Showing papers in "International Journal of Mathematics in Operational Research in 2015"

A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost

Abstract: In this paper, we propose a partial backlogging inventory model for deteriorating items with time-varying demand and holding cost. Deterioration rate is assumed to be constant. The demand rate varies with time until the shortage occurs; during shortages, demand rate becomes constant. Shortages are allowed and assumed to be partially backlogged. The backlogging rate is variable and is inversely proportional to the length of the waiting time for next replenishment. Taylor series is used for exponential terms approximating up to second degree terms. We solve the proposed model to obtain the optimal value of order quantity and total cost. The purpose of this paper is to minimise the total cost of inventory with optimal order quantity. The convexity of the cost function is shown graphically. Two numerical examples are given in order to show the applicability of the proposed model. Sensitivity analysis is also carried out to identify the most sensitive parameters in the system.

Analysis of M[X]/G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown

Abstract: This paper investigates the steady state behaviour of an M[x]/G/1 retrial queue with two phases of service under Bernoulli vacation schedule and breakdown. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters the service immediately while the rest join the orbit. After completion of each two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1-p). While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We construct the mathematical model and derive the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair. Some system performances are obtained.

Simulated annealing approach to solve dual resource constrained job shop scheduling problems:layout impact analysis on solution quality

Abstract: Real-world manufacturing systems are operating subject to a substantial level of resource constraints. One characteristic model that considers the combination of human and machine resource constraints is called dual resource constrained (DRC). In this context a number of machines nmach is managed by a selection of operators nop, with typically nop ≤ nmach.. A real life case study for an Italian manufacturing company is introduced that uses a set of identical parallel machines being operated by a set of operators. Each job is scheduled to one machine with corresponding loading and unloading process times. A simulated annealing approach is proposed to solve the DRC job shop scheduling problem. A sensitivity analysis is conducted for a selection of algorithm-specific parameters used to solve characteristic DRC layouts. Being characteristic for the just-in-time (JIT) production environment, the high variability in job times has also been taken into account. The results show that the selected layout nmach./nop ratio strongly influences the production system performance. The impact of the ratio of constrained resources has been analysed for different layouts, showing that simulated annealing performs better for single resource constrained problems while also demonstrating that this trend is not symmetrical for different layouts, either operator or machine constrained.

Steady state analysis of batch arrival feedback retrial queue with two phases of service, negative customers, Bernoulli vacation and server breakdown

Abstract: In steady state, a batch arrival feedback retrial queue with negative customers has been discussed. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them join into the orbit/retrial group, where the server provides two essential phases of service to each positive customer. The negative customer, arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters into the orbit with probability θ or leaves the system with probability 1-θ. The busy server may breakdown at any instant and the service channel will fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Numerical illustrations are analysed to see the effect of system parameters.

Fuzzy programming technique for solving the shortest path problem on networks under triangular and trapezoidal fuzzy environment

Abstract: In this paper, a well-known problem called the shortest path problem (SPP) has been considered in an uncertain environment. The cost parameters for travelling each arc have been considered as triangular or trapezoidal fuzzy numbers (TFNs or TrFNs) which are the more generalised form of fuzzy numbers involving a lower limit and an upper limit. A methodology has been developed for solving the fuzzy shortest path problem (FSPP), which results in lowest cost solution corresponding to the minimum-cost path or the shortest path. In the proposed method, the FSPP has been written in the form of single-objective fuzzy linear programming problem with fuzzy costs, which has been transformed into a crisp multi-objective linear programming problem. This in turn has been solved by the well-known fuzzy programming technique. Comparisons of the proposed methodology with some latest researches in this field have been discussed. Numerical examples illustrate the effectiveness of the proposed method.

Multi-objective linear fractional inventory model of multi-products with price-dependant demand rate in fuzzy environment

Abstract: In this paper, we propose a multi-criteria decision making approach for the solution of a multi-product inventory model without shortages. The model is considered over infinite horizon with price-dependant demand rate. The proposed model is formulated as a fractional multi-objective optimisation problem along with four constraints: budget constraint, space constraint, number of order constraint, and budgetary constraint on ordering cost of each item. The proposed inventory model becomes a multiple criteria decision making (MCDM) problem in fuzzy environment. This model is solved by multi-objective fuzzy goal programming (MOFGP) approach. Two numerical examples are given to illustrate the proposed model.

