A polynomial-time algorithm to solve the large scale of airplane refueling problem

Airplane refueling problem is a nonlinear combinatorial optimization problem with $n!$ feasible feasible solutions. Given a fleet of $n$ airplanes with mid-air refueling technique, each airplane has a specific fuel capacity and fuel consumption rate. The fleet starts to fly together to a same target and during the trip each airplane could instantaneously refuel to other airplanes and then be dropped out. The question is how to find the best refueling policy to make the last remaining airplane travels the farthest. To solve the large scale of the airplane refueling problem in polynomial-time, we propose the definition of the sequential feasible solution by employing the data structural properties of the airplane refueling problem. We prove that if an airplane refueling problem has feasible solutions, it must have sequential feasible solutions, and its optimal feasible solution must be the optimal sequential feasible solution. Then we present the sequential search algorithm which has a computational complexity that depends on the number of sequential feasible solutions referred to $Q_n$, which is proved to be upper bounded by $2^{n-2}$ as an exponential bound that lacks of applicability on larger input for worst case. Therefore we investigate the complexity behavior of the sequential search algorithm from dynamic perspective, and find out that $Q_n$ is bounded by $\frac{m^2}{n}C_n^m$ when the input $n$ is greater than $2m$. Here $m$ is a constant and $2m$ is regarded as the "inflection point" of the complexity of the sequential search algorithm from exponential-time to polynomial-time. Moreover, we build an efficient computability scheme according to which we shall predict the specific complexity of the sequential search algorithm to choose a proper algorithm considering the available running time for decision makers or users.Comment: 18 pages, 2 figure

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques

Optimizing Vaccine Supply Chains with Drones in Less-Developed Regions: Multimodal Vaccine Distribution in Vanuatu

In recent years, many less-developed countries (LDCs) have been exploring new opportunities provided by drones, such as the capability to deliver items with minimal infrastructure, fast speed, and relatively low cost, especially for high value-added products such as lifesaving medical products and vaccines. This dissertation optimizes the delivery network and operations for routine childhood vaccines in LDCs. It analyzes two important problems using mathematical programming, with an application in the South Pacific nation of Vanuatu. The first problem is to optimize the nation-wide multi-modal vaccine supply chain with drones to deliver vaccines from the national depot to all health zones in an LDC. The second problem is to optimize vaccine delivery using drones within a single health zone while considering the synchronization of drone deliveries with health worker outreach trips to remote clinics. Both problems consider a cold chain time limit to ensure vaccine viability. The two research problems together provide a holistic solution at the strategic and operational levels for the vaccine supply chain network in LDCs. Results from the first problem show that drones can reduce cost and delivery time simultaneously by replacing expensive and/or slow modes. The use of large drones is shown to save up to 60% of the delivery cost and the use of small drones is shown to save up to 43% of the delivery cost. The research highlights the tradeoff between delivery cost and service, with tighter cold chain limits providing faster delivery to health zones at the expense of added cost. Results from the second problem show that adding drones to delivery plans can save up to 40% of the delivery cost and improve the service time simultaneously by resupplying vaccines when the cold chain and payload limit of health workers are reached. This research contributes to both literature and practice. It develops innovative methodologies to model drone paths with relay stations and to optimize synchronized multi-stop drone trips with health worker trips. The models are tested with real-world data for an island nation (Vanuatu), which provides data for a geographic setting new to the literature on drone delivery and vaccine distribution

Aerial health care system for remote areas and under-developed regions

Aeromedical rescue has been around for more than 100 years. They are being implemented in more and more countries or areas of the world and this is a consequence of the constant population growth. This growth affects both urban and rural areas differently. The latter receive less variety of health aid, due to a lack of hospitals and specialized doctors or because they do not have it directly. Public or private, there are already many organizations in charge of providing these Medevac services, which includes the rescue of a patient in a medical emergency, providing medical care to this patient during the journey until he/she arrives at the hospital. It has been proven that the implementation of these services reduces the mortality rate by shortening the emergency response time and stabilizing the patient during transfer. However, there are still many areas without this medical coverage and the organizations that offer these services are very different from one another. They can be public or private organizations, operate in urban or remote areas, have a fleet and a specific base, etc. This is the origin of the proposal to continue researching this subject by means of this final thesis: Aerial Health Care system for remote areas and under-developed regions. One of the objectives is to seek and contrast information to understand the differences and similarities between the different types of air medical services: what services are offered, what crew is needed, the special equipment carried by the fleet and the type of air bases used. The aim is to analyze the aeronautical part of the operation, the requirements and needs that must be met for the rescues to be a success. Finally, the last objective is to be able to carry out a preliminary study simulating the implementation of an air medical service in an area that requires this assistance.Objectius de Desenvolupament Sostenible::3 - Salut i BenestarObjectius de Desenvolupament Sostenible::10 - Reducció de les Desigualtat

Optimization of transportation requirements in the deployment of military units

Cataloged from PDF version of article.We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which no analytical models are existent. In this study, we define the problem in detail and analyze it with respect to the academic literature. We propose three mixed integer programming models with the objectives of cost, lateness (the difference between the arrival time of a unit and its earliest allowable arrival time at its destination), and tardiness (the difference between the arrival time of a unit and its latest arrival time at its destination) minimization to solve the problem. The cost-minimization model minimizes total transportation cost of a deployment and is of use for investment decisions in transportation resources during peacetime and for deployment planning in cases where the operation is not imminent and there is enough time to do deliberate planning that takes costs into account. The lateness and tardiness minimization models are of min-max type and are of use when quick deployment is of utmost concern. The lateness minimization model is for cases when the given fleet of transportation assets is sufficient to deploy units within their allowable time windows and the tardiness minimization model is for cases when the given fleet is not sufficient. We propose a solution methodology for solving all three models. The solution methodology involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branchand-bound. The solution times for intermediate sized problems are around one hour at maximum for cost and lateness minimization models and around two hours for the tardiness minimization model. Producing a suboptimal feasible solution based on trial and error methods for a problem of the same size takes about a week in the current practice in the Turkish Armed Forces. We also propose a heuristic that is essentially based on solving the models incrementally rather than at one step. Computational results show that the heuristic can be used to find good feasible solutions for the models. We conclude the study with comments on how to use the models in the realworld.Akgün, İbrahimPh.D