Sensitivity analysis as a means of reducing the dimensionality of a certain class of transportation problems

Sensitivity analysis of the transportation problem is developed in a way which enables reducing the dimensionality of the associated tableau. This technique is used to reduce the dimensionality of a transportation problem whose origin requirements are relatively small at the majority of origins. A long transportation problem, for which efficient solution procedures exist, results. A second application relates to the location-allocation problem. Reducing the dimensionality of such a problem, accompanied by the partial determination of the optimal solution, should prove helpful in the quest for an analytic solution to the aforementioned problem. In the meantime, reducing dimensionality greatly decreases the effort involved in solution by trial and error. Examples of the two applications are provided.     

Production to order and off‐line inspection when the production process is partially observable

This study combines inspection and lot‐sizing decisions. The issue is whether to INSPECT another unit or PRODUCE a new lot. A unit produced is either conforming or defective. Demand need to be satisfied in full, by conforming units only. The production process may switch from a “good” state to a “bad” state, at constant rate. The proportion of conforming units in the good state is higher than in the bad state. The true state is unobservable and can only be inferred from the quality of units inspected. We thus update, after each inspection, the probability that the unit, next candidate for inspection, was produced while the production process was in the good state. That “good‐state‐probability” is the basis for our decision to INSPECT or PRODUCE. We prove that the optimal policy has a simple form: INSPECT only if the good‐state‐probability exceeds a control limit. We provide a methodology to calculate the optimal lot size and the expected costs associated with INSPECT and PRODUCE. Surprisingly, we find that the control limit, as a function of the demand (and other problem parameters) is not necessarily monotone. Also, counter to intuition, it is possible that the optimal action is PRODUCE, after revealing a conforming unit. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Optimal refueling sequence for a mixed fleet with limited refuelings

Consider a fleet of vehicles comprised of K₁ identical tankers and K₂ identical nontankers (small aircraft). Tankers are capable of refueling other tankers as well as nontankers. The problem is to find that refueling sequence of the tankers that maximizes the range simultaneously attainable by all K₂ nontankers. A recent paper established that the “unit refueling sequence,” comprised of one tanker refueling at each of K₁ refueling operations, is optimal. The same paper also proffered the following conjecture for the case that the number of refueling operations is constrained to be less than the number of tankers: A nonincreasing refueling sequence is optimal. This article proves the conjecture.     

Landmarks in defense literature

A soldier's Duty By Marshal K. Rokossovsky Progress Publishers, Moscow (1985)     

Vehicle fleet refueling strategies to maximize operational range

The focus of this research is on self-contained missions requiring round-trip vehicle travel from a common origin. For a single vehicle the maximal distance that can be reached without refueling is defined as its operational range. Operational range is a function of a vehicle's fuel capacity and fuel consumption characteristics. In order to increase a vehicle's range beyond its operational range replenishment from a secondary fuel source is necessary. In this article, the problem of maximizing the range of any single vehicle from a fleet of n vehicles is investigated. This is done for four types of fleet configurations: (1) identical vehicles, (2) vehicles with identical fuel consumption rates but different fuel capacities, (3) vehicles which have the same fuel capacity but different fuel consumption rates, and (4) vehicles with both different fuel capacities and different consumption rates. For each of the first three configurations the optimal refueling policy that provides the maximal range is determined for a sequential refueling chain strategy. In such a strategy the last vehicle to be refueled is the next vehicle to transfer its fuel. Several mathematical programming formulations are given and their solutions determined in closed form. One of the major conclusions is that for an identical fleet the range of the farthest vehicle can be increased by at most 50% more than the operational range of a single vehicle. Moreover, this limit is reached very quickly with small values of n. The performance of the identical fleet configuration is further investigated for a refueling strategy involving a multiple-transfer refueling chain, stochastic vehicle failures, finite refueling times, and prepositioned fleets. No simple refueling ordering rules were found for the most general case (configuration 4). In addition, the case of vehicles with different fuel capacities is investigated under a budget constraint. The analysis provides several benchmarks or bounds for which more realistic structures may be compared. Some of the more complex structures left for future study are described.     

Comparative analysis of Arab Spring determinants

The Arab Spring, a pro-democracy uprising that has been sweeping through North Africa and the entire Arab world since 2010, has been described as a cataclysmic revolutionary wave that has left the overthrow of political regimes in its wake. Studies have comprehensively x-rayed the political and socio-economic circumstances that gave rise to the uprising. Apart from the impact of the uprising on political developments and democratic governance in the Arab world in particular and the world in general, the circumstances that resulted in the revolutions constitute empirical security implications for Nigeria. This is the focus of this article. Using the Ibrahim Index of African Governance (IIAG) and other selected indicators, this article draws a comparative analysis of the key factors that led to the uprisings in Egypt, Libya and Tunisia, pointing out areas of social and security tensions in Nigeria. Based on these findings, it points out the urgency of and imperative for security sector reforms in Nigeria.     

Optimal refueling strategies for a mixed-vehicle fleet

The problem treated here involves a mixed fleet of vehicles comprising two types of vehicles: K₁ tanker-type vehicles capable of refueling themselves and other vehicles, and K₂ nontanker vehicles incapable of refueling. The two groups of vehicles have different fuel capacities as well as different fuel consumption rates. The problem is to find the tanker refueling sequence that maximizes the range attainable for the K₂ nontankers. A tanker refueling sequence is a partition of the tankers into m subsets (2 ≤ m ≤ K₁). A given sequence of the partition provides a realization of the number of tankers participating in each successive refueling operation. The problem is first formulated as a nonlinear mixed-integer program and reduced to a linear program for a fixed sequence which may be solved by a simple recursive procedure. It is proven that a “unit refueling sequence” composed of one tanker refueling at each of K₁ refueling operations is optimal. In addition, the problem of designing the “minimum fleet” (minimum number of tankers) required for a given set of K₂ nontankers to attain maximal range is resolved. Also studied are extensions to the problem with a constraint on the number of refueling operations, different nontanker recovery base geometry, and refueling on the return trip.     

A dynamic-programming approach to continuous-review obsolescent inventory problems

Inventory models of modern production and service operations should take into consideration possible exogenous failures or the abrupt decline of demand resulting from obsolescence. This article analyzes continuous-review versions of the classical obsolescence problem in inventory theory. We assume a deterministic demand model and general continuous random times to obsolescence (“failure”). Using continuous dynamic programming, we investigate structural properties of the problem and propose explicit and workable solution techniques. These techniques apply to two fairly wide (and sometimes overlapping) classes of failure distributions: those which are increasing in failure rate and those which have finite support. Consequently, several specific failure processes in continuous time are given exact solutions. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 757–774, 1997