Daniel Solow

Vehicle Routing and Scheduling with Full Truckloads

Truckload carriers are constantly faced with the problem of shipping full truckloads of goods at minimum cost between pairs of cities or customers, using a fleet of trucks located at one or more depots. In this paper, a new branch-and-bound algorithm for solving an integer-programming formulation of this vehicle-routing problem (VRP) with full truckloads is developed. The algorithm also takes into consideration the time-window constraints and waiting costs. The resulting efficiency, validated by computational tests on random problems, is due to a column-generation scheme that exploits the special structure of the problem to solve the linear-programming relaxation problems that arise at the nodes.

Mathematical Models for Studying the Value of Motivational Leadership in Teams

Mathematical models are presented for studying the value of leadership in a team where the members interact with each other. The models are based on a leader’s role of motivating each team member to perform closer to his/her maximum ability. These models include controllable parameters whose values reflect the amount of task interdependence among the workers as well as the motivational skill and variability in the skill of the leader. Confirming results—such as the fact that the skill level of the leader is a critical factor in the expected performance of the team—establish credibility in the models. Mathematical analysis and computer simulations are used to provide new managerial insights into the value of the leader—such as the fact that the skill of the leader can be more important than controlling the amount of interdependence among the team members and that having a choice of multiple leaders with no particular motivating skill is beneficial to the performance of small teams but not to large teams.

Mathematical Models for Studying the Value of Cooperational Leadership in Team Replacement

Mathematical models are presented for studying the value of leadership in a team whose composition is changing over time. The models are based on a leaders role of achieving cooperation among the interacting members so that they perform their tasks better and hence improve overall team performance. Three different approaches, modified from Kauffmans NK model, are proposed. Each model includes controllable parameters whose values reflect the amount of interaction among the workers as well as the skill and variance of the leader in achieving cooperation. Computer simulations are used to show how the skill level and variance of the leader affect the expected performance of the team. Managerial insights into the value of the leader—such as the fact that finding a more skillful leader can be more important to team performance than controlling the amount of interaction among the team members—are provided.

Managerial Insights into the Effects of Interactions on Replacing Members of a Team

A mathematical model is presented for studying the effects of interactions among team members on the process of replacing members of a team in an organization. The model provides the ability to control the number of members that interact with each individual on the team. Through the use of analysis and computer simulations, it is shown how the amount of interaction affects the tradeoff between the expected performance and the number of replacements and interviews needed to find a good team using various replacement policies. New managerial insights into this process--such as the fact that it is not necessarily optimal to replace the worst-performing team member--are provided.

Understanding and attenuating the complexity catastrophe in Kauffman's N K model of genome evolution

Kauffmans N K model—used for studying the performance of systems consisting of a finite number of components that interact with each other in complex ways—exhibits the complexity catastrophe, in which high levels of interaction in systems with a large number of components lead to a decrease in performance. It is shown here that the complexity catastrophe is a consequence of the mathematical assumptions underlying the N K model. Analysis and simulations are used to establish the idea that relaxing any one of these assumptions results in a new model in which the complexity catastrophe is attenuated. Thus, good performance from systems having high levels of interactions is possible. ©1999 John Wiley & Sons, Inc.

Understanding the Role of Worker Interdependence in Team Selection

In this paper, we evaluate the effectiveness of policies for assigning interdependent workers to teams. Using a computational simulation, we contrast distributing workers equitably across teams based on prior individual performance with policies that distribute workers based on how well people work together. First, we test a policy that clusters workers into teams by finding natural breakpoints among them where their mutual support is weak. Then we test two other policies that both protect the strongest interdependent core of high performers but differ in that one policy separates workers who give little support to interdependent partners and the other separates workers who receive little support from their partners. All three policies outperform the equitable-distribution approach in some circumstances. We make recommendations to managers for harnessing interdependence when forming teams, whether the managers are familiar or unfamiliar with how well their people work together.

An analysis and implementation of an efficient in-place bucket sort

Abstract. Various methods, such as address-calculation sorts, distribution counting sorts, radix sorts, and bucket sorts, use the values of the numbers being sorted to increase efficiency but do so at the expense of requiring additional storage space. In this paper, a specific implementation of bucket sort is presented whose primary advantanges are that (i) linear average-time performance is achieved with an additional amount of storage equal to any fraction of the number of elements being sorted and (ii) no linked-list data structures are used (all sorting is done with arrays). Analytical and empirical results show the trade-off between the additional storage space used and the improved computational efficiency obtained. Computer simulations show that for lists containing 1,000 to 30,000 uniformly distributed positive integers, the sort developed here is faster than both Quicksort and a standard implementation of bucket sort. Furthermore, the running time increases with size at a slower rate.

Mathematical models for explaining the emergence of specialization in performing tasks

In an evolving community consisting of many individuals, it is often the case that the individuals tend, over time, to become more specialized in performing the tasks necessary for survival and growth of the community as a whole. In this work, linear and nonlinear mathematical models are presented for providing insights as to when and why this functional specialization emerges.

The effectiveness of finite improvement algorithms for finding global optima

This paper investigates the effectiveness of using finite improvement algorithms for solving decision, search, and optimization problems. Finite improvement algorithms operate in a finite number of iterations, each taking a polynomial amount of work, where strict improvement is required from iteration to iteration. The hardware, software, and way of measuring complexity found in the polynomial setting are modified to identify the concept of repetition and define the new classes of decision problems,FI andNFI. A firstNFI-complete problem is given using the idea ofFI-transformations. Results relating these new classes toP, NP, andNP-complete are given. It is shown that if an optimization problem in a new classPGS isNP-hard, thenNP=co-NP. TwoPGS problems are given for which no polynomial algorithms are known to exist.

How large should a complex system be? An application in organizational teams

This article investigates when a growing team benefits from being divided and how complex interactions among workers and management impact this decision. The proposed model—a modification of Kauffmans NK model—has the property that team performance decreases as the size of the team increases. Analytical results and computer simulations show how team size, the amount of supervision, worker performance, interaction among employees, relationships between management and labor, and leadership skill affect when a team should be split.