Failure-prone manufacturing systems with setups: feasibility and optimality under various hypotheses about perturbations and setup interplay

Abstract: A failure-prone manufacturing system producing two part types and requiring a setup for switching from one part type to another is considered. Both setup cost and time are taken into account. Various hypotheses regarding the interactions between random perturbations (failures and repairs) and setup strategies are used in the scientific literature, without clarifications provided for their relationships and possible consequences. In this paper, we close this gap and address feasibility and optimality conditions under various hypotheses. The feasibility conditions are obtained and studied analytically, and are shown to be dependent on the choice of an adopted hypothesis. This finding will prevent feasibility conditions not matching the underlying hypothesis from being applied. Optimality conditions in the form of Hamilton-Jacobi-Bellman equations are obtained and shown to be also dependent on the adopted hypothesis. A numerical example illustrating a comparison of the results obtained with the solutions of HJB equations is presented.

Availability modelling and evaluation of a repairable system subject to minor deterioration under imperfect repairs

Abstract: Many engineering systems are subjected to deterioration, meaning that during the course of time their conditions fall to failure levels. Such systems and their components are either repaired at failure or replaced before or after failure. However not every deterioration can bring about sudden failure of the system. Some deterioration can slightly reduce the strength of the system until at some point failure occurs. Such deterioration is said to be minor deterioration. This paper deals with the modelling and evaluation of availability of a system subjected to minor deterioration under imperfect repair. In this paper, we developed the explicit expression of system availability using probabilistic approach and determine the effect of failure, repair rate and number of states on system availability. The optimal availability level the system can attain is also determined. The results of this paper will enhance the system performance and useful for timely execution of proper maintenance improvement, decision, planning and optimisation.

An integrated production-inventory model with backorder and lot for lot policy in fuzzy sense

Abstract: In this paper, an inventory model for two-stage supply chain is investigated in the fuzzy sense. A supply chain with single vendor and single buyer is considered. We assume that shortage as a backorder is allowed for the buyer and the vendor makes the production set up every time the buyer places an order and supplies on a lot for lot basis. The decision variables are fuzzy order quantity and fuzzy shortage quantity which are expressed as triangular fuzzy numbers. After developing the mathematical model for the joint total relevant cost in fuzzy sense, its membership function is calculated and then defuzzified with the centroid method. The proposed model is solved and the amount of joint total relevant cost function in fuzzy sense is compared with the crisp one.

A proxy partially blind signature approach using elliptic curve cryptosystem

Abstract: Partially blind signature is cryptographic system that is used in several protocols including e-cash and e-commerce systems. In proxy partially blind signature, part of the message is approved by the signer and the signature supplicant. Elliptic curve discrete logarithmic (ECDL) is an extremely difficult to solve problem as compared to any standard inverse operation of a one-way-trap door function including discrete logarithm problem or factorisation problem. In this paper, we propose a new proxy partially blind signature scheme based on ECDL. The main attractive features of the proposed scheme are the low computational cost and the low communication overhead. Moreover, the new scheme provides an extra level of security properties of both the partially blind signature and proxy signature. Several security analysis are shown to prove the security and the efficiency of the proposed scheme.

Supply chain model with stock dependent demand, quadratic rate of deterioration with allowable shortage

Abstract: The goal of this devotion of time and attention to acquiring knowledge is to develop assist calculations and prediction for supply chain (three echelons), in which an optimal ordering decision for the manufacturer–supplier–retailer chain is developed when the supplier's lead–time is considered. This paper examines deterministic inventory model with variable deterioration and stock dependent demand, where the unsatisfied demand is partially backlogged which depends on waiting time. A solution procedure is presented to determine a stock dependent demand, variable deterioration rate, shortage period and the demand during the shortage is partially backlogged which is dependent on the waiting time such that the difference between an initial outlay and the subsequent amount earned for the supply chain is maximised. Sensitivity analyses are given to illustrate the model with the help of profit maximum principle.

Economic lot sizing for unreliable production system with shortages

Abstract: The purpose of the present study is to analyse the optimal lot size in an unreliable single-machine production system with shortages. The production system is subject to failure due to machine breakdown. Breakdown times are considered to be according to Weibull distribution. It is assumed that the shortages are allowed and backlogged. During each production, the set-up preventive (regular) maintenance is performed. The corrective (i.e., emergency) maintenance is carried out immediately after breakdown. For the illustration purpose, numerical results are provided for the special cases. To obtain the optimal cost per unit time, we also employ the artificial neuro-fuzzy inference system (ANFIS) approach which has the learning capability of neural network as well as advantages of rule-base fuzzy system. It is noted that the results obtained by neuro-fuzzy technique are at par with the results computed by the analytical techniques.

