Showing papers in "International Journal of Mathematics in Operational Research in 2011"

Balking and reneging in multiserver Markovian queuing system

Abstract: In the analysis of many queuing systems, it is assumed that customers who arrive stay on till they receive service. In real life, this does not always happen. We shall assume that customers may balk if service is not instantly available on arrival. Even if a customer joins the system, the customer may renege. In this paper, we consider a multi server Markovian queuing system where the customers may balk as well as renege. Explicit closed form expressions are presented. A numerical problem with design aspects has also been presented to demonstrate results derived.

An extension of the linear programming method with fuzzy parameters

Abstract: In a recent paper, Jimenez et al. (2007) propose a 'general' and 'interactive' method for solving linear programming problems with fuzzy parameters. In this study, we propose a revision to the optimal crisp value of the objective function to eliminate the restrictive constraints imposed by Jimenez et al. (2007). The revised approach can be generalised to solve many real-world linear programming problems where the coefficients are fuzzy numbers. In contrary to the approach proposed by Jimenez et al. (2007), our method is rightfully general and interactive, as it provides an optimal solution that is not subject to specific restrictive conditions and supports the interactive participation of the Decision-Maker (DM) in all steps of the decision-making process. We also present a counterexample to illustrate the merits of the proposed method and the drawbacks of Jimenez et al.'s (2007) method.

Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs

Abstract: In this paper, a bulk service queueing system with variant threshold policy for secondary jobs is considered. On completion of service, if the queue length is less than ‘ a ’, the server performs a secondary job of type one, repeatedly, until the queue length reaches ‘ a ’. On returning from a secondary job of type one, if the queue length is at least ‘ a ’, the server performs another secondary job of type two, repeatedly, until the queue length reaches the threshold value ‘ N ’ ( N ≥ b > a ), then the server serves a batch of ‘b’ customers. Various performance measures and a cost model are presented.

Queueing model with state-dependent bulk arrival and second optional service

Abstract: This paper investigates a single server bulk queueing system with state-dependent rates and second optional service. The service time of the essential service is general-distributed whereas that of optional service follows the exponential distribution. By using supplementary variable technique, the probability-generating functions of the queue length distribution have been obtained. Further, the queue length distribution is established by using maximum entropy approach. The numerical illustrations are provided to verify the tractability of performance measures. The sensitivity analysis is also carried out to examine the effect of system descriptors.

Renewal input infinite buffer batch service queue with single exponential working vacation and accessibility to batches

Abstract: This paper considers an infinite buffer single server batch service queue with single exponential working vacation policy. The inter-arrival times are generally independent and identically distributed random variables and the service times are exponential. The server accesses new arrivals even after service has started on any batch of initial number a. This operation continues till the service time of the ongoing batch is completed or the maximum accessible limit d of the batch being served is attained whichever occurs first. The supplementary variable technique and the recursive method are used to develop the steady-state queue length distributions at pre-arrival and arbitrary epochs. Some performance measures and numerical results are discussed.

A fuzzy multi-item production model with reliability and flexibility under limited storage capacity with deterioration via geometric programming

Abstract: A multi-item EPQ model for deteriorating items is built-up with limited storage space and with flexibility and reliability of production process. Here, production rate for the items is depends on the demand and items deteriorate at constant rates. Due to high rent in market place, storage space is considered limited and imprecise in nature. Inventory related costs, storage space and other parameters are imprecise and taken as it triangular fuzzy number. We solve this inventory decision problem using Modified Geometric Programming (MGP) method. Following the theoretical treatment, we provide a numerical example to demonstrate that MGP has potential as a valuable analytical tool for researchers. At the end some sensitivity analysis with different parameters are made.

An integrated cost model for production scheduling and perfect maintenance

Abstract: Production scheduling deals with scheduling production jobs on a machine (single or multiple) in order to optimise a specific objective such as total weighted completion times or total weighted tardiness. The assumption that machines are always available for processing jobs is generally used in the production scheduling literature. In reality, machines often are unavailable due to preventive maintenance activities or machine failure. Production scheduling and preventive maintenance planning are interrelated, but are most often treated separately. This interdependency seems to be overlooked in the literature. This work integrates, simultaneously, the decisions of preventive maintenance and job order sequencing for a single machine. The objective is to find the job order sequence and maintenance decisions that would minimise the expected cost.

Emergency logistics strategy in response to anthrax attacks based on system dynamics

Abstract: To find the efficient logistics strategy for the anthrax attack, the anthrax progression model and emergency logistics model under the traditional and collaboration modes are constructed based on the System Dynamics (SD) approach. Then, a combination mode that integrates the two modes is proposed. Through the simulation, we analysed some factors which can affect the rescue effect, and we studied which mode is the best logistics strategy response to the anthrax attacks. This study provides insights for the decision-makers who cope with the emergency events, such as the bioterrorists attacks.

