A note on the strategy of restriction and degenerate linear programming problems

Using the general computational strategy of restriction, necessary conditions for optimality provide an alternative criterion for entering variables when degeneracies arises in linear programming problems. Although cycling may still occur, it is shown that if it is possible to make progress at the next iteration, the criterion is guaranteed to identify a non-basic variable which increases the value of the basic solution, thereby reducing stalling. An alternative method for determining variables to exit the basis when degeneracies occur is also suggested.     

A note on explicit solution in linear fractional programming

In this note we analyze the fractional interval programming problem (FIP) and find, explicitly, all its optimal solutions. Though our results are essentially the same as those in Charnes and Cooper [4], the proofs and analysis we provide here are considerably simpler.     

Flowshop sequencing problem with ordered processing time matrices: A general case

The ordered matrix flow shop problem with no passing of jobs is considered. In an earlier paper, the authors have considered a special case of the problem and have proposed a simple and efficient algorithm that finds a sequence with minimum makespan for a special problem. This paper considers a more general case. This technique is shown to be considerably more efficient than are existing methods for the conventional flow shop problems.     

An algorithm for solving general fractional interval programming problems

A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.     

On labeling the vertices of products of complete graphs with distance constraints

Variations of Hale's channel assignment problem, the L(j, k)‐labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various distance constraints. The λ_j,k‐number of G and the radio number of G are respectively the minimum span among all L(j, k)‐labelings, and the minimum span plus 1 of all radio labelings of G (defined in the Introduction). In this paper, we establish the λ_j,k‐number of ∏ K for pairwise relatively prime integers t₁ < t₂ < … < t_q, t₁ ≥ 2. We also show the existence of an infinite class of graphs G with radio number |V(G)| for any diameter d(G). © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Benders' cuts guided large neighborhood search for the traveling umpire problem

This article introduces the use of Benders' cuts to guide a large neighborhood search to solve the traveling umpire problem, a sports scheduling problem inspired by the real‐life needs of the officials of a sports league. At each time slot, a greedy matching heuristic is used to construct a schedule. When an infeasibility is recognized first a single step backtracking is tried to resolve the infeasibility. If unsuccessful, Benders' cuts are generated to guide a large neighborhood search to ensure feasibility and to improve the solution. Realizing the inherent symmetry present in the problem, a large family of cuts are generated and their effectiveness is tested. The resulting approach is able to find better solutions to many instances of this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Technical note: Find a hidden “treasure”

This paper deals with a two searchers game and it investigates the problem of how the possibility of finding a hidden object simultaneously by players influences their behavior. Namely, we consider the following two‐sided allocation non‐zero‐sum game on an integer interval [1,n]. Two teams (Player 1 and 2) want to find an immobile object (say, a treasure) hidden at one of n points. Each point i ∈ [1,n] is characterized by a detection parameter λ_i (μ_i) for Player 1 (Player 2) such that p_i(1 ? exp(?λ_ix_i)) (p_i(1 ? exp(?μ_iy_i))) is the probability that Player 1 (Player 2) discovers the hidden object with amount of search effort x_i (y_i) applied at point i where p_i ∈ (0,1) is the probability that the object is hidden at point i. Player 1 (Player 2) undertakes the search by allocating the total amount of effort X(Y). The payoff for Player 1 (Player 2) is 1 if he detects the object but his opponent does not. If both players detect the object they can share it proportionally and even can pay some share to an umpire who takes care that the players do not cheat each other, namely Player 1 gets q₁ and Player 2 gets q₂ where q₁ + q₂ ≤ 1. The Nash equilibrium of this game is found and numerical examples are given. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Terrorism as Method in Nepali Maoist Insurgency, 1996–2016

During the period 1996–2006, the Communist Party of Nepal (Maoist) waged overt people’s war to seize state power and institute a new order that realized the party’s understanding of ‘New Democracy’ as posited by Mao Tse-tung. Contextual shifts led to a crucial strategic turning point in September 2005, when the Maoists agreed to a united front with estranged legal parties to oust the monarchy and establish a republic. Though touted as acceptance of political reintegration, the move was tactical rather than strategic. The party had no intention of supporting a parliamentary version of democracy and thus, 2006–2016, engaged in a covert effort to seize power. Central to this effort was the paramilitary Young Communist League (YCL), the members of which responded to inflammatory party verbiage and exhortations with attacks upon rival political actors. These attacks, academically and legally, were terrorism and offered a salient illustration of intra-state unrestricted warfare. Ultimately, organizational, national, and regional circumstances caused the main Maoist movement to move decisively away from its covert approach. By that time, however, radical splinters had embraced the use of terrorism against rival political actors, creating a situation whereby local politics is yet a dangerous endeavor in certain areas and at certain times.