Admission control of bulk retrial feedback queue with K-optional vacations

Abstract: In this study, we have made an attempt to provide a ready reckoner for solving many congestion problems of day–to–day life under techno–economic constraints which can be seen in many industrial organisations and computer and communication systems. This can be made possible by designing a control policy called Bernoulli Admission Control Policy (BACP) wherein one can control the arrival rate of the customers by allowing only some of them to enter the system. We have applied this policy to a bulk retrial queueing system with Bernoulli feedback under Bernoulli vacation schedule. For the proper utilisation of the server's resources, there is a provision for the server to go for a fixed number of optional vacations (say K) depending upon its choice. We have provided a numerical simulation for solving the problem dealing with local area networks (LAN) especially relating to mobile IP. The service time, repair time, vacation time and setup time are assumed to be generally distributed. We have used supplementary variable technique (SVT) and probability generating function (PGF) method to compute various queueing and reliability measures of interest.

A bi-level multi-choice programming problem

Abstract: A Bi-level linear programming problem is treated as a multi-objective optimisation problem where the decision is taken by two different decision makers who are at two different levels. In this paper we consider a bi-level linear programming problem where some of the cost coefficient of the objectives, and some of the right hand side parameters of the constraints are multi-choice parameters. The aim of this paper is to establish a suitable solution procedure to solve the stated bi-level programming problem. To tackle the multi-choice parameters of the bi-level programming problem, we use some interpolating polynomials. Multi-choice parameters are replaced with interpolating polynomials. Then we use fuzzy programming method to solve the transformed bi-level programming problem. We present a numerical example to illustrate the solution procedure of the bi-level linear programming problem involving some multi-choice parameters.

Economic order quantity model for deteriorating items with time-dependent demand rate under time varying shortages

Abstract: This paper derives an economic order quantity model for deteriorating items with linearly time-dependent demand rate and shortages, where demand rate is differentiable function of time. Under these assumptions, mathematical formulations are derived for finding optimal time to finish positive inventory, cycle time, initial inventory and total cost per cycle. We show that the total cost per unit time is a concave function of cycle time. The results are illustrated with numerical example. Finally, sensitivity analyses have been performed to study the effects of changes with different parameters like: ordering cost, holding cost, purchase cost, deterioration rate, shortage cost and demand on optimal policies.

Estimation of stress-strength reliability from truncated type-I generalised logistic distribution

Abstract: In this paper, we are mainly interested in estimating the stress-strength reliability R = P(Y < X) when X and Y are two independent truncated type-I generalised logistic distributions with different shape parameters but having the same scale parameters. The model arises from type-I generalised logistic distribution truncated at zero, because lifetime data is always non-negative. Assuming that the common scale parameter is known, the maximum likelihood estimators of the parameters are developed and an asymptotic confidence interval for R is obtained. Extensive simulation studies are carried out to investigate the performance of these intervals. Using real data we illustrate the procedure.

EOQ model with backorders under linear combination of possibility and necessity measure

Abstract: This paper considers an EOQ model with backorders and imprecise holding cost, ordering cost and shortage cost under linear combination of possibility measure and necessity measure. The objective function of this model is to minimise fuzzy total annual cost, which includes fuzzy annual holding cost, fuzzy annual ordering cost and fuzzy annual shortage penalty cost. Making use of mλ–measure, a linear combination of possibility measure and necessity measure, two fuzzy chance–constrained programming models are constructed to determine optimistic and pessimistic values of the objective function. An objective function is optimised with some predefined degree of mλ–measure and accordingly the problem is transferred to an equivalent crisp problem. An analytical approach is developed to resolve the reduced models. To analyse the characteristics of the proposed model and to find the optimal decision under different situations, numerical illustrations are presented along with a sensitivity analysis.

