International Journal of Industrial Engineering & Production Research

---

  This article investigates integrated production-inventory models with backorder. A single supplier and a single buyer are considered and shortage as backorder is allowed for the buyer. The proposed models determine optimal order quantity, optimal backorder quantity and optimal number of deliveries on the joint total cost for both buyer and supplier. Two cases are discussed: single-setup-single-delivery (SSSD) case and single-setup-multiple-deliveries (SSMD) case. Two algorithms are applied for optimizing SSMD case: Gradient search and particle swarm optimization (PSO) algorithms. Finally, numerical example and sensitivity analysis are provided to compare the total cost of the SSSD and SSMD cases and effectiveness of the considered algorithms. Findings show that the policy of frequent shipments in small lot sizes results in less total cost than single shipment policy .

---

  Fuzzy time series have been developed during the last decade to improve the forecast accuracy. Many algorithms have been applied in this approach of forecasting such as high order time invariant fuzzy time series. In this paper, we present a hybrid algorithm to deal with the forecasting problem based on time variant fuzzy time series and particle swarm optimization algorithm, as a highly efficient and a new evolutionary computation technique inspired by birds’ flight and communication behaviors. The proposed algorithm determines the length of each interval in the universe of discourse and degree of membership values, simultaneously. Two numerical data sets are selected to illustrate the proposed method and compare the forecasting accuracy with four fuzzy time series methods. The results indicate that the proposed algorithm satisfactorily competes well with similar approaches.

---

This article develops an integrated JIT lot-splitting model for a single supplier and a single buyer. In this model we consider reduction of setup time, and the optimal lot size are obtained due to reduced setup time in the context of joint optimization for both buyer and supplier, under deterministic condition with a single product. Two cases are discussed: Single Delivery (SD) case, and Multiple Delivery (MD) case. These two cases are investigated before and after setup time reduction. The proposed model determines the optimal order quantity (Q*), optimal rate of setup reduction (R*), and the optimal number of deliveries (N*) -just for multiple deliveries case- on the joint total cost for both buyer and supplier. For optimizing our model two algorithm including Gradient Search and Particle Swarm Optimization (PSO), which is a population-based search algorithm, are applied. Finally numerical example and sensitivity analysis are provided to compare the aggregate total cost for two cases and effectiveness of the considered algorithm. The results show that which policy for lot-sizing is leading to less total cost.

---

Bus systems are unstable without considering any control. Thus, we are able to consider some control strategies to alleviate this problem. A holding control strategy is one commonly used real-time control strategy that can improve service quality. This paper develops a mathematical model for a holding control strategy. The objective of this model is to minimize the total cost related to passengers at any stop. To solve the model, particle swarm optimization (PSO) is proposed. The results of the numerical examples show that the additional total cost caused by service irregularity is reduced by 25% by applying the presented holding model to the given problem.

---

The present paper aims to investigate the effects of modularity and the layout of subsystems and parts of a complex system on its maintainability. For this purpose, four objective functions have been considered simultaneously: I) maximizing the level of accordance between system design and optimum modularity design,II) maximizing the level of accessibility and the maintenance space required,III) maximizing the providing of distance requirement and IV) minimizing the layout space. The first objective function has been put forward for the first time in the present paper and in it, the optimum system modularity design was determined using the Design Structure Matrix (DSM) technique.The second objective function is combined with the concept of Level of Repair Analysis (LoRA) and developed. Simultaneous optimization of the above-mentioned objective functions has not been considered in previous studies. The multi objective problem which has been put forward was applied on a laser range finder containing 17 subsystems and the modularity and optimum layout was determined using a multi objective particle swarm optimization (MOPSO) algorithm.

---

In this paper, a stochastic cell formation problem is studied using queuing theory framework and considering reliability. Since cell formation problem is NP-Hard, two algorithms based on genetic and modified particle swarm optimization (MPSO) algorithms are developed to solve the problem. For generating initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Moreover, full factorial and Taguchi methods are implemented to set crucial parameters in the solutions procedures. Deterministic method of branch and bound (B&B) algorithm is used to evaluate the results of modified particle swarm optimization algorithm and the genetic algorithm. The results indicate that proposed algorithms have better performance in quality of the metaheurstic algorithms final answer and solving time compared with the method of Lingo software’s B&B algorithm. The solution of two metaheurstic algorithms is compared by t test. Ultimately, the results of numerical examples indicate that considering reliability has significant effect on block structures of machine-part matrixes.

---

In this article, a multi objective model is presented to select and allocate the order to suppliers in uncertainty condition and in a multi source, multi customer and multiproduct case in a multi period state at two levels of supply chain. Objective functions considered in this study as the measures to evaluate suppliers are cost including purchase, transportation and ordering costs, timely delivering, shipment quality or wastages which are amongst major quality aspects, partial and general coverage of suppliers in respect of distance and finally suppliers weights making the products orders amount more realistic. The major limitations are price discount for products by suppliers which are calculated using signal function. In addition, suppliers weights in the fifth objective function is calculated using fuzzy Topsis technique. Lateness and wastes parameters in this model are considered as uncertain and random triangular fuzzy number. Finally the multi objective model is solved using two multi objective algorithms of Non-dominated Sorting Genetic Algorithm (NSGA-II) and Particle Swarm Optimization (PSO) and the results are analyzed using quantitative criteria Taguchi technique was used to regulate the parameters of two algorithms. 

