Optimization Model for Base-Level Delivery Routes and Crew Scheduling

In the U.S. Air Force, a Logistic Readiness Squadron (LRS) provides material management, distribution, and oversight of contingency operations. Dispatchers in the LRS must quickly prepare schedules that meet the needs of their customers while dealing with real-world constraints, such as time windows, delivery priorities, and intermittent recurring missions. Currently, LRS vehicle operation elements are faced with a shortage of manpower and lack an efficient scheduling algorithm and tool. The purpose of this research is to enhance the dispatchers\u27 capability to handle flexible situations and produce good schedules within current manpower restrictions. In this research, a new scheduling model and algorithm are provided as an approach to crew scheduling for a base-level delivery system with a single depot. A Microsoft Excel application, the Daily Squadron Scheduler (DSS), was built to implement the algorithm. DSS combines generated duties with the concept of a set covering problem. It utilizes a Linear Programming pricing algorithm and Excel Solver as the primary engine to solve the problem. Reduced costs and shadow prices from subproblems are used to generate a set of feasible duties from which an optimal solution to the LP relaxation can be found. From these candidate duties the best IP solution is then found. The culmination of this effort was the development of both a scheduling tool and an analysis tool to guide the LRS dispatcher toward efficient current and future schedules

New valid inequalities for knapsack and fixed-charge problems

A wide variety of important problems, in Operational Research and other fields, can be modelled as optimisation problems with integer-constrained variables. Algorithms and software for integer programming have improved substantially. One of the key ingredients to this success is the use of strong valid linear inequalities, also known as cutting planes. A key concept is that the convex hull of feasible solutions forms a polyhedron. One strand of the literature on cutting planes is concerned with the knapsack polytope. In the 1970s, Balas and Wolsey derived a family of inequalities, called lifted cover inequalities (LCIs), for the knapsack polytope. We have taken a lifting procedure due to Balas, and shown that it can be substantially improved, so that it yields stronger and more general LCIs. In 2000, Carr and co-authors introduced another family of valid inequalities for the knapsack polytope. These inequalities, called knapsack cover inequalities, can be rather weak. We have used two lifting procedures to strengthen these inequalities. The first procedure is based on integer rounding, whereas the second uses superadditivity. Another important class of optimisation problems are those that involve fixed charges. In 1985, Padberg, Van Roy and Wolsey introduced a procedure which enables one to take known valid inequalities for the knapsack polytope, and convert them into valid inequalities for the fixed-charge polytope. We have shown how this procedure can be extended to obtain a wider family of inequalities for the fixed-charge and single-node flow polytopes. Finally, we have considered problems where a fixed charge is incurred if and only if at least one variable in a set takes a positive value. We have derived strong valid inequalities for these problems and shown that they generalise and dominate a subclass of the flow cover inequalities for the classical fixed-charge problem

A separation routine for the set covering polytope

SIGLEITItal

Das Partial Set Covering Problem und Erweiterungen: Modellierung und Lösungsverfahren

In this thesis, we study the Partial Set Covering Problem (PSCP) as well as some new extensions of the PSCP. We present a new extension of the PSCP which is called the Multiple Coverage Partial Set Covering Problem (MCPSCP). The model combines the aspect of multiple coverage with the PSCP. Heuristic and approximative algorithms are proposed. Here, the focus lies on the PSCP and the MCPSCP for which several local search and Langrangean-based algorithms are presented. The heuristics are tested on a wide variety of benchmark problems. Furthermore, we report about an application of the PSCP and the MCPSCP in railway networks. The models are used to find optimal positions for vehicle testing stations