1 Publication in International journal

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1 1 Publication in International journal Title: A bi-objective stochastic programming model for a centralized green supply chain with deteriorating products Authors: Y. PEZESHKI, A. BABOLI, N. CHEIKHROUHOU, M. MODARRES, M. R. AKBARI JOKAR Journal: International Journal of Production Economics (ISI Web of Science), (2014), 150: , Impact factor: 2,081 Abstract: In recent years consumers and legislation have been pushing companies to design their activities in such a way as to reduce negative environmental impacts more and more. It is therefore important to examine the optimization of total supply chain costs and environmental impacts together. However, because of the recycling of deteriorated items, the environmental impacts of deteriorating items are more significant than those of non-deteriorating ones. The objective of this paper is to develop a stochastic mathematical model and to propose a new replenishment policy in a centralized supply chain for deteriorating items. In this model, we consider inventory and transportation costs, as well as the environmental impacts under uncertain demand. Several transportation vehicles producing various greenhouse gas (GHG) levels are considered. The best transportation vehicles and inventory policy are determined by finding a balance between financial and environmental criteria. In this way, we develop a linear mathematical model and present a numerical example from the real world to demonstrate its applicability and effectiveness. We then perform a sensitivity analysis and provide some managerial insights. Finally, more promising directions are suggested for future research. Key words: Green supply chain; Two-stage stochastic programming; Deteriorating products; Transportation; Uncertain demandtion URL:

2 Title: A rewarding-punishing coordination mechanism based on Trust in a divergent supply chain Authors: Y. PEZESHKI, A. BABOLI, N. CHEIKHROUHOU, M. MODARRES, M. R. AKBARI JOKAR Journal: European Journal of Operational Research (ISI Web of Science), 230 (2013) Impact factor: 2,038 Abstract: Coordination of decentralized supply chains using contract design is a problem that has been widely addressed in the literature. We consider a divergent supply chain including a manufacturer and several retailers producing fashion products with short sale seasons. The retailers cooperate with the manufacturer as sales agents; i.e., they work in the framework of revenue sharing contracts. Because of their proximity to the market, retailers can provide more accurate demand forecasts to the manufacturer that is used to decide on issues such as capacity building and market prices with regard to retailers stiff due dates, different lead times and different price-dependent demand functions. To ensure abundant supply and cope with the demand variability, the retailers have an incentive to exaggerate their private forecast information. In this study, we propose a new rewarding-punishing coordination mechanism based on trust between supply chain tiers, considered as a differentiation factor between honest and deceptive partners. An optimization model is developed as a building block of this mechanism. An approximation method is used to simplify and solve the problem. The model is then implemented using Monte-Carlo simulation in four different situations, according to ten different strategies for forecast information sharing. The findings from the tests show that the mechanism including trust as a decisional factor performs better than No Trust mechanism in all situations. These results suggest that taking into account Trust in designing coordination mechanism may have significant influence on the financial performance of the supply chain. Key words: Supply chain management, Coordination, Divergent supply chain, contract design, Trust, Monte Carlo simulation URL:

3 Title: Comparing three proposed meta-heuristics to solve a new p-hub location-allocation problem Authors: A. GHODRATNAMA, R. TAVAKKOLI-MOGHADDAM, A. BABOLI, Journal: International Journal of Engineering, Transactions C: Aspects, (2013), 26-9, , Abstract: This paper presents a new mathematical model, in which the location of hubs is fixed and their capacity is determined based on facilities and factories allocated to it. In order to feed the client's nodes, different types of vehicles of different capacities are considered, in which the clients are allocated to hubs, and types and numbers of vehicles are allocated to the factory's facilities. To come up with solutions we propose to use three meta-heuristics, namely genetic algorithm, particle swarm optimization, and simulated annealing. The efficiency and computational results of the foregoing algorithms are compared with one another. Finally, the conclusion is presented. Key words: Hub location-allocation, Vehicle capacity, Plant production capacity, Simulated annealing, Genetic algorithm, Particle swarm optimization. URL:

4 Title: A stochastic aggregate production planning model in a green supply chain: considering flexible lead times, nonlinear purchase and shortage cost functions Authors: S.M.J. MIRZAPOUR AL-E-HASHEM, A. BABOLI, Z. SAZVAR, Journal: European Journal of Operational Research(ISI Web of Science), 230 (2013) 26 41, Impact factor: 2,038 Abstract: In this paper we develop a stochastic programming approach to solve a multi-period multi-product multi-site aggregate production planning problem in a green supply chain for a medium-term planning horizon under the assumption of demand uncertainty. the proposed model has the following features: (i) the majority of supply chain cost parameters are considered; (ii) quantity discounts to encourage the producer to order more from the suppliers in one period, instead of splitting the order into periodical small quantities, are considered; (iii) the interrelationship between lead time and transportation cost is considered, as well as that between lead time and greenhouse gas emission level; (iv) demand uncertainty is assumed to follow from a pre-specified distribution function; (v) shortages are penalized by a general multiple breakpoint function, to persuade producers to reduce backorders as much as possible; (vi) some indicators of a green supply chain, such as greenhouse gas emissions and waste management are also incorporated in to the model. The proposed model is first a nonlinear mixed integer programming which is converted into a linear one by applying some theoretical and numerical techniques. Due to the convexity of the model, the local solution obtained from linear programming solvers is also the global solution. Finally, a numerical example is presented to demonstrate the validity of the proposed model. Key words: supply chain management, Aggregate production planning, green principles, quantity discount, multiple breakpoint shortage cost, demand uncertainty URL:

5 Title: Coordination mechanism for capacity reservation by considering production time, production rate and order quantity Authors: Y. PEZESHKI, M. R. AKBARI JOKAR, A. BABOLI, J.P. CAMPAGNE, Journal: Applied Mathematical Modelling, (ISI Web of Science), 37 (2013) , Impact factor: 1,706 Abstract: In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed. Key words: Supply chain coordination, Contracts, Capacity reservation, Inventory cost, Information updating URL:

6 Title: A new mathematical model for Weber location problem with a probabilistic polyhedral barrier Authors: M. AMIRI-AREF, N. JAVADIAN, R. TAVAKKOLI-MOGHADDAM, A. BABOLI, Journal: International Journal of Production Research (ISI Web of Science), (2013), DOI: / , Impact factor: 1,460 Abstract: With widely applications of location theory in a variety of industries, presence of barrier should be paid attention by managers and engineers. In this paper, we assess the Weber location problem in the presence of a polyhedral barrier which probabilistically occurs on a given horizontal barrier route in the rectilinear space. A left triangular distribution function is used for starting point of the barrier and therefore an expected rectilinear barrier distance function is formulated. Besides, a modification of the polyhedral barrier is presented which is equivalent to the original problem. This modification is applicable for both convex and nonconvex polyhedral barriers. The objective is to find a new facility location so that the summation of the expected traveled barrier distance to the demand points is at minimum. Therefore, a mixed integer nonlinear programming model, which has a nonconvex solution space, is presented. Furthermore, by decomposing the feasible space to a finite number of convex solution spaces, an exact heuristic solution method is proposed. Then, a lower bound problem based on the forbidden region is applied. Some theorems and an example are reported. Key words: Weber location problem; polyhedral barrier; mixed integer nonlinear programming; optimization; URL:

7 Title: The Center Location-Dependent Relocation Problem with a Probabilistic Line Barrier Authors: M. AMIRI-AREF, N. JAVADIAN,; R. TAVAKKOLI-MOGHADDAM, A. BABOLI, S. SHIRIPOUR, Journal: Applied Soft Computing (ISI Web of Science), 13 (2013) , Impact factor: 2,140 Abstract: This paper presents a new mixed-integer nonlinear programming (MINLP) for a single-facility multi-period rectilinear distance center location-dependent relocation problem with a probabilistic line barrier that uniformly occurs on a given horizontal route. In this problem, the demand and location of the existing facilities have a dynamic nature. The objective function of the presented model is to minimize the maximum expected weighted barrier distance between the new facility and the existing facilities during the planning horizon. The optimum solution of solving small-sized test problems is obtained. For large-size test problems, two meta-heuristics based on the genetic algorithm (GA) and imperialist competitive algorithm (ICA) are proposed. Furthermore, a lower bound can be found for the given problems. To validate the presented model, a number of numerical experiments are illustrated and the related results are reported. Key words: Multi-period facility location problem; Probabilistic line barrier; Rectilinear distance; Genetic algorithm; Imperialist competitive algorithm. URL:

8 Title: A new order splitting model with stochastic lead times for deterioration items Authors: Z. SAZVAR, M. R. AKBARI JOKAR, A. BABOLI, Journal: International Journal of Systems Science (ISI Web of Science), (2013), DOI: / , Impact factor: 1,305 Abstract: In unreliable supply environments, the strategy of pooling lead time risks by splitting replenishment orders among multiple suppliers simultaneously is an attractive sourcing policy that has captured the attention of academic researchers and corporate managers alike. While various assumptions are considered in the models developed, researchers tend to overlook an important inventory category in order splitting models: deteriorating items. In this paper we study an order splitting policy for a retailer that sells a deteriorating product. The inventory system is modeled as a continuous review system (s, Q) under stochastic lead time. Demand rate per unit time is assumed to be constant over an infinite planning horizon and shortages are backordered completely. We develