On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

Algorithms for Online Advertising Portfolio Optimization and Capacitated Mobile Facility Location

In this dissertation, we apply large-scale optimization techniques including column generation and heuristic approaches to problems in the domains of online advertising and mobile facility location. First, we study the online advertising portfolio optimization problem (OAPOP) of an advertiser. In the OAPOP, the advertiser has a set of targeting items of interest (in the order of tens of millions for large enterprises) and a daily budget. The objective is to determine how much to bid on each targeting item to maximize the return on investment. We show the OAPOP can be represented by the Multiple Choice Knapsack Problem (MCKP). We propose an efficient column generation (CG) algorithm for the linear programming relaxation of the problem. The computations demonstrate that our CG algorithm significantly outperforms the state-of-the-art linear time algorithm used to solve the MCKP relaxation for the OAPOP. Second, we study the problem faced by the advertiser in online advertising in the presence of bid adjustments. In addition to bids, the advertisers are able to submit bid adjustments for ad query features such as geographical location, time of day, device, and audience. We introduce the Bid Adjustments Problem in Online Advertising (BAPOA) where an advertiser determines base bids and bid adjustments to maximize the return on investment. We develop an efficient algorithm to solve the BAPOA. We perform computational experiments and demonstrate, in the presence of high revenue-per-click variation across features, the revenue benefit of using bid adjustments can exceed 20%. Third, we study the capacitated mobile facility location problem (CMFLP), which is a generalization of the well-known capacitated facility location problem that has applications in supply chain and humanitarian logistics. We provide two integer programming formulations for the CMFLP. The first is on a layered graph, while the second is a set partitioning formulation. We develop a branch-and-price algorithm on the set partitioning formulation. We find that the branch-and-price procedure is particularly effective, when the ratio of the number of clients to the number of facilities is small and the facility capacities are tight. We also develop a local search heuristic and a rounding heuristic for the CMFLP

Supply Chain Optimisation in Animal Husbandry

The pig husbandry is an important economic sector. In the last decade, major changes have been made. As a result, farmers came together to introduce the "Eco Label pig", meeting the strong consumer and governmental call for high quality, animal friendly and environmentally friendly food. The market for Eco Label food is expected to grow enormously in the next years, asking for the development of an efficient and effective supply chain consisting of farmers, slaughter houses, wholesalers and retailers. We present some mathematical models to support decision making and evaluation of a large number of growth scenario's, using cost minimization given a number of Eco Label conditions.supply chain management;logistics;agricultural logistics;network configuration