Applications – OR and Management Sciences

Improving Public Transport Accessibility via Provision of a Dial-a-Ride Shuttle-Bus Service, Incorporating Passenger Travel-Mode Heterogeneity

Categories Scheduling Tags , ,

In many real-world transportation systems, passengers are often required to make a number of interchanges between different modes of transport. As cities continue to grow, a greater number of these connections tend to occur within centrally located Transport Hubs. In order to encourage the uptake of public transport in major cities, it is important for … Read more

The impact of the existence of multiple adjustable robust solutions

Categories Applications - OR and Management Sciences, Robust Optimization

In this note we show that multiple solutions exist for the production-inventory example in the seminal paper on adjustable robust optimization in [2]. All these optimal robust solutions have the same worst-case objective value, but the mean objective values differ up to 21.9% and for individual realizations this difference can be up to 59.4%. We … Read more

A Quantitative Comparison of Risk Measures

Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags ,

The choice of a risk measure reflects a subjective preference of the decision maker in many managerial, or real world economic problem formulations. To evaluate the impact of personal preferences it is thus of interest to have comparisons with other risk measures at hand. This paper develops a framework for comparing different risk measures. We … Read more

The Ramping Polytope and Cut Generation for the Unit Commitment Problem

Categories Applications - OR and Management Sciences Tags , ,

We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramping constraints, time-dependent start-up costs, and start-up/shut-down ramping. To develop this perfect formulation we extend the result of Balas on unions of polyhedra … Read more

Variational Analysis and Applications to Group Dynamics

Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , ,

In this paper, we establish a new version of Ekeland’s variational principle in a new setting of cone pseudo-quasimetric spaces. In constrast to metric spaces, we do not require that each forward Cauchy sequence is forward convergent and that each forward convergent sequence has the unique forward limit. The motivation of this paper comes from … Read more

A Stochastic Programming Approach for Shelter Location and Evacuation Planning

Categories Second-Order Cone Programming, Stochastic Programming, Transportation Tags , , , , ,

Shelter location and traffic allocation decisions are critical for an efficient evacuation plan. In this study, we propose a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to nearest shelters and to shortest paths within a tolerance degree to minimize the expected total evacuation time. Our model considers … Read more

A State Transition MIP Formulation for the Unit Commitment Problem

Categories Applications - OR and Management Sciences Tags ,

In this paper, we present the state-transition formulation for the unit commitment problem. This formulation is based on the definition of new decision variables, which, instead of indicating the on/off statuses of a generator, captures its state transitions between consecutive time periods. We show that this new approach produces a formulation which naturally includes valid … Read more

Integer Programming Approaches for Appointment Scheduling with Random No-shows and Service Durations

Categories (Mixed) Integer Linear Programming, Scheduling, Stochastic Programming

We consider a single-server scheduling problem given a fixed sequence of appointment arrivals with random no-shows and service durations. The probability distribution of the uncertain parameters is assumed to be ambiguous and only the support and first moments are known. We formulate a class of distributionally robust (DR) optimization models that incorporate the worst-case expectation/conditional … Read more

Uniqueness of Market Equilibrium on a Network: A Peak-Load Pricing Approach

Categories Convex Optimization, Finance and Economics, Network Optimization Tags , , ,

In this paper we establish conditions under which uniqueness of market equilibrium is obtained in a setup where prior to trading of electricity, transmission capacities between different market regions are fixed. In our setup, firms facing fluctuating demand decide on the size and location of production facilities. They make production decisions constrained by the invested … Read more

A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope

Categories Applications - OR and Management Sciences

In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope, which has broad applications in power generation scheduling problems. The generalized polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints. We derive strong valid inequalities for this polytope by utilizing its specialized structures. … Read more