Tanka Nath Dhamala

Tribhuvan University · Central Department of Mathematics

The flow maximization problem being a leading problem in network optimization is widely studied with many applications. In this work, we find the maximum flow pulled out from the source and sent to the sink using the uncertainty theory. We develop a flow function to get maximum flow for the network having uncertain arc capacities and sufficient sto...

When uncertain and random arcs coexist with non-deterministic arc capacities in network optimization issues, chance space is used as the product of uncertain and probability space to arrive at the required answer. In order to determine the maximum flow in the hybrid network in this study, the intermediate storage at the vertices together with both...

Uncertainty theory examines the behaviors of uncertain parameters on networks. We consider uncertain and predetermined capacities, respectively, on arcs and intermediate vertices of an uncertain network. An objective is to find the non-conservative flow that is maximum at the destination and also at intermediate nodes with minimum cost. This goal i...

Probability theory in decision science fails in the absence of sufficient data. In these situations, uncertainty theory is applied to the problem-solving process, taking into account the opinions of the domain experts. In order to minimize the maximum flow carried by the evader, we describe an interdiction problem in an uncertain network with inter...

We consider two classical network flow problems. First, it is possible to store excess flow in the intermediate nodes to improve the total amount of flow that can be transported through the network. Second, we consider lossy network, where each arc has certain gain factor along with capacity and some portion of the flow is lost while traversing thr...

Contraflow means lane reversals on networks. In lane reversal reconfiguration, the capacity of the arc increases by reorienting arcs towards demand nodes, which maximizes the flow value and reduces the travel time. In this work, we survey the existing pieces of literature on single and multi-commodity contraflow problems with symmetric and asymmetr...

From different disasters such as earthquakes, flooding, landslides, hurricanes, blizzards, etc., thousands of people have lost their lives and millions of people have to be rescued each year. To reduce the losses from different disasters, appropriate emergency plannings are essential. The allocation of facility in an appropriate location of priorit...

This article is dedicated to the memory of Professor Urmila Pyakurel who passed away at an early age. It includes her short biography and also several testimonials from collaborators, sponsors, scholars and well-wishers whose involvements with her inspired and enriched both them and her and the story of her success. The description of the major sci...

Reversing the direction of traffic flow in necessary road segments is an important strategy to optimize the flow, especially, in an emergency evacuation. The configuration may, however, block the paths toward the source. Sometimes, it may be necessary to save a path for some facility movements from a specific node towards the source. We consider su...

During the transmission of several different commodities from respective sources to the sinks, there may be loss due to leakage, evaporation, or damage. The generalized multi-commodity flow problem on a lossy network deals with the transshipment of these commodities from the origin nodes to the destination nodes − not violating the capacity constra...

Network associated with the set of elements and linearly ordered subset of elements, known as paths, satisfying the switching property is an abstract network. Due to the switching property, flows crossing at intersections are diverted to the non-crossing sides. Each element of an abstract network is equipped with two types of integral capacities: o...

The tragic circumstances caused by natural or human-made (unexpected human or technological errors) hazard such as earthquakes, floods, glaciers, fires or industrial explosions causing significant physical damages, loss of lives or destruction of environment as well as economic and social life of people are known as disasters. Planned evacuation is...

Discrete and continuous time dynamic flow problems have been studied for decades. The purpose of the network flow problem is to find the maximum flow that can be sent from the source node to the destination node. Our aim is to review the general class of continuous time dynamic flow problems. We discuss about static cut and generalized dynamic cut,...

An important aspect of evacuation planning is to save human population by sending the people in dangerous areas (sources) to the safe places (sinks). Optimization models for evacuation planning focus on regulating the tra_c ow in urban road networks so as to maximize the number of evacuees reaching the safe places or to minimize the evacuation time...

One of the challenges in operations research is to route numerous commodities from particular supply locations to the corresponding demand points across the lanes of a network infrastructure while maintaining capacity restrictions. The quickest multi-commodity flow problem would be one of those that reduces the time it takes to complete the process...

The abstract network is a generalization of the classical network which is associated with the set of elements and linearly ordered subset of elements, known as paths, that satisfy switching property. Each element is equipped with an integral capacity of two types, movement capacity which transships the flow from the element and storage capacity wh...

Continuous-time dynamic flow problems are one of the most important aspects of evacuation planning with a given capacity and travel time on the network. The objective of the problem is to send the maximum number of evacuees from the given source to the sink as soon as possible. The continuous-time dynamic solution approach to this problem decreases...

A maximum dynamic multicommodity flow problem concerns with the transportation of several different commodities through the specific source-sink path of an underlying capacity network with the objective of maximizing the sum of commodity flows within a given time horizon. Motivated by the uneven road condition of transportation network topology, we...

