (Inf Syst Front 3:417–426, 2001), restructuring of a logistics network has the effect of reducing logistics costs by 5–15%. In this chapter, we consider a logistics network model considering demand uncertainty, and we propose a mathematical planning model using the stochastic programming method. Variables related to warehouse maintenance, integration, opening are called first stage variables, and variables related to transport determined under demand scenario are referred to as second stage variables. We propose a Conditional Value-at-Risk (CVaR) minimization model developed by Rockafellar and Uryasev (J Risk 2:21–41, 2000) employing the CVaR risk measure, and we apply the solution using the L-shaped method. First, divide the original problem into a first stage problem and a second stage problem. We solve the second stage problem using the solution obtained by solving the first stage problem, and approximates the objective function when it is feasible. Then, we compare the results with cases using the conventional expected cost minimization model. In numerical experiments, it is expected that the algorithm of this research is more effective than the conventional branch and bound method when the number of scenarios increases. The CVaR minimization model shows that the expected cost rises slightly more than the expected cost minimized model, while the worst case scenario can reduce the cost.

Inventory Distribution Problem

In Chap. 7, stochastic programming model is employed to formulate a lateral transshipment problem, and different solution methods were examined for their efficiency in providing solutions and in combining policies enforcing preventive or emergency lateral transshipments. The importance of improving the efficiency of the whole production and distribution system is increasing while the competition among companies is becoming severe in the recent economic environment. Companies need to review the entire supply chain for productivity improvement, the importance of tools to support optimal supply chain design is increasing. Numerous studies of mathematical programming for supply chain design problems have been made. Research that attempts to construct an efficient solution to the problem is mainstream. When applying supply chain design problems to real problems, these problems become often a large-scale problems where the number of data is huge. It is extremely difficult to solve the problem and calculate a good solution. In order to properly implement the supply chain design, collecting related data also takes enormous time and cost. Constructing an efficient solution is important in order to make effective use of the collected data to achieve cost reduction. In recent supply chains, suppliers aim to improve service levels while satisfying the diverse needs of consumers. At the same time we are considering reducing inventory and related expenses. However, in order to improve the service level, many inventories are required. There is a trade-off between inventory retention and service level. In order to improve both at the same time, it is necessary to construct a supply chain from the planning stage. Therefore, it may cost a lot of investment cost. Meanwhile, as a method of improving both inventory and service at the operation level, inventory distribution among sites has been drawing attention, and it is beginning to be utilized at actual companies’ sites. Conventional research on inventory distribution involves preventive transshipment and emergency transshipment, however two inventory transfer strategies are studied separately. Each of them has merits and demerits, and it is considered that higher service levels can be achieved by using these two policies in combination. In this chapter, considering combining these policies, and the effectiveness of the model is verified.

Optimal location problem for the installation of power flow controller

In power delivery systems, the use of dispersed generation and security control to improve network utilization requires the optimal use of system control devices. The installation of loop controller allows the distribution system to operate in a loop configuration, achieving effective management of voltage and power flow. In the investment planning process, it is important to identify the optimal location and installed capacity of the equipment such that all operational constraints are satisfied. This paper presents a method for identifying the optimal location and capacity with the minimum installation cost. Our novel approach uses an economic model that considers the fixed costs. A slope scaling procedure is presented, and its efficiency is demonstrated using numerical experiments.

Optimization of Railway Timetable by Allocation of Extra Time Supplements

We consider the allocation of a running time supplement to a railway timetable. Previously, Vekas et al. developed a stochastic programming model. In this paper, their optimization model is improved by adding bound constraints on the supplements. It is shown that the probability of delays decreases when using the proposed model. In addition, an effective L-shaped algorithm is presented.

Optimization Models for Multi-period Railway Rolling Stock Assignment

It is necessary for railway companies to construct daily schedules of assigning rolling stocks to utilization paths. A utilization path consists of a series of trains that a particular rolling stock performs in a day. A mixed integer programming model based on Lai et al. [1] is presented and is shown that straightforward applications of the model result in too much computational time and also inappropriate assignment schedules due to end effects. We show that the model can be modified to alleviate these difficulties, and also show that the repeated applications of the optimization model in the rolling horizon allow to generate a feasible assignment schedule for a longer period of time thus indicating the feasibility of the optimization approach.

Solution Method for the Inventory Distribution Problem

Previous research on inventory distributions between local warehouses or retailers (bases) has focused separately on either of two types of stock transshipment policies: preventive lateral transshipments or emergency lateral transshipments. Each of these has its advantages and disadvantages, and combining these policies may well enable merchandisers to achieve higher service levels. Thus, the combined use of these policies is the focus of the present study. A stochastic programming problem is formulated with demand as a stochastic variable, and the policy of using both preventive and emergency lateral transshipment is examined for its effectiveness while solution methods are examined for their efficiency.

Stochastic programming with binary second stage variables

Abstract We consider a class of stochastic programming with binary recourse variables in which a fixed cost is imposed if the value of the continuous recourse variable is strictly positive. The algorithm of a branch-and-cut method to solve the problem is developed by using the property of the expected recourse function. The problem is applied to a power generating system. The numerical experiments show that the proposed algorithm is quite efficient. The mathematical programming model defined in this paper is quite useful for a variety of design and operational problems.