Multi-level linear programming problem involving some multi-choice parameters

Abstract: In a multi-level decision making problem the decision is taken jointly by several decision makers who are at different levels. In this paper, we consider a multi-level linear programming problem where some of the cost coefficients of the objective functions and some of the right hand side parameters of the constraints are multi-choice type. The aim of this paper is to establish a suitable solution procedure to solve the stated multi-level programming problem. To tackle the multi-choice parameters of the multi-level programming problem, we use some interpolating polynomials and transform the stated problem into a multi-level mixed integer non-linear programming problem. Then we apply fuzzy programming method to solve the transformed multi-level programming problem. One numerical example is included to illustrate the solution procedure of the multi-level linear programming problem which has some multi-choice parameters.

Hidden Markov models for inventory systems with deteriorating items

Abstract: In this paper, we propose to apply hidden Markov model (HMM) in modelling an inventory system for deteriorating items. Each item in the inventory has certain chance to deteriorate in a fixed period of time. We propose models for both cases of deterministic and stochastic demands. With the information provided by customers, the inventory levels in the system, which are unknown, can be estimated. Numerical examples are provided to demonstrate the effectiveness of the proposed models.

Optimal replenishment policies of an EOQ model for non-instantaneous Weibull deteriorating items with ramp-type of demand under shortages

Abstract: This paper discusses the effects of ramp-type of demand on an EOQ model for non-instantaneous Weibull deteriorating items under time-dependent partial backlogging. Here, we consider a retailer who purchases and sells a single product over an infinite time horizon faces a ramp-type of demand. Shortages are allowed and partially backlogged. The time to the deterioration of the item is distributed as Weibull. Total cost and the optimum number of replenishments are taken here as decision variables. The objective is to obtain the optimal replenishment policies that minimise the total cost. For demonstrating the model numerical samples are explained in the following sections.

Designing a computational tool for supplier selection using analytical hierarchy process

Abstract: With increasingly competitive global world markets, companies are under intense pressure to find ways to cut production and material costs to survive and sustain their competitive position. Since a qualified supplier is a key element and a good resource for a buyer in reducing such costs at optimum material quality, evaluation and selection of the right suppliers is critical to maintain competitiveness. This decision becomes more complicated in case of multiple suppliers, multiple conflicting criteria, and imprecise parameters. Most supplier selection models consider the buyer's viewpoints and maximise only the buyer's advantages and thus do not necessarily lead to an optimal situation for business competitiveness. This paper deals with a multi attribute decision model using AHP for the justification of supplier selection, explore the factors influencing the supplier selection, the relationship between the identified factors and the firm's performance with reference to manufacturing industries in Bhubaneswar City.

Second-order symmetric duality in non-differentiable multiobjective programming over cones

Abstract: In this paper, a pair of Wolfe type second-order symmetric dual non-differentiable multiobjective programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are established under K-η-bonvexity assumptions. Self-duality has also been discussed assuming the functions involved to be skew-symmetric.

Incremental quantity discounts in a periodic–review stochastic inventory model with a general demand distribution

Abstract: We examine a periodic–review stochastic inventory model in which the buyer places orders to meet stochastic demands under an incremental quantity discount schedule with a single price–break point. With a general demand distribution, we prove the optimality of a state–dependent base–stock policy for the single–period problem and provide simple bounds on the optimal order–up–to levels for the multiple–period problem. We also solve the infinite horizon problem by using the policy iteration method. Our computational results suggest that a state–dependent base–stock policy is also optimal for the multiple–period and infinite–horizon problems.

A hybrid method for solving multi–objective geometric programming problem

Abstract: A multi–objective geometric programming problem contains more than one objective that needs to be achieved simultaneously. Such problems arise in many applications where two or more, sometimes conflicting objective functions have to be minimised concurrently. In this paper a new adaptive strategy called hybrid method proposed to find Pareto optimal solutions of the multi–objective geometric programming problem. Using geometric programming technique, a global best optimal solution is obtained from a set of Pareto optimal solution having a great impact on convergence of solution. The discussed hybrid method having a goal to enhance the optimisers over all performance by combining different optimisation techniques. In the proposed method we have combined e–constraint and weighted mean method and finally the result so obtained compared with the result obtained by fuzzy programming method. The solution procedure of the proposed hybrid method is illustrated by the numerical examples.

Efficiency improvement of decision making units: a new data envelopment analysis model

Abstract: The main goal of this paper is to develop a new data envelopment analysis (DEA) model to use optimal weights of each decision making unit (DMU) to improve its relative efficiency aligned with other DMUs. In spite of the vast amount of studies in this area and related tools and techniques, current literature deploys the optimal weights of DMUs to calculate the DMUs' relative efficiency and benchmarking for each DMU is less investigated. In order to fill this gap, this paper proposes a model for obtaining benchmark(s) for each DMU. Furthermore, a numerical example is used to illustrate the capability of the proposed model.