---

In today's world, natural disasters such as earthquakes, floods, crises such as terrorist attacks and protests threaten the lives of many people. Hence, in this research we present a mathematical modeling that provide efficient and effective model to locate temporary depot, equitable distribution of resources and movement of injured people to health centers, with the aim of developing the multi-objective model and considering multiple central depot, multiple temporary depot and several type of relief items in the model . This paper is considered certainty state and uncertainty of influencing parameters of the models in robust optimization for three different levels uncertainty and in different size with consideration of traditional goals function and humanitarian purposes functions simultaneously. The model has been solved with multi-objective Particle Swarm optimization algorithm (MOPSO) and GAMS software to validate the model. Some numerical examples are presented. In Addition, we present sensitivity analyzes of model and study the relationship of the number of temporary depot location and the number of injured people to move to health centers and the number of uncovered damaged points.

---

In the new strategies of purchasing and production, suppliers play a key role in achieving of competitive capability for big companies. The selection of suitable suppliers is a critical component of this strategy. The problem of allocation order to supplier is a multi-objective problem that includes fuzzy parameters and also suppliers usually consider discount due to different levels of purchase amount. Since there is not a multi-objective fuzzy model for allocating orders in the literature that consider discount and shortfall simultaneously in the planning horizon of multi-products, this research proposes a new model includes minimization of costs, delays and the percentage of defective parts as objective functions. Jimenez method is used to defuzzy price, demand, delay and percentage of defective parts. Since the model is NP-hard, the two metaheuristic algorithms, NSGAII and MOPSO that their parameters were set by the Taguchi method has been developed. According to the results of numerical problems, the proposed algorithms can provide a good approximation of the optimal solutions for intended objectives.
 

---

In many real scheduling situations, it is necessary to deal with the worker assignment and job scheduling together. However, in traditional scheduling problems, only the machine is assumed to be a constraint and there isn’t any constraint about workers. This assumption could be due to the lower cost of workers compared to machines or the complexity of workers' assignment problems. This research proposes a flexible flow shop scheduling problem with two simultaneous issues: finding the best worker assignment, and solving the corresponding scheduling problem. We present a mathematical model that extends flexible flow shop scheduling problem to admit the worker assignment. Due to the NP-hardness of the research problem, two approximation approaches based on particle swarm optimization, named PSO and SPSO, are applied to minimize the makespan. The experimental results show that the proposed algorithms can efficiently minimize the makespan but the SPSO generates better solutions especially for large-size problems.

---

The blood supply chain network is an especial case of the general supply chain network, which starts with the blood donating and ends with patients. Disasters such as earthquakes, floods, storms, and accidents usually event suddenly. Therefore, designing an efficient network for the blood supply chain network at emergencies is one of the most important challenging decisions for related managers. This paper aims to introduce a new blood supply chain network in disasters using the hub location approach. After introducing the last studies in blood supply chain and hub location separately, a new mixed-integer linear programming model based on hub location is presented for intercity transportation. Due to the complexity of this problem, two new methods are developed based on Particle Swarm Optimization and Differential Evolution algorithms to solve practical-sized problems. Real data related to a case study is used to test the developed mathematical model and to investigate the performance of the proposed algorithms. The result approves the accuracy of the new mathematical model and also the good performance of the proposed algorithms in solving the considered problem in real-sized dimensions. The proposed model is applicable considering new variables and operational constraints to more compatibility with reality. However, we considered the maximum possible demand for blood products in the proposed approach and so, lack of investigation of uncertainty conditions in key parameters is one of the most important limitations of this research.

---

Integrated treatment planning for cancer patients has high importance in intensity modulated radiation therapy (IMRT). Direct aperture optimization (DAO) is one of the prominent approaches used in recent years to attain this goal. Considering a set of beam directions, DAO is an integrated approach to optimize the intensity and leaf position of apertures in each direction. In this paper, first, a mixed integer-nonlinear mathematical formulation for the DAO problem in IMRT treatment planning is presented. Regarding the complexity of the problem, two well-known metaheuristic algorithms, particle swarm optimization (PSO) and differential evolution (DE), are utilized to solve the model. The parameters of both algorithms are calibrated using the Taguchi method. The performance of two proposed algorithms is evaluated by 10 real patients with liver cancer disease. The statistical analysis of results using paired samples t-test demonstrates the outperformance of the PSO algorithm compared to differential evolution, in terms of both the treatment plan quality and the computational time. Finally, a sensitivity analysis is performed to provide more insights about the performance of algorithms and the results revealed that increasing the number of beam angles and allowable apertures improve the treatment quality with a computational cost.