Multi-commodity flow problems concerned with the transshipment of more than one commodity from respective sources to the corresponding sinks without violating the capacity constraints on the arcs. If the objective of the problem is to send the maximum amount of flow within a given time horizon, then it becomes the maximum flow problem. In multi-com...

The quickest contraflow in a single-source-single-sink network is a dynamic flow that minimizes the time horizon of a given flow value at the source to be sent to the sink allowing arc reversals. Because of the arc reversals, for a sufficiently large value of the flow, the residual capacity of all or most of the paths towards the source, from a giv...

The quickest contraflow in a single-source-single-sink network is a dynamic flow that minimizes the time horizon of a given flow value at the source to be sent to the sink allowing arc reversals. Because of the arc reversals, for a sufficiently large value of the flow, the residual capacity of all or most of the paths towards the source, from a giv...

The quickest transshipment of the evacuees in an integrated evacuation network topology depends upon the evacuee arrival pattern in the collection network and their better assignment in the assignment network with appropriate traffic route guidance, destination optimization, and an optimal route. In this work, the quickest transshipment aspect in a...

e multicommodity flow problem deals with the transshipment of more than one commodity from respective sources to corresponding sinks without violating the capacity constraints. Due to the capacity constraints, flows out from the sources may not reach their sinks, and so, the storage of excess flows at intermediate nodes plays an important role in t...

In dynamic network flows, when some commodities move from one place to another, time taken by them to traverse the path are taken into account, unlike the static flows. Time being continuous entity, network flow problems are modeled in its continuous setting to get more realistic solution to the optimization problems. Rather, it can also be discret...

In many real-world situations, there are numerous network optimization problems where the network attributes depend on time. In this paper, we consider single-source single-sink discrete-time dynamic network flow problems. We review some algorithms for the quickest flow problems in two environments (to the network attributes): time-invariant and ti...

The maximum dynamic contraflow problem in transportation networks seeks to maximize the flow from a source to a sink within a given time horizon with a possibility of arc reversals. This may result into blockage of paths of desired length from some node of the network towards the source. In some cases such as the evacuation planning, we may require...

The contraflow technique has been extensively used to evacuate people in disasters situation. By flipping the orientation of necessary road segments, the flow value increases, and the evacuation time decreases significantly. Contraflow problems with asymmetric capacity and symmetric transit time on arcs have polynomial-time solutions. But in uneven...

In a transportation network such as an evacuation planning, if we transmit the people or goods from the dangerous zones to the safety places, there are chances of loss due to death, leakage or damage. To address this issue, the generalized network flow model incorporates a gain factor on each arc, which makes it different from the classical network...

Motivated by applications in evacuation planning, we consider a problem of optimizing flow with arc reversals in which the transit time depends on the orientation of the arc. In the considered problems, the transit time on an arc may change when it is reversed, contrary to the problems considered in the existing literature. Extending the existing i...

Evacuation planning problem deals with sending the maximum number of evacuees from the danger zone to the safe zone in minimum time as eciently as possible. The dynamic network flow models for various evacuation network topology have been found suitable for the solution of such a problem. Bus based evacuation planning problem (BEPP), as an importan...

Multi-commodity flow problem appears when several distinct commodities are shipped from supply nodes to the demand nodes through a network without violating the capacity constraints. The quickest multi-commodity flow problem deals with the minimization of time satisfying given demand. Ingeneral, the quickest multi-commodity flow problems are comput...

Prioritization is the process of deciding the relative importance or urgency of things or objects. It helps to focus on the objectives and goals in an efficient way. Prioritized flow problems are applicable for large scale disaster management problems. In this work, we introduce the priority based multi-commodity flow problem and develop a mathemat...

In this paper, we study the quickest flow problem. The objective is to determine the minimum time to transmit a given flow value through a given network. Firstly, the time expanded network is used to find maximum dynamic flow for each fixed time bound. Secondly, the time bounds are tightened by using improved binary search algorithm, including Regu...

The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow p...

Routing of more than one different commodity from specific origin nodes to the corresponding destination nodes through the arcs of an underlying network respecting the capacity constraints is one of the main problems in operational research. Among them, the quickest multi-commodity flow problem concerns with minimization of time taken to complete t...

The evacuation planning problem can be viewed as different variants of dynamic flow maximization and time minimization problems. An optimal solution to the latter problem sends a given amount of flow from disaster zones to safe zones in minimum time. We solve this problem on an embedded integrated network of a prioritized primary and a bus-routed s...

Dynamic network flow problems have wide applications in evacuation planning. From a given subset of arcs in a directed network, choosing the suitable arcs for facility location with a given objective is very important in the optimization of flow in emergency cases. Because of the decrease in capacity of an arc by placing a facility in it, there may...