A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times

Abstract: This paper deals with the steady state behaviour of an Mx/G/1 retrial queue with two successive phases of service and general retrial times under Bernoulli vacation schedule for an unreliable server. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The primary customers finding the server busy, down, or on vacation are queued in the orbit in accordance with first come, first served (FCFS) retrial policy. After the completion of the second phase of service, the server either goes for a vacation of random length with probability p or may serve the next unit, if any, with probability (1 - p). For this model, we first obtain the condition under which the system is stable. Then, we derive the system size distribution at a departure epoch and the probability generating function of the joint distributions of the server state and orbit size, and prove the decomposition property.

On a class of capacitated transshipment problems with bounds on rim conditions

Abstract: The transshipment technique is used to find the shortest route from one point in a network to another point and is useful to truncate the cost of transportation. Inspired by dead mileage problem evaluated in terms of running empty buses from various depots to starting points, in this paper we study capacitated transshipment problems with bounds on total availabilities at sources and total destination requirements. Sometimes because of the budget/political constraints, the total flow of transportation is stipulated by some external decision maker which thereby results in impaired or enhanced flow in the market. This motivated us to explore such problems as a particular case of the original problem. The optimal solution of the specified problem is obtained by transforming it into an equivalent capacitated transportation problem. We have also discussed various situations emerging out of unbalanced capacitated transshipment problems in the form of inequalities and numerical examples are also given to illustrate the theory.

Studies on inventory model for deteriorating items with Weibull replenishment and generalised Pareto decay having time dependent demand

Abstract: Inventory models play an important role in determining the optimal ordering and pricing policies. Much work has been reported in literature regarding inventory models with finite or infinite replenishment. But in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material, etc. Hence, it is needed to develop inventory models with random replenishment. In this paper an EPQ model for deteriorating items is developed and analysed with the assumption that the replenishment is random and follows a Weibull distribution. It is further assumed that the life time of a commodity is random and follows a generalised Pareto distribution and demand is a function of time. Using the differential equations the instantaneous state of inventory is derived. With suitable cost considerations the total cost function is obtained. By minimising the total cost function the optimal ordering policies are derived. Through numerical illustrations the sensitivity analysis is carried. The sensitivity analysis of the model reveals that the random replenishment has significance influence on the ordering and pricing policies of the model. This model also includes some of the earlier models as particular cases for specific values of the parameters.

A simulation- and genetic algorithm-based optimisation of closed-loop multi-echelon inventory system

Abstract: The objective of this research is to develop a genetic algorithm (GA)-based optimisation approach for a multi-echelon closed-loop inventory system of items, which are repairable in nature. In the context of the passenger transportation industry, engineering aggregates like engines, alternators, axles and tyres are representative examples of such systems. The present work is motivated by a real-life example of state-owned transport corporation having more than 9,000 buses. Operationally, the corporation is divided across several depots (the lower most echelon) and divisions (the next higher echelon). The contribution from this research is manifold. In terms of specific insights, it is established that keeping a higher base stock of spare tyres at the divisions than at the depots is operationally better. This is a consequence of the risk pooling effect. The present research enables us to understand the optimal policy parameters of a complex multi-echelon inventory system. The whole optimisation approach and the simulation model can be generalised and can fit well in several other related problems and their contexts. Typically, the approach is applicable to the problems of repairable-parts inventory related to industries with heavy utilisation of equipments like the chemical and the petrochemical industries.

A new mathematical model for single machine scheduling with learning effect: continuous approach

Abstract: In the literature of scheduling, many studies have been devoted to schedule single machine activities. Despite numerous studies done to bridge the gap between the mathematical models and real-life scheduling problems, there is still gap remained to be covered. In this study, position-based, time-based and experience-based learning effect calculations are employed simultaneously in order to extend applicability of the proposed model. At first, the modified single machine scheduling problem is formulated as a mixed integer mathematical model with non-linear terms. Finally, a hybrid imperialistic competitive algorithm and genetic algorithm is designed to solve this complex problem. The hybrid ICA-GA algorithm is modified in order to take advantage of ICAs intelligence and GAs operators such as crossover and mutation simultaneously.