(p − 1)(p + 1)-approximate algorithms for p-traveling salesmen problems on a tree with minmax objective

AbstractSuppose p traveling salesmen must visit together all points/nodes of a tree, and the objective is to minimize the maximum of lengths of their tours. For location-allocation problems (where both optimal home locations of the salesmen and their tours must be found), which are NP-complete, fast polynomial heuristics with worst-case relative error (p − 1)(p + 1) are presented

Locating Mobile Servers on a Network with Markovian Processes

The median problem has been generalized to the case in which facilities can be moved, at a cost, on the network in response to changes in the state of the network. Such changes are brought about by changes in travel times on the links of the network due to the occurrence of probabilistic events. For the case examined here, transitions among states of the network are assumed to be Markovian. The problem is examined for an objective which is a weighted function of demand travel times and of facility relocation costs. It is shown that when these latter costs are a concave function of travel time, an optimal set of facility locations exists solely on the nodes of the network. The location-relocation problem is formulated as an integer programming problem and its computational complexity is discussed. An example illustrates the basic concepts of this paper

Scheduling Workforce and Workflow in a Service Factory

We define a service factory to be a network of service-related-workstations, at which assigned workers process work-in-progress that flows through the workstations. Examples of service factory work include mail processing and sorting, check processing and telephoned order processing. Exogenous work may enter the factory at any workstation according to any time-of-day profile. Work-in-progress flows though the factory in discrete time according to Markovian routings. Workers, who in general are cross trained, may work part time or full time shifts, may start work only at designated shift starting times, and may change job assignments at midshift. In order to smooth the flow of work-in-progress through the service factory, work-in-progress may be temporarily inventoried (in buffers) at work stations. The objective is to schedule the workers (and correspondingly, the workflow) in a manner that minimizes labor costs subject to a variety of service-level, contractural and physical constraints. Motivated in part by analysis techniques of discrete time linear time-invariant (LTI) systems, an object-oriented linear programming (OOLP) model is developed. Using exogenous input work profiles typical of large U. S. mail processingfacilities, illustrative computational results are included

The Congested Median Problem

The median problem has been generalized to include queueing-like congestion of facilities (which are assumed to have finite numbers of servers). In one statement of the problem, a closest available server is assumed to handle each service request. More general server assignment policies are allowed, however. The analysis requires keeping track of the states (available or unavailable) of all servers. Paralleling the standard deterministic median problem, the objective is to minimize the expected travel time associated with a random service request, weighted appropriately by the equilibrium state probabilities of the system. Under suitable conditions, it is shown that at least one set of optimal locations exists solely on the nodes of the network. This analysis ties together previously disparate efforts in network analysis and spatial queueing analysis.Prepared under Grant Number 78NI-AX-0007 from the National Institute of Law Enforcement and Criminal Justice, Law Enforcement Assistance Administration, U.S. Department of Justice

Locating Discretionary Service Facilities II: Maximizing Market Size, Minimizing Inconvenience

Revised November 1992Discretionary service facilities are providers of products and/or services that are purchased by customers who are traveling on otherwise pre-planned trips such as the daily commute. Optimum location of such facilities requires them to be at or near points in the transportation network having sizable flows of different potential customers. In [1] a first version of this problem was formulated, assuming that customers would make no deviations, no matter how small, from the pre-planned route to visit a discretionary service facility. Here the model is generalized in a number of directions, all sharing the property that the customer may deviate from the pre-planned route to visit a discretionary service facility. Three different generalizations are offered, two of which can be solved approximately by greedy heuristics and the third by any approximate or exact method used to solve the pmedian problem. It is shown for those formulations yielding to a greedy heuristic approximate solution, including the formulation in [1], that the problems are examples of optimizing submodular functions for which the Nemhauser et. al. [51 bound on the performance of a greedy algorithm holds. In particular, the greedy solution is always within 37% of optimal, and for one of the formulations it is proved that the bound is tight

Endogenous (In)Formal Institutions.

Despite the huge evidence documenting the relevance of inclusive political institutions and a culture of cooperation, we still lack a framework that identifies their origins and interaction. In a model in which an elite and a citizenry try to cooperate in consumption risk-sharing and investment, we show that a rise in the investment value encourages the elite to introduce more inclusive political institutions to convince the citizenry that a sufficient part of the returns on joint investments will be shared. In addition, accumulation of culture rises with the severity of consumption risk if this is not too large and thus cheating is not too appealing. Finally, the citizenry may over-accumulate culture to credibly commit to cooperate in investment when its value falls and so inclusive political institutions are at risk. These predictions are consistent with the evolution of activity-specific geographic factors, monasticism, and political institutions in a panel of 90 European regions spanning the 1000-1600 period. Evidence from several identification strategies suggests that the relationships we uncover are causal

Optimal Server Location on a Network Operating as and M/G/1 Queue

Not Availabl