A linear Goal Programming approach to multiobjective fractional programming with interval parameter sets

Abstract: This paper presents a Goal Programming (GP) approach to solving multiobjective fractional programming problems (MOFPPs) involving interval coefficients and target intervals. In the proposed approach, interval-valued fractional objectives are converted into the standard fractional objective goals in GP formulation. The fractional goals are then transformed into linear goals within the framework of GP by using the linear transformation approach. In the GP model formulation, the goal achievement function for minimising the lower bounds of the necessary regret intervals of the goal objectives for the defined interval parameter sets from the optimistic point of view is taken into consideration. In the solution process, the mixed 0–1 method is used to overcome the computational complexity arises for non-convex in nature of the formulated model of the problem. Two numerical examples are provided to illustrate the solution approach.

Bi-criterion release time problem for a discrete SRGM under fuzzy environment

Abstract: Software Release Time Problems is a well known domain in the field of Software Optimisation. To determine when to stop testing and release software becomes one of the important decision for management. In real life the developers can only make ambiguous estimates on the available resources and their aspirations bringing uncertainty (fuzziness) in the problem formulation. In this paper, we have formulated a fuzzy bi-criterion release time problem optimising the two conflicting cost minimisation and reliability maximisation objectives under budgetary constraint. Fuzzy optimisation technique is discussed to solve such problem with numerical illustration.

Single-server Poisson queueing system with splitting and delayed-feedback: Part I

Abstract: M/M/ 1 queueing models with immediate feedback and splitting have been considered in the literature. However, with the advancement of communication technologies and increased complexity of the service processes, there is a need to take into account situations where a feedback with delays is required. In this paper, a Poisson arrival with exponential single-processor model with splitter, feedback and three buffers is considered. Feedback occurs exponentially with delay and in bounded random batch size (in this case with size 1). The steady-state system of differential-difference equations is solved analytically that reduces to a functional equation. The mean queue length at each station is found.

Optimal pricing and replenishment policy in a declining price sensitive environment under continuous unit cost decrease

Abstract: Decreasing component price and diminishing demand over time due to introduction of upgraded versions of components are now important characteristics of high-tech industrial market. From a practical point of view there is a need for searching ideal selling price and lot-size over a finite time horizon for a retailer when purchase cost and customers demand decrease rapidly. In this paper we address the issue by jointly determining lot-size and optimal prices for an inventory system which experiences continuous unit cost decrease under time and price dependent decreasing demand structure. It is assumed that the decision maker has the opportunity to adjust replenishment cycle lengths and selling prices, which depends on unit purchase cost, to enhance demand. A mathematical model is developed and existence of the optimal solution is verified. Closed form values of the prices and number of price changes are derived. A solution procedure is developed to determine lot-size, prices and number of pricing cycles. The model is illustrated by a numerical example.

An inventory model for a deteriorating item with two levels of storage and stock-dependent demand

Abstract: This paper deals with an inventory model for a deteriorating item with two levels of storage where the demand rate is a function of the on-hand inventory. When the stock level exceeds the capacity of the Own Warehouse (OW), a Rented Warehouse (RW) is used. The stock is transported periodically in bulk from RW to OW and there is an associated transportation cost. Shortages are not allowed and an algorithm is developed to obtain the optimal solution of the model. The optimal solution is illustrated with the help of a numerical example. Sensitivity of the optimal solution is also carried out with respect to changes in different system parameters.

Mixed-collaborative distribution mode for emergency resources in an anti-bioterrorism system

Abstract: In this paper, a unique forecasting model for the demand of emergency resources based on epidemic diffusion rule is constructed. We find that both the pure point-to-point delivery mode (PTP) and the pure multi-depot, multiple travelling salesmen delivery system (MMTS) are difficult to operate in an actual emergency situation. Thus, we propose a mixed-collaborative distribution mode, which can equilibrate the contradiction between these two pure modes. A special time window for such a mixed-collaborative mode is designed. A Genetic Algorithm (GA) is adopted to solve the optimisation model. At last, we compare it with these two pure distribution modes from both aspects of total distance and timeliness.

An EOQ model for a deteriorating item with time-varying demand and time-dependent partial backlogging

Abstract: This paper describes an EOQ model for a deteriorating item considering time-dependent demand and time-dependent partial backlogging, which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. Equal replenishment cycle length in case of fixed planning horizon is relaxed in this model. Also, backlogging rate is taken to be dependent on waiting time of the customers, instead of waiting line of the customers. This seems to be better representation since impatient customers naturally want to know how long time they have to wait for receiving their goods, not how many customers are ahead. The model is solved analytically to obtain the optimal solution of the problem for a general time-dependent demand pattern. It is then illustrated with the help of numerical examples.

