Industrial engineering and management

We consider a partial ordered set (POSET) of assembling operations, with known execution durations, that must be accomplished. The assembling operations can be executed on an acyclic network with an identical set of robots on each conveyer (arc). The number of depots (nodes) is a known integer. Between each pair of depots we can locate only one conveyer. We seek an arrangement of the network and a plan that divides the task operations among the conveyers, minimizing the overall task completion time. We use linear programming optimization, subject to reasonably general rules for distributing the operation-fragments among the conveyers.

We evaluate the possible benefit from improving the workload distribution in a directed acyclic graph (DAG) (e.g. a project network), by determining a lower bound for the project completion time. It is shown that a lower bound can be obtained by equally distributing the workload over the max-cut in the graph which separates the nodes 1 and n. It is also shown that for a complete n-node DAG, practitioners can quickly compute a lower bound for the project completion time. The max-cut can be found by any linear programming algorithm or by reducing the problem to the problem of finding a maximum matching in a bipartite graph. Our results can help planners and project managers to characterize the "ideal case" in which the optimal workload distribution among the arc networks minimizes the project completion time. That can be done for a non-complete DAG as well as for a complete one. A lower bound can then be used to evaluate the maximum potential for reducing the project completion time in real-life cases.

Given an Eulerian multigraph, a subset T of its vertices, and a collection H of subsets of T, we ask how few edge-disjoint paths can contain maximum (A, T "A)flows, for all A # H at once. We answer the question for a certain class of hypergraphs H by presenting a strongly polynomial construction of a minimum set of such paths and a min-max formula for its cardinality. The method consists in reducing the problem to maximizing a b-matching in some graph. The result provides a solution to one interesting class of path packing problems.

We consider a partial ordered set (POSET) of assembling operations, with known execution durations, that must be accomplished. The assembling operations can be executed on an acyclic network with an identical set of robots on each conveyer (arc). The number of depots (nodes) is a known integer. Between each pair of depots we can locate only one conveyer. We seek an arrangement of the network and a plan that divides the task operations among the conveyers, minimizing the overall task completion time. We use linear programming optimization, subject to reasonably general rules for distributing the operation-fragments among the conveyers.

The partially-concurrent open shop scheduling problem is presented. The standard open shop scheduling problem is generalized by allowing some operations to be processed concurrently. This generalization is directly motivated from a real-life timetabling project of assigning technicians to airplanes in an airplane garage. A schedule for the partially-concurrent problem is represented by a digraph. We show that the scheduling problem is equivalent to a problem of orienting a given undirected graph, called a conflict graph. The schedule digraph is then modeled by a matrix, generalizing the rank matrix representation. The problem is shown to be NP-Hard. The rank matrix representation is also used in an algorithm that heuristically constructs an open shop schedule.

Partially Concurrent Open Shop Scheduling (PCOSS) is a relaxation of the well-known Open Shop Scheduling (OSS) problem, where some of the operations that refer to the same job may be processed concurrently. Here we extend the study of the PCOSS model by considering the addition of limited resources. We deal with the case of preemption PCOSS, where a few polynomial algorithms are known for its OSS counterpart. The scheduling problem is equivalent to the problem of conflict graph colouring. The restriction on the number of resources bounds the size of colour classes. We thus study the problem of bounded vertex colouring and focus on bounds. In particular, we introduce a new bound for this problem, propose a colouring procedure that is inspired by this new bound, and show that for perfect graphs with two resources the procedure attains the bound, and hence is optimal. The model correlates to a real-life timetabling project of assigning technicians to vehicles in a garage, with addition...

The presented two-campus transport problem (TCTP) is a pickup-anddelivery scheduling problem. It is a problem of a college with two campuses located at two different cities. Lecturers living in one city should sometimes teach at the other city campus. The problem is that of transporting N lecturers from one campus to the other, using a fleet of k vehicles, so as to minimize the time the lecturers wait for their transport. This is an optimal set partition problem. We mathematically model the one-directional case of the TCTP. The feasible space solution is represented by linear extensions of the requested departure time partially ordered set and reduction to the shortest path problem. This enables finding the optimal solution for the one directional case. TCTP is a two-destinations version of a dial-a-ride problem (DARP).

The two-campus transport problem (TCTP) is a dial-a-ride problem with only two destinations. The problem is motivated by a transport problem between two campuses of an academic college. The two campuses are located in two different cities. Lecturers living in one city are sometimes asked to teach at the other city's campus. The problem is that of transporting the lecturers from one campus to the other, using a known set of vehicles, so as to minimize the time the lecturers wait for their transport. We mathematically model the general TCTP, and provide an algorithm that solves it, which is polynomial in the number of lecturers. The algorithm is based on a reduction to a shortest path problem.

We study all-pay auctions with multiple prizes. The players have the same value for all the certain prizes except for one uncertain prize for which each player has a private value. We characterize the equilibrium strategy and show that if the number of prizes is smaller than the number of players, independent of the ranking of the uncertain prize, a player's probability to win as well as his expected utility increases in his value for this prize. We demonstrate that a stochastic dominance relation between two distribution functions of the players'private values may increase but also even decrease the players' ex-ante expected utility as well the players' expected total e¤ort. Also, increasing the number of prizes may decrease the players' ex-ante expected utility. Thus, we may conclude that a larger number of prizes does not necessarily bene…t the players in a contest.

This paper explores the issue of accountability in democratic systems by addressing the issue of the deliberate distortion (gaming) of performance measures in the context of the principal-agent theory. Our model identifies the conditions required for principals to invest effort in monitoring agents' gaming activities, and for agents to minimize the effort they invest in such activities. We show that the principal can reduce the agents' gaming efforts by introducing value-added reporting systems that benefit them or impose painful penalties on their gaming. Alternatively, the principal may find ways to reduce the costs of monitoring, for example, through organizational changes. We use the model to explore a variety of principal-agent relations in democratic systems where citizens are weak principals. Politicians, regulators, and senior administrators, who play as both principals and agents, have motivation to invest in gaming the system leading to acute problems of accountability and responsibility in democratic systems.

A major question in the economics and managerial literatures is whether decentralized structures in which authority is delegated across the organization's units are superior to centralized structures. The problems of incomplete information and the lack of truthful reporting intersect in many streams of research that consider this dilemma. Although an efficient management mechanism requires designing conditions under which agents will report truthfully to principals, most of the literature does not explicitly model the motivation of agents to distort the measures and data that they report to principals and the possible outcomes of adopting such gaming strategies. The possible implications of such behavior on the delegation structure are not considered either. This paper addresses these questions from the perspective of performance management in multi-level principal-agent relations. We show that agents are key players in ensuring truthful reporting and that monitoring and sanctioning for gaming should be included in the explicit contract between principals and subordinates. In addition, the conditions needed to minimize gaming are less favorable in the public sector than they are in the private sector.

We study standard rent-seeking contests in which there are two forms of sabotaging. This study is conducted for a symmetric model of two contestants with complete information, when the first form of sabotaging negatively affects the probability of winning the contest while the second form increases the marginal cost of the standard rent-seeking effort. We show that only those forms of sabotage that increase the marginal cost of the rent-seeking effort affect the productive rent-seeking effort. Thus, from a designer's point of view, if monitoring is feasible, the only form of sabotaging effort that should be monitored is the second one.