Showing papers in "Opsearch in 2012"

The single row facility layout problem: state of the art

Abstract: The single row facility layout problem (SRFLP) is a NP-hard problem concerned with the arrangement of facilities of given lengths on a line so as to minimize the weighted sum of the distances between all the pairs of facilities. The SRFLP and its special cases often arise while modeling a large variety of applications. It has been actively researched until the mid-nineties, and then again since 2005. Interestingly, research on many aspects of this problem is still in the initial stages, and hence the SRFLP is an interesting problem to work on. In this paper, we review the literature on the SRFLP and comment on its relationship with other layout problems. We then provide an overview of different formulations of the problem that appear in the literature. We provide exact and heuristic approaches that have been used to solve SRFLPs, and also present details about the benchmark instances widely used in the literature. We finally point out research gaps and promising directions for future research on this problem.

Reinforcement learning: exploration–exploitation dilemma in multi-agent foraging task

Abstract: The exploration–exploitation dilemma has been an unresolved issue within the framework of multi-agent reinforcement learning. The agents have to explore in order to improve the state which potentially yields higher rewards in the future or exploit the state that yields the highest reward based on the existing knowledge. Pure exploration degrades the agent’s learning but increases the flexibility of the agent to adapt in a dynamic environment. On the other hand pure exploitation drives the agent’s learning process to locally optimal solutions. Various learning policies have been studied to address this issue. This paper presents critical experimental results on a number of learning policies reported in the open literatures. Learning policies namely greedy, ξ-greedy, Boltzmann Distribution (BD), Simulated Annealing (SA), Probability Matching (PM) and Optimistic Initial Values (OIV) are implemented to study on their performances on a multi-agent foraging-task modelled. Based on the numerical results that were obtained, the performances of the learning policies are discussed.

Mixed integer linear programming model for multi-commodity multi-depot inventory routing problem

Abstract: Multi-Commodity, Multi-Depot Inventory Routing Problem (MCMDIRP) is relevant to vendors who have to make decisions about timing of delivery, size of shipment and routing for multiple commodities from multiple manufacturing plants to warehouses in a Vendor Managed Inventory (VMI) scenario. We propose a Mixed Integer Linear Program (MILP) for the MCMDIRP. The model is tested on a real life case study and a set of test data sets.

Multi criteria genetic algorithm for optimal blending of coal

Abstract: The present paper deals with the optimal planning for blending of coal of different grades for beneficiation of coal with a view to satisfy the requirements of the end users with desired specifications. The input specifications are known whereas aspiration levels of the characteristics washed coal have been specified. Beneficiation of coal refers to the production of wash coal from raw coal with the help of some suitable beneficiation/coal washing technologies. The processed coal is used by the different steel plants to serve their purpose during the manufacturing process of steel. The aim is to fix the level of the raw coal samples from different coal seams to be used/fed for the beneficiation to meet the desired target of the coal blending indicators, yield to maximum extent and to restrict the input cost of raw coal to be fed for beneficiation. The problem is considered as multi criteria decision making problem and solved using multi objective genetic algorithm. A case study from a regional coal company situated at Jharia coalfield, India has been made and solved using the proposed model.

A new approach for ranking of candidates in voting systems

Abstract: This paper proposes a new approach to allow the voters to express their preferences on a set of candidates in ranked voting systems. This approach assumes that the votes of all voters have not equal importance and there is a priority among voters. Here, voters are classified into several groups in terms of their priorities that the vote of a higher category has a greater important than that of lower category. Then, the existing ranking methods are extended to discriminate efficient candidates in our proposed model. Moreover, a new criterion to obtain a total ranking by evaluating different ranking methods based on classical voting system is given. Finally the proposed method is illustrated with an application example and shows to be effective and practical.

Time dependent analysis of an M/M/ 1 /N queue with catastrophes and a repairable server

Abstract: In this paper, we consider a single server Markovian queueing system with a finite buffer. In addition to a Poisson stream of positive arrivals we assume that there is a also a Poisson stream of negative arrivals into the system. These negative arrivals which may be called as catastrophes may occur at any instant of time, whether the server is idle or busy. The time dependent performance measures and the busy period of the system are discussed. The corresponding steady state results are derived. We present a few numerical examples to illustrate the behavior of the time dependent probabilities, the time dependent expected system size and the time dependent variance of the system size distribution.