Traffic route guidance, destination optimization, and optimal route choice are some of the approaches to accelerate the evacuation planning process. Their effectiveness depends upon the evacuee arrival patterns at the pickup locations and their appropriate assignment to transit-vehicles in the network. Here, the integrated evacuation network topolo...

Many large-scale natural and human-created disasters have drawn the attention of researchers towards the solutions of evacuation planning problems and their applications. The main focus of these solution strategies is to protect the life, property, and their surroundings during the disasters. With limited resources, it is not an easy task to develo...

The challenges in evacuation planning have been vital because of rapid disasters and limited road capacity. Contraflow strategy is very effective and widely accepted approach for the optimal use of available road network in evacuation management that increases the outward road capacities from the disastrous areas towards the safe destinations. Mode...

Contraflow technique has gained a considerable focus in evacuation planning research over the past several years. In this work, we design efficient algorithms to solve the maximum, lex-maximum, earliest arrival, and quickest dynamic flow problems having constant attributes and their generalizations with partial contraflow reconfiguration in the con...

Despite of implicit flow conservation on every arc of traditional network flow model, the generalized network flow model assumes the proportional and symmetric loss factor on each arc. This paper considers two terminal lossy networks specifying the portion of flow entering an arc at its tail node that reaches to its head node. We studied the genera...

The large scale calamities caused by natural or human-created disasters are the challenging issues to protect the life and their surroundings. It is a complex task to develop the significant and universally accepted solution strategy for handling these issues. Appropriate facility locations and transportation facilities are essential components for...

People have unpleasant experience of driving through congested road network of urban areas, where transit time is not constant but flow-dependent. Network flow over time with flow-dependent transit times is more realistic than flow over time with fixed transit time on arcs which is an active area of research from last two decades. In traffic assign...

The field of evacuation planning is a very fertile research area of mathematical sciences and operational research in these days. A large number of scientists from the field of mathematical sciences, operational research, management science, engineering and even from social sciences are involved in solving the challenging issues raised form differe...

The very unfortunate natural and man-created disasters are increasing in current world scenarios and they are unavoidable because of today's complex environment. A lot of operational research models have been developed to deal with these issues from the prospective of preparedness, planning, response and recovery depending on the nature of disaster...

Mathematical modeling of evacuation planning problems focus on sending evacuees from danger areas (sources) to safe places (sinks). Contraflow strategy, i.e. reversing the direction of usual traffic flow towards the sinks, is an effective strategy in such cases, to increase the outbound capacity of the road segments so that there is an increase in...

A minimization on the occurrence of frequent natural or human created disasters alone cannot supplement a research potential of today's very complex but unavoidable emergency planning issues. efficiently saving the people and property at maximum in minimum time a is a quite challenging planning problem in emergencies. Highest attention has been mad...

Network flow over time is an important area for the researcher relating to the traffic assignment problem. Transmission times of the vehicles directly depend on the number of vehicles entering the road. Flow over time with fixed transit times can be solved by using classical (static) flow algorithms in a corresponding time expanded network which is...

Network flow models have been widely applied for evacuation planning, which involves moving people from risk areas (sources) to safe places (sinks) using some means of transportation, to optimize traffic flow in urban road networks. The decisions related to the locations of the sinks are also important to maximize the number of evacuees or minimize...

The abstract flow model is the generalization of network flow model which deals with the flow paths (routes) satisfying the switching property. Contraflow model increases the flow value by reversing the required arc directions from the sources to the sinks. In this paper, we integrate the concepts of abstract flow and contraflow to introduce abstra...

In the context of growing number of natural or man-made disasters, operations research methodologies are imperative for optimal and equitable use of resources available for saving life and relief supports. On the PPRR risk management model, preparedness or planning is most important in unavoidable disasters, as most of the damages are due to lack o...

In the last decades, research on emergency traffic management has received high attention from the operations research community and many pioneer researchers have established it as one of the most fertile research areas. We consider the computationally hard flows over time problems from wider perspective including flow/time dependent attributes (dy...

The FlowLoc problem allocates the facilities in the network with minimum flow loss. Contraflow is widely accepted solution approach for evacuation planning as it maximizes the outbound capacities of roads by reversing the required road directions from risk areas to safe places. In this work, the network facility location and the contraflow approach...

Contraflow evacuation planning is the process of shifting maximum number of evacuees from the dangerous areas to the safer places with arc reversals capability as quickly and efficiently as possible. We introduce the partial contraflow approach with the inflow dependent and load dependent transit times. In both cases, we present efficient algorithm...

Because of rapidly increasing number of natural and human-created disasters worldwide, researchers in the field of emergency management are highly motivated towards emergency planning and the field is being quite emerging. The operations research modeling has been the most effective approach in addressing these issues, at least partially. Although...

