Dynamic Surgery Scheduling Based on an Improved Genetic Algorithm

We formulated a new stochastic programming formulation to solve the dynamic scheduling problem in a given set of elective surgeries in the day of operation. The problem is complicated by the fact that the exact surgery durations are not known in advance. Elective surgeries could be performed in parallel in a subset of operating rooms. The appointment times and assignments of surgeries were planned by an experienced nurses in advance. We present a mathematical model to capture the nature of dynamic scheduling problem. We propose an efficient solution based on an improved genetic algorithm (IGA). Our numerical results showed that dynamic scheduling with the IGA improves the resource utilization as measured by surgeon waiting time and operation room idle time.

A Matheuristic approach for the maximum balanced subgraph of a signed graph

A graph G=(V,E) with its edges labeled in the set {+, -} is called a signed graph. It is balanced if its set of vertices V can be partitioned into two sets V 1 and V 2 , such that all positive edges connect nodes within V 1 or V 2 , and all negative edges connect nodes between V 1 and V 2 . The maximum balanced subgraph problem (MBSP) for a signed graph is the problem of finding a balanced subgraph with the maximum number of vertices. In this work, we present the first polynomial integer linear programming formulation for this problem and a matheuristic to obtain good quality solutions in a short time. The results obtained for different sets of instances show the effectiveness of the matheuristic, optimally solving several instances and finding better results than the exact method in a much shorter computational time.

A New Binary Programming Formulation and Social Choice Property for Kemeny Rank Aggregation

Rank aggregation is widely used in group decision making and many other applications, where it is of interest to consolidate heterogeneous ordered lists. Oftentimes, these rankings may involve a large number of alternatives, contain ties, and/or be incomplete, all of which complicate the use of robust aggregation methods. In particular, these characteristics have limited the applicability of the aggregation framework based on the Kemeny-Snell distance, which satisfies key social choice properties that have been shown to engender improved decisions. This work introduces a binary programming formulation for the generalized Kemeny rank aggregation problem—whose ranking inputs may be complete and incomplete, with and without ties. Moreover, it leverages the equivalence of two ranking aggregation problems, namely, that of minimizing the Kemeny-Snell distance and of maximizing the Kendall-τ correlation, to compare the newly introduced binary programming formulation to a modified version of an existing integer programming formulation associated with the Kendall-τ distance. The new formulation has fewer variables and constraints, which leads to faster solution times. Moreover, we develop a new social choice property, the nonstrict extended Condorcet criterion, which can be regarded as a natural extension of the well-known Condorcet criterion and the Extended Condorcet criterion. Unlike its parent properties, the new property is adequate for handling complete rankings with ties. The property is leveraged to develop a structural decomposition algorithm, through which certain large instances of the NP-hard Kemeny rank aggregation problem can be solved exactly in a practical amount of time. To test the practical implications of the new formulation and social choice property, we work with instances constructed from a probabilistic distribution and with benchmark instances from PrefLib, a library of preference data.

Formulation Matters: Reciprocating Integer Programming for Birchbox Product Assortment

Birchbox created a mixed-integer programming formulation to determine the products that it will send to its subscribers in individual boxes on a monthly basis. The goal of this formulation is to produce a set of different box configurations that are then assigned to customers to meet the diverse needs of its varied customer base. As Birchbox’s business grew, the mixed-integer program was taking days to solve, and experimenting with different business requirements to determine the best set of configurations became impossible. Therefore, Princeton Consultants created the Reciprocating Integer Programming technique to reduce these solution times, thus decreasing them to typically under 20 minutes. This has dramatically changed the way that Birchbox can run its subscription business.