Order acceptance and scheduling problems in two-machine flow shops: new mixed integer programming formulations

We present two new mixed integer programming formulations for the order acceptance and scheduling problem in two machine flow shops. Solving this optimization problem is challenging because two types of decisions must be made simultaneously: which orders to be accepted for processing and how to schedule them. To speed up the solution procedure, we present several techniques such as preprocessing and valid inequalities. An extensive computational study, using different instances, demonstrates the efficacy of the new formulations in comparison to some previous ones found in the relevant literature

An analytical bound on the fleet size in vehicle routing problems: A dynamic programming approach

We present an analytical upper bound on the number of required vehicles for vehicle routing problems with split deliveries and any number of capacitated depots. We show that a fleet size greater than the proposed bound is not achievable based on a set of common assumptions. This property of the upper bound is proved through a dynamic programming approach. We also discuss the validity of the bound for a wide variety of routing problems with or without split deliveries

New formulations for the setup assembly line balancing and scheduling problem

We present three new formulations for the setup assembly line balancing and scheduling problem (SUALBSP). Unlike the simple assembly line balancing problem, sequence-dependent setup times are considered between the tasks in the SUALBSP. These setup times may significantly influence the station times. Thus, there is a need for scheduling the list of tasks within each station so as to optimize the overall performance of the assembly line. In this study, we first scrutinize the previous formulation of the problem, which is a <i>station-based</i> model. Then, three new formulations are developed by the use of new sets of decision variables. In one of these formulations, the <i>schedule-based</i> formulation, SUALBSP is completely formulated as a scheduling problem. That is, no decision variable in the model directly denotes a station. All the proposed formulations will be improved by the use of several enhancement techniques such as preprocessing and valid inequalities. These improved formulations can be applied to establishing lower bounds on the problem. To assess the performance of new formulations, results of an extensive computational study on the benchmark data sets are also reported

An Estimated Formulation for the Capacitated Single Alocation p-hub Median Problem with Fixed Costs of Opening Facilities

In this paper, we consider the capacitated single allocation p-hub median problem generalized with fixed costs of opening facilities. The quadratic mathematical formulation of this problem is first adapted and then linearized. The typical approaches of linearization result in a high size complexity, i.e., having a large number of variables. To downsize the complexity, variables of the formulation are analyzed and some preprocessing approaches are defined. An estimated formulation is then developed to approximately solve large instances of the problem by commercial optimization solvers. The basic idea of this formulation is mapping the linearized formulation of the problem to a new formulation with fewer variables and a modified objective function. The efficacy of this formulation is shown by a computational study, where the estimated formulation is compared to a modified genetic algorithm from the literature. Results of computational experiments indicate that the estimated formulation is capable of generating good solutions within reasonable amount of time

The magic of Nash social welfare in optimization: Do not sum, just multiply!

We explain some key challenges when dealing with a single- or multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes the Nash social welfare function. We refer to this mathematical program as the Nash social welfare program (NSWP). An interesting property of the NSWP is that it can be constructed for any single- or multi-objective optimization problem. We show that solving the NSWP could result in more desirable solutions in practice than its single- or multi-objective counterpart. We also discuss several promising approaches that could be employed to solve the NSWP in practice. doi:10.1017/S1446181122000074