When facilities are to be placed on the arcs of an evacuation network, it is imperative to find the appropriate arcs to place the facilities to minimize the effect of the reduction in arc capacities in the efficiency of evacuation. In this work, we introduce quickest FlowLoc problem to identify the optimal arcs to place emergency facilities so that...

Dissimilar to conventional static flow problem, this research studies network flows in relation to time. Any one caught up in a traffic jam would know that the existing premise of flow overtime with constant transit times on the arcs cannot access the real life road traffic. Challenges with flows overtime and constant transit times can be rephrased...

Network flow over time is an important area for the researcher relating to the traffic assignment problem. Transmission time of the vehicles directly depends on the number of vehicles entering the road. Flow over time with fixed transit times can be solved by using classical (static) flow algorithms in a corresponding time expanded network which is...

flow model deals with the flow paths (routes) that satisfy the switching property. Contraflow is a widely accepted solution approach that increases the flow and decreases the evacuation time making the traffic smooth during evacuation by reversing the required road directions from the risk areas to the safe places. In this paper, we integrate the c...

flow model deals with the flow paths (routes) that satisfy the switching property. Contraflow is a widely accepted solution approach that increases the flow and decreases the evacuation time making the traffic smooth during evacuation by reversing the required road directions from the risk areas to the safe places. In this paper, we integrate the c...

Impacts of the threats mainly caused by increasing number of natural and men-created disasters all over the world have been extremely costly. Many nations are much affected by such, including Nepal suffered by frequent devastating earthquake kills and damages. The OR models and solution techniques, for saving and serving the life and property, have...

Increasing number of complex traffic networks and disasters today has brought difficulty in managing the rush hours traffic as well as the large events in urban areas. The optimal use of the vehicles and their assignments to the appropriate shelters from the disastrous zones are highly complicated in emergency situations. The maximum efficiency and...

The optimization models and algorithms with their implementations on flow over time problems have been emerging field of research because of largely increasing human-created and natural disasters worldwide. For an optimal use of transportation network to shift affected people and normalize the disastrous situation as quickly and efficiently as poss...

A productive research in the emerging field of disaster management plays a quite important role in relaxing this disastrous advanced society. The planning problem of saving affected areas and normalizing the situation after any kind of disasters is very challenging. For the optimal use of available road network, the contraflow technique increases t...

The research in evacuation planning has been very much motivated due to the rapidly increased number of disasters world-wide. It is the process of shifting maximum number of evacuees from the disastrous areas to the safe destinations as quickly and efficiently as possible. The contraflow model allows the arc reversals that increase the outbound roa...

Increasing disasters worldwide have drawn the attention of researchers to the emerging field of disaster management. We consider the key models on transportation and planning networks for maximizing the flow and minimizing the cost within the limited time horizon in emergencies. Although there are varieties of models and solution techniques in evac...

The dynamic flow optimization problems covering wider spectrum of modeling aspects from diversified field of mathematical sciences play significant roles in dealing with real-life problems caused by natural or human-created disasters in today’s complex disastrous world. In addition, the global optimal strategies, like logistic supports in emergenci...

Due to the different disasters, the challenges of emergency management have been increased day by day. After disasters, efficient evacuation transportation is required for the evacuation planning. We have limited time to evacuate the evacuees from the dangerous state (source) to safe place (sink). Thus, it is necessary to evacuate as many evacuees...

Due to the different disasters, the challenges of emergency management have been increased day by day. After disasters, efficient evacuation transportation is required for the evacuation planning. We have limited time to evacuate the evacuees from the dangerous state (source) to safe place (sink). Thus, it is necessary to evacuate as many evacuees...

Transportation network models within the framework of operations research have been established as one of the emerging field of research frontiers in today's very disastrous life and dense traffic system. The discrete as well as continuous flow over time models have been widely considered by social, engineering and applied scientists with wide vari...

Due to the increasing number of natural or man-made disasters, the application of operations research methods in evacuation planning has seen a rising interest in the research community. From the beginning, evacuation planning has been highly focused on car-based evacuation. Recently, also the evacuation of transit depended evacuees with the help o...

The research on evacuation planning problem is promoted by the very challenging emergency issues due to large scale natural or man-created disasters. It is the process of shifting the maximum number of evacuees from the disastrous areas to the safe destinations as quickly and efficiently as possible. Contraflow is a widely accepted model for good s...

After different disasters the evacuation planning support to remove the residence from accidental areas to safe destinations. Contraflow solutions minimize the congestion and make the traffic smooth during evacuation by reversing the required road directions from risk areas to safe places. Mathematical models and solution approaches appear for the...

Efficient evacuation transportation is important for the evacuation planning since one needs to evacuate as many evacuees as possible within the limited time. Contraflow problem, which increases the outbound capacity of the transportation network by reversing the direction, has been important for efficient evacuation. Various aspects of the contraf...