A new approach for fuzzy critical path analysis

Abstract: A new method, named as Mehar’s method is proposed to solve fuzzy critical path problems. To show the advantages of the Mehar’s method over an existing method the results of a fuzzy critical path problem, obtained by using the existing and Mehar’s method, are compared. Also, it is shown that although the results, obtained by using the existing and Mehar’s method, are mathematically correct but the obtained and the existing results have no physical meaning. To overcome this shortcoming a new subtraction operation, named as Mehar’s subtraction, is introduced and the Mehar’s method is further modified with Mehar’s subtraction.

An EOQ model for rebate value and selling-price-dependent demand rate with shortages

Abstract: In this paper, we develop a deterministic purchasing inventory model for a single item over an infinite horizon. In addition, shortages are allowed and the unsatisfied demand is partially backlogged. The model is studied under the replenishment policy, shortages followed by inventory. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximise the Total Profit (TP), which includes sales revenue, purchase cost, the set-up cost, holding cost, rebate redemption cost, shortage cost and opportunity cost due to lost sales. Here, demand varies with price and rebate value. The existence and uniqueness of the proposed systems are examined. Finally, numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out. We propose a solution procedure to find the solution and obtain some managerial results by using sensitivity analysis.

Dominant retailer’s optimal policy in a supply chain under Advance Payment scheme and trade credit

Abstract: In a supply chain, a large and powerful retailer has the power of influencing another member’s decisions. In real life situations, the retailer provides price discount under Advance Payment (AP) scheme in order to attract customers in today’s business such as bricks, tiles, books etc. Due to the advancement of the internet and online money transactions, the AP scheme is common and useful to estimate the demand well in advance and to increase the market sales. In this paper, we consider a two-echelon supply chain with single supplier and multiple retailers. Among all the retailers, we intend to find optimal policy at the dominant retailer who offers AP scheme and trade credit in order to attract more customers. An Economic Order Quantity (EOQ) model with perfect items is developed to investigate the dominant retailer’s inventory system as a cost minimisation problem. A lot of managerial phenomena are obtained through numerical examples.

A copula-based approach to financial contagion in the foreign exchange markets

Abstract: In this paper, we try to find out if the foreign exchange markets of developed countries reflect the effects of financial contagion of the 2007 subprime financial crisis and the intensity of contagion differs across countries. In fact, we have defined contagion as the significant increase in co-movement of foreign exchange markets during the crisis period for reasons that are not explained by fundamentals. This paper investigates the dependence structure between the following three foreign exchange currencies (the British pound, the French franc and the German mark) by using copulas. Our results suggest that the current crisis does not affect the exchange markets of these three developed countries.

A production lot-size model with Fuzzy-Ramp type demand and fuzzy deterioration rate under permissible delay in payments

Abstract: A production lot-size inventory model is developed with finite production rate, fuzzy deterioration and demand rate under permissible delay in payments. Here it is assumed that the initial demand rate of ramp-type demand and the deterioration rate are uncertain in fuzzy sense i.e., imprecise in nature. The initial demand rate and deterioration rate are taken as triangular fuzzy number. Using α -cut for defuzzification, the total variable cost per unit time is derived. The multi-objective model is solved using Global Criteria Method and is illustrated with a numerical example. Sensitivity analysis has been made for different values of α .

Sensitivity analysis of portfolio properties with budget constraints

Abstract: We develop a framework for understanding how variations of portfolio properties are apportioned to changes in portfolio composition as trading is performed in the presence of budget constraints Our approach is based on the concept of constrained derivative It allows one to obtain the simultaneous sensitivity of portfolio properties wrt assets groups for any choice of pivotal asset Analytical expressions for the sensitivity of portfolio returns, variance, GARCH volatility and Value at Risk (VaR) are derived A numerical exemplification is proposed with reference to the 30 assets of the Dow Jones Index

On the asymptotic effect of examination malpractice on the structure of a Markovian multi-echelon educational system

Abstract: The theoretical framework in modelling the transition process in this study is analogous to the imbedding transformation of the transition process in a manpower system into a k × k matrix space as in the Young/Almond-type model. We prove that in an environment saddled with examination malpractice, where strategies to curb the malpractice rate are generally not effective, then, against every possible growth rate, the students’ stocks in each level of an educational institution where examination malpractice is prohibited will degenerate to zero in the long-run. An example problem is included to illustrate this assertion.

Design of GAmut-Lssahc: a solver for course timetabling problem

Abstract: In this paper, the problem of course timetabling is studied extensively and its constraints are represented using mathematical representation. Analysing the existing GA-based methodologies for solving University Course Timetabling problem, a new method has been proposed probably, which has not yet been attempted for this problem. It employs GA with a variety of proposed MUTation operators (Random-Selection; Adaptive; Goal-Directed) and Local Search of Steepest Ascent Hill Climbing (GAmut-LSsahc) to increase the fitness value and could produce optimal course timetable at the earliest. It was experimentally proved that goal-directed converges 6% faster than adaptive and 10% faster than random-selection mutation.

Approximation algorithm for optimal location of concentrators and design of Capacitated Survivable Backbone Networks

Abstract: We focus on the problem of selecting concentrator locations to minimise the access network costs. This falls under the general class of Uncapacitated Facility Location (UFL) problem. We present an approximation algorithm along with some computational results. We also study the problem of designing a Capacitated Survivable Backbone Network (CSBN) with the property that there is at least one route present between all the communicating node pairs in the case of a single link failure. Mathematical formulation to efficiently solve the survivable backbone network design problem is presented. The methodologies developed are applied to a real world setting obtaining optimal or near-optimal results.

Mond-Weir type nondifferentiable multiobjective second-order symmetric duality with cone constraints

Abstract: In this paper, a pair of Mond-Weir type nondifferentiable multiobjective second-order symmetric dual programs over arbitrary cones is first formulated, where each of the objective function contains a square root term with positive semidefinite matrix in R n × n . Weak, strong and converse duality results are proved for aforesaid model under second-order K - F -convexity/ K - η -bonvexity assumptions. Several known results are obtained as special cases.

Shared resources in production systems: (max,+) analysis

Abstract: This paper deals with formal modelling of Petri nets including shared resources These phenomena appear widely in the production management context, for the modelling of manufacturing cells But, they usually cannot be formally represented in dioid algebraic structures based on sets of scalars In this paper, we design a method to describe such a phenomenon in a dioid of intervals In fact, the resource-sharing problem is turned into a time uncertainty problem, regarding the access to the shared resource In this new problem, time uncertainties are bounded and can be described by intervals Both bounds of the behaviours of the studied production systems can be manipulated in the scope of the

An analytic process model for selection of infectious waste management contractors

Abstract: Infectious or bio-medical waste so far has not received its due attention. Hospitals in developing countries dispose large amounts of medical waste inefficiently, creating potential environmental hazards and increasing operational expenses, along with the Municipal Solid Waste (MSW). The hospitals lack objective criteria to select the most appropriate waste disposal firm and evaluate its performance, relying on their own subjective judgment and previous experiences. This paper presents an Analytic Network Process (ANP) methodology to objectively select infectious waste disposal contractors. The suggested methodology would reduce overhead costs and enhance medical waste management.

A two-level interior-point decomposition algorithm for multi-stage stochastic capacity planning and technology acquisition

Abstract: Manufacturing flexibility is recognised as one of the key strategies to address uncertain future products demand. Therefore, a growing need exists to investigate the strategic aspect of flexibility. To capture the different aspects of market flexibility in the face of this dynamic demand, this paper focuses on the role of product, volume, and expansion flexibility in the context of the multi-stage stochastic program. Moreover, we implement a two-level, interior-point decomposition algorithm based on the Analytic Center Cutting Plane Method (ACCPM) to solve the model. The central prices obtained by the ACCPM provides a fast convergence and promising computational results in terms of the number of iterations.

Enumeration of spanning trees of graph: alternative methods

Abstract: All the trees of the graph are not important, but spanning trees have a special significance in the analysis of networks and systems. The simplest of the prototype methods is based on incidence matrix. Two new approaches have been proposed in this paper, which makes use of few other matrices used to represent topology of the network graph. Some optimisation techniques are also developed to reduce the number of calculations and computer time as well. Comparison is made between prototype and proposed methods using programs developed in MATLAB. Efficiency of the proposed method is proved with a simple case study.

Optimality conditions and solution methodology for parameter selection in DEA

Abstract: This paper focuses on developing optimality conditions and a solution methodology for generalised Data Envelopment Analysis (GDEA). The GDEA framework determines input and output parameters in DEA models of internal managerial performance of Decision Making Units (DMUs) based on an optimisation criterion involving an external non-managerial reward function on DMU performance. The resulting problem is a difficult non-convex integer optimisation model. In this paper, first-order optimality conditions are first derived, and then, these are utilised within a hybrid scheme of gradient-based search and a metaheuristic such as simulated annealing for efficient solution. Data from a financial application are used to illustrate the methodology.