Meta-Heuristics for Dynamic Lot Sizing: a review and comparison of solution approaches

Proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve. Because these problems are so difficult, various solution techniques have been proposed to solve them. In the past decade, meta-heuristics such as tabu search, genetic algorithms and simulated annealing, have become popular and efficient tools for solving hard combinational optimization problems. We review the various meta-heuristics that have been specifically developed to solve lot sizing problems, discussing their main components such as representation, evaluation neighborhood definition and genetic operators. Further, we briefly review other solution approaches, such as dynamic programming, cutting planes, Dantzig-Wolfe decomposition, Lagrange relaxation and dedicated heuristics. This allows us to compare these techniques. Understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms. Finally, we discuss general guidelines for computational experiments and illustrate these with several examples

The two-dimensional bin packing problem with variable bin sizes and costs

AbstractThe two-dimensional variable sized bin packing problem (2DVSBPP) is the problem of packing a set of rectangular items into a set of rectangular bins. The bins have different sizes and different costs, and the objective is to minimize the overall cost of bins used for packing the rectangles. We present an integer-linear formulation of the 2DVSBPP and introduce several lower bounds for the problem. By using Dantzig–Wolfe decomposition we are able to obtain lower bounds of very good quality. The LP-relaxation of the decomposed problem is solved through delayed column generation, and an exact algorithm based on branch-and-price is developed. The paper is concluded with a computational study, comparing the tightness of the various lower bounds, as well as the performance of the exact algorithm for instances with up to 100 items

Scheduling inbound calls in call centers

Scheduling inbound calls, namely assigning calls to Customer Service Representatives (CSRs) and sequencing the calls waiting for each CSR, is a key task in call center operations. In most call center this is achieved using simple priority rules, but in this dissertation we show that performance can be significantly improved by employing an optimization approach. Specifically, we formulate three different Integer Programming (IP) problems for such call scheduling, with objective functions of 1) minimizing the Total Flow Time (TFT), 2) minimizing the Maximum Flow Time (MFT) of any call, and 3) minimizing the Maximum Deviation of Cumulative Assigned Workload (MDCAW) for CSRs. We also report the results of a numerical experiment designed to evaluate under what conditions these IP formulations give superior performance and which objective should be chosen. Our findings indicate that optimization is most valuable under realistic scenarios involving specialized but broadly trained CSRs and high call centre utilization rates. Furthermore, both the flow time and workload related objective functions are found to be useful, depending on the characteristics of the call center and the performance measures that are most important to call center management. We explore several solution techniques such as IP reformulation, Lagrangian relaxation and duality, cutting plane algorithm, and heuristic approach for solving the formulated IPs. For those solution algorithms, the qualities of the solution and the computational times of solving the IPs using a standard solver are compared to signify the effective approaches that make the optimization a competitive approach for scheduling inbound calls. Numerical results show that the heuristics optimization approach is preferable to any other solution investigated in terms of solution quality while the cutting plane algorithm is preferable in terms of computational times. Additionally, a case study comparing performances of a call center as resulted from using its current routing method with the performance resulted from the suggested solution techniques is presented