Multiobjective integer nonlinear fractional programming problem: A cutting plane approach

Abstract: The present paper discusses a multiobjective integer nonlinear fractional programming problem based on cutting plane technique. The methodology discussed is such that it finds all the nondominated t-tuples of the multiobjective nonlinear fractional programming problem by exploiting the quasimonotone character of the nonlinear fractional functions involved. The cut discussed in the present paper scans and truncates a portion of the feasible region in such way that once truncated, it does not reappear, thereby leading to the convergence of the proposed algorithm in finite number of steps. Further, the quasimonotone character of the objective functions involved enables us to find all the nondominated t-tuples at extreme points of the truncated feasible region obtained after repeated applications of the cut developed in the paper.

An economic production lot size model for product life cycle (maturity stage) with defective items with shortages

Abstract: A product life cycle is the life span of a product which the period begins with initial product specification and ends with the withdrawal from the market of both the product and its support. A product life cycle can be divided into several stages characterized by the revenue generated by the product. The purpose of this paper is to investigate the optimal production lot size and total cost during the Product Life Cycle which consists of introduction, growth, maturity and decline stages. The defective rate is considered as a variable of known proportions. The relevant model is built and it is also solved. Necessary and sufficient conditions for a unique and global optimal solution are derived. A numerical example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.

TOPSIS and AHP techniques for selecting the most efficient marine container yard gantry crane

Abstract: Increasing global usage of containerised cargo in maritime trade imposes heavy traffic on both of the quayside and landside marine container terminals. Untangling this problem, terminal operators have to choose the most efficient operating system in their terminals. This study analyses the concept of Multiple Attribute Decision Making (MADM) for selecting the most efficient yard gantry crane in marine container terminals among three alternatives including Straddle Carrier (SC), Rail Mounted Gantry Crane (RMG), and Rubber Tyred Gantry Crane (RTG). Analytical Hierarchy Process (AHP) and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) are used as decision making tools during this research. The paper also provides an accurate comparison on the results of AHP and TOPSIS techniques.

Application of Petri nets for systems modelling and analysis

Abstract: Petri nets are powerful graphical and mathematical modelling tool for describing and studying various types of system. Petri nets can be used not only to express the static behaviours of logic operation such as logical relations between system components, but also to study the dynamic behaviours such as operating sequence, workflow, maintenance process, failure occurrence and concurrent activities of the system Petri net model has been developed for LHD motor-overheating problem. Petri nets have been used to identify minimum cut sets finding, marking transfer, firing sequence, reachability tree and dynamic behaviour of machine failure. A model is formulated for fault detection and isolation.

Neighborhood reduction strategy for tabu search implementation in asymmetric traveling salesman problem

Abstract: The Traveling Salesman Problem (TSP) is one of the most widely discussed problems in combinatorial optimization. It has many practical applications in fields of distribution and logistics management, scheduling problems etc. Since these problems are hard, in addition to exact algorithms, research has focused on heuristic techniques to solve TSPs. Computational time is a major concern while solving large TSPs. This problem intensifies further if the graph becomes asymmetric (ATSP). Metaheuristics like tabu search are widely used to find a reasonably good tour fast. Given the practical relevance of ATSPs the lack of literature on it is surprising. The primary objective of our work is to implement tabu search for large ATSPs to obtain good tours in reasonable time. To do that, we make the underlying graph sparse by developing an elite tour based preprocessing scheme. Tabu search is implemented on this reduced graph which results in a reduction of computational time. We also create diversified initial tours suitable for multi-start tabu search in this process. We present our computational experiences both on randomly generated instances and benchmark instances.

Markov decision processes in service facilities holding perishable inventory

Abstract: In this article, we consider a single server queueing system with finite waiting space N (including one customer in service) and an inventory is attached with the maximum capacity S. The arrival of customer at the system is according to independent Poisson Processes with rate λ through a single channel. The service time is exponentially distributed with mean 1/μ and the item in stock has exponential life time with perishable rate γ(>0). When we place the order due to the demand of the customers, we assume that the lead time of procurement of item is exponentially distributed with parameter δ. Our object is to make a decision at each state of the system to operate the server by minimizing the entire service cost. The problem is modelled as a Markov decision problem by using the value iteration algorithm to obtain the minimal average cost of the service. The unique equilibrium probability distributions {p(q, i)} is also obtained by using Matrix geometric form in which the two dimensional state space contains infinite queue length and finite capacity of inventory. Numerical examples are provided to obtain the optimal average cost.

On constrained optimization by interval arithmetic and interval order relations

Abstract: The goal of this article is to develop an optimization technique based on the splitting criterion of search region into several equal and disjoint subregions for solving the constrained optimization problems by finite interval arithmetic and interval order relations in the context of a decision maker’s point of view. This method has been applied for solving some benchmark test problems taken from the literature and the results are compared with those obtained from several existing different heuristic or meta-heuristic methods.

Two-stage stochastic programming problems involving interval discrete random variables

Abstract: In this paper, we propose a two-stage stochastic linear programming problem considering some of the left hand side and right hand side of linear constraints parameters as interval discrete random variables with known probability distribution and rest of the parameters are precisely known. Both the randomness and discrete intervals are simultaneously considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are studied in two-stage stochastic programming. To solve the stated problem, first we remove the randomness from the problem and formulate an equivalent deterministic linear programming model with interval coefficients. Then the deterministic model is solved using the solution procedure of linear programming with interval coefficients. We obtain the upper bound and lower bound of the objective function as the best and the worst value respectively. It highlights the possible risk involved in the decision making process. A numerical example is presented to demonstrate the usefulness of the proposed methodology.

A deterministic inventory model with permissible delay in payment and price discount on backorders

Abstract: In this paper we study a deterministic inventory model with shortages, where only a fraction of the unmet demand is backlogged, and the inventory manager offers a discount on it. Conditions of permissible delay in payments are also taken into account. Numerical examples are cited to illustrate the model.

A diversification operator for genetic algorithms

Abstract: Conventional genetic algorithms suffer from a dependence on the initial generation used by the algorithm. In case the generation consists of solutions which are not close enough to a global optimum but some of which are close to a relatively good local optimum, the algorithm is often guided to converge to the local optimum. In this paper, we provide a method which allows a genetic algorithm to search the solution space more effectively, and increases its chance to attain a global optimum. Our computational experience demonstrates the superiority of our method over conventional genetic algorithms.

An inventory model for product life cycle with maturity stage and defective items

Abstract: A product life cycle is the life span of a product which the period begins with initial product specification and ends with the withdrawal from the market of both the product and its support. A product life cycle can be divided into several stages characterized by the revenue generated by the product. This paper deals with an inventory model for Product Life Cycle with defective items for single manufacturing system which consists of introduction, growth, maturity and decline stages. The defective rate is considered as a variable of known proportions. The main objective is to minimize the total net inventory cost and optimal quantity in product life cycle. The relevant model is built and solved. Necessary and sufficient conditions for a unique and global optimal solution are derived. A numerical example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.

Observations on some heuristic methods for the capacitated facility location problem

Abstract: We consider a few types of heuristics, namely, add-drop-interchange, Lagrangean relaxation-based and random rounding heuristics for the capacitated facility location problem. Some instances of the problem are constructed and performance, with respect to such instances, of the heuristics is studied. It is observed that, performance of the heuristics is often not satisfactory. The instances presented in this article may be used as some critical instances to test heuristics for the problem.

Multi-period optimal defective production problem with variable preparation time

Abstract: In this paper, a multi-period optimal production control problem with variable preparation time is formulated and solved. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is linearly stock dependent. Defective rate is taken in four forms namely constant, fuzzy, random and fuzzy-random. The presented preparation time is assumed to be deterministic and treated as a variable. Production cost and set-up cost depend on preparation time. Here, preparation time influences the production cost negatively and set-up cost positively. The model is formulated as an optimal control problem and solved with the help of Calculus method and Generalised Reduced Gradient (GRG) technique. The optimum results are obtained and presented in tabular forms and graphically.

Diesel locomotive fueling problem (LFP) in railroad operations

Abstract: About 75 % of the world’s railroads operate with diesel fuel. Even though European railroads rely on electric traction to a large extent, US railroads rely mostly on diesel fuel (100 % of US freight is hauled by diesel locomotives). Like in other industries there is intense competition to keep costs low; and in railroad operations based on diesel locomotives, the cost of fuel and its delivery is the major component of the overall cost. Since the cost of fuel is highly location dependent (due to local taxes and transportation costs between supply and demand points), locomotive fueling problem discussed in this paper is a critical problem in railroad operations. Given: the set of yards, the set of trains to operate, the locomotive assignments to trains, and the fuel cost and capacity data; this problem deals with finding the fueling plan for the various trains to minimize the total cost of fueling the locomotives. We describe three different algorithms, two based on greedy method and one using MIP model, that we used to solve this problem and highlight the summary of solutions obtained by each of them for comparisons of these algorithms.

