Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models

Lagrangian relaxation schemes, coupled with a subgradient procedure, are frequently employed to solve chance-constrained optimization models. The subgradient procedure typically relies on a step-size update rule. Although there is extensive research on the properties of these step-size update rules, there is little consensus on which rules are most suited in practice. This is especially so … Read more

Balancing preferential access and fairness with an application to waste management: mathematical models, optimality conditions, and heuristics

Typically, within facility location problems, fairness is defined in terms of accessibility of users. However, for facilities perceived as undesirable by communities hosting them, fairness between the usage of facilities becomes especially important. Limited research exists on this notion of fairness. To close this gap, we develop an optimization framework for the allocation of populations … Read more

Boole-Bonferroni Inequalities to Approximately Determine Optimal Arrangements

We consider the problem of laying out several objects in an equal number of pre-defined positions. Objects are allowed finitely many orientations, can overlap each other, and must be arranged contiguously. We are particularly interested in the case when the evaluation of the dimensions of the objects requires computational or physical effort. We develop a … Read more

An Application of a Traveling Salesman Problem with Independent Clusters for Cash-Collection Routing

Motivated by a routing problem faced by banks to enhance their encashment services in the  city of Perm, Russia, we solve versions of the traveling salesman problem with clustering. To minimize the risk of theft, suppliers seek to operate multiple vehicles and determine an efficient routing; and, a single vehicle serves a set of locations that … Read more

Lagrangian relaxation based heuristics for a chance-constrained optimization model of a hybrid solar-battery storage system

We develop a stochastic optimization model for scheduling a hybrid solar-battery storage system. Solar power in excess of the promise can be used to charge the battery, while power short of the promise is met by discharging the battery. We ensure reliable operations by using a joint chance constraint. Models with a few hundred scenarios … Read more