A new approach for solving the network problems

Abstract: This study aims to optimize the number of nodes and arcs in a constructed network employing a given criteria. For this, we subject the constructed network using the methods like Shortest Path (SP), Critical Path (CP) and Max-Flow (MF) between any pair of nodes. A set of iterative algorithms have been generated using matrix operations to meet the above requirement, which is named as Pandit’s algorithm. The equivalent algorithms for SP, CP and MF are hereby represented as Pandit’s Mini-additive, Maxi-additive and Max-min algorithms respectively. The generated algorithms take less number of iterations when compared to the established methods. The proposed new algorithms are shown with suitable numerical examples and discuss their merits over the established methods. These new algorithms take less computational time and hence suggested for solving the bulk networks such as transportation GIS, telecommunication networks, information systems, project scheduling etc.

Multi-item two storage inventory models for breakable items with fuzzy cost and resources based on different defuzzification techniques

Abstract: This paper develops multi-item Economic Order Quantity (EOQ) inventory models for breakable units with stock and selling price dependent demand under imprecise space and budget constraints with two storage facilities. There are one rented warehouse called own warehouse (OW) at the market place and another rented warehouse (RW) at a little distance away from the market place. The sale is conducted from OW and the sold items are replaced continuously by the items at RW. The units at RW are damaged due to the accumulated stress of the stocked items kept in stacked form and the damaged function i.e. rate of breakability per unit time be linear function of current stock level. Here shortages are not allowed. Normally inventory models involve imprecise parameters or resources like imprecise inventory costs, fuzzy storage area, fuzzy budget allocation etc. Here, main emphasis has been given on the different defuzzification techniques such as min operator method, average operator method, two-phase approach and compromise technique for the fuzzy programming problems having fuzzy technical coefficients and fuzzy resources and the application of these techniques to a two-storage inventory problems for breakable items. Two two-warehouse fuzzy inventory models have been formulated as maximization problems with the above assumptions and solved using various defuzzification techniques and a gradient based non-linear programming technique - Generalised Reduced Gradient (GRG) method. The models are illustrated with numerical examples. Results from different techniques are graphically compared and some sensitivity analyses have been presented.

Flow constrained minimum cost flow problem

Abstract: The paper deals with the uncapacitated minimum cost flow problems subject to additional flow constraints whether or not the sum of node capacities is zero. This is a generalization and extension of transportation problems with restrictions on total flow value. The relationship between the desired flow value and the sum of node capacities of source(s) and sink(s) gives rise to the different set of problems. Mathematical models for the various cases are formulated. For each case an equivalent standard minimum cost flow problem (MCFP) is formulated whose optimal solution provides the optimal solution to the original flow constrained problem. The paper not only extends the similar concept of transportation problem to the case of MCFP but also suggests an alternative equivalent formulation. Solving the alternative problem is computationally better in comparison to the formulation analogous to the transportation case. A broad computational comparison is carried out at the end.

Location models with stochastic demand points

Abstract: This paper presents two approaches for solving both the minimax and minisum location problems and as well as a bi-objective location problem. The bi-objective location problem is a combination of both minimax and minisum location problems with recti-linear distances and randomly distributed destinations. Wesolowsky. G.O. [Journal of Regional Science 18: 53–60, 1977] has considered the stochastic extension of Weber problem with rectilinear distance norm and suggested some iterative method after dividing the problem into two parts, one for the X coordinates and other for the Y coordinates, where these co-ordinates may be correlated. In the present investigation exact approaches for both Minisum and Minimax objectives with randomly distributed destinations have been considered separately with both bi-variate exponential and bi-variate uniform distributions and formulated as a non-linear programming problem. Also the area restriction concept has been introduced so that the facility to be located should be within certain restricted area. The consideration of area restrictions has been implemented by incorporating a convex polygon as the constraint set. It has been proved that the solution obtained by this method will give the global optimal solution. The second part of this investigation is the bi-objective problem. The aim of the bi-objective problem is to find the satisfying solution which is desired in many realistic situations. Situation in which the proposed model is applicable is the location of a new warehouse where the sources of goods shipped to the warehouse and also the supply points to which the goods will be shipped is not known in advance. Due to the volatile and competitive nature of the market the supply and the demand points or in other words the variable points are not known in advance but some probability distribution can be predicted. It is required to find the location of a new warehouse which is closer to the variable points and simultaneously the total shipping cost per month from the warehouse to the variable points is minimum. For both single as well as bi-objective problems rectilinear distance norm has been considered as it is more appropriate to the different realistic situations. Two types of compromise solution methods have been suggested to get a satisfactory solution of the bi-objective problem.

The oil tankers dispatching problem

Abstract: The paper aims at obtaining an optimal route of a fleet of oil-delivery tankers from a source to a number of service stations. The distance between any two stations and demand(s) for each station are given. The objective is to find an optimal route undertaken by tankers such that the requirements of stations are met, the total distance travelled by the Tankers and the backload of the Tankers is to be minimized under the considerations. Also, the Tanker should visit a pair of stations exactly once. Further, a tanker does not supply the requirements of the stations partially. Here the tanker carries back the residue to the depot the available amount of oil will be considered as Backload or undelivered oil when the Tanker returns to depot (source station) or the maximum utilization of the capacity of Tankers in a trip schedule. Dantzig and Ramser—[4] investigated the problem of “The Truck Dispatching Problem” without the minimum backload and obtained a near optimal solution with the dynamic programming approach. For obtaining the optimal solution of the same problem with minimum backload, we proposed the Lexicographic Search approach. The algorithm is tested using C-language and the computational details are also reported, observed that it takes less computational time for higher size of problems.

How effective is aggregation for solving 0-1 models?

Abstract: Aggregation of constraints in a mathematical programming model is the process of replacing a set of constraints in the model by a single new constraint obtained from a combination of constraints in the set. It is generally believed that if such an aggregation step can be carried out without changing the set of feasible solutions of the problem, then it is highly desirable as it reduces the number of constraints in the model and thus makes it simpler to solve. We show that such an aggregation step may not be in general desirable for solving integer programming models by the branch and bound approach using lower bounds obtained from Linear Programming relaxation.

A pattern recognition lexi search approach to generalized time-dependent travelling salesman problem

Abstract: In this paper the “Generalized Time-dependent Travelling Salesman Problem” is a three dimensional travelling salesman problem where the cost matrix C (i, j, k) is the cost of the salesman visiting from city i to city j at time (facility) k. The cost matrix C(i,j,k) [i,j = 1,2,3,…..,n;k = 1,2,3,…..,m] is given. There are n cities and N = {1, 2, 3,…, n}. We are given a partition of cities into groups and we require to find a minimum length tour that includes at least one city from each group. The problem is to find a feasible tour for m(

Canonical correlation analysis on joint production: empirical study for the desirability of linear and log linear estimation in terms of crude oil and petroleum products

Abstract: Canonical correlation analysis seeks to identify and quantify the associations between two sets of variables. Harold Hotelling, who initially developed the technique, provided the example of relating arithmetic speed and arithmetic power to reading speed and reading power. Relating governmental policy variables with economic goal variables and relating college performance variables with precollege variables are other examples of this type. Canonical correlation analysis focuses on the correlation between a linear combination of the variables in one set and a linear combination of the variables in another set. The idea is first to determine the pair of linear combinations having the largest correlation. Next, we determine the pair of linear combinations having the largest correlation among all pairs uncorrelated with the initially selected pair. The process continues. The pairs of linear combinations are called the canonical variables, and their correlations are called canonical correlations. The canonical correlations measure the strength of association between the two sets of variables. The maximization aspect of the technique represents an attempt to concentrate a high-dimensional relationship between two sets of variables into a few pairs of canonical variables. An attempt has been made here to analyse the jointly produced goods crude oil and petroleum products using linear and log-linear estimation based on Harold Hotelling canonical correlation approach and to compare these two estimation procedures among themselves. The analysis suggests that log-linear estimation is superior to the linear estimation for such type of study.

A theoretical framework for optimal observability and detectability of spilled oil in aquatic environment

Abstract: A departure from ecosystem quality objectives can be defined as effects, which may vary in magnitude and occur over different time scales. Some effects may be reversible while others may persist for long periods. Thus, compared with other sources of pollution in the oceans, the risk of crude oil spillage to the sea presents the major threat for the marine ecology. This study considers the combination of information from diverse sources relating to a similar endpoint in formulating an operational research model to tackle the problem of false alarm from the use of remote sensing in spill detection. A common rubric for this combination is to apply a meta-analysis. The term suggests a move past an analysis of standalone data to one incorporating and synthesizing information from many associated sources.

Reliability of a system with m -stresses and n -strengths

Abstract: In certain situations many stresses and strengths may act on a system. It is observed that if more than one stress act on a single strength system then the reliability of the system is same as the reliability of the single stress strength components in series system when stress and strength follow exponential distribution. It is also observed that if more than one strength act on a single stress system then the reliability of the system is same as the reliability of the single stress strength components in parallel system when stress and strength follow exponential distribution. There may be a chance that m-stresses act on a n-strengths system. It is observed by the computations that the reliability of the system is approximately equivalent to the average of the reliability of series–parallel and parallel–series system when stress and strength follow exponential distribution. And also observed that if stress parameter μ i increases then the reliability of the system increases. If strength parameter λ j increases then the reliability of the system decreases. Here μ i and λ j are the reciprocal to the means of the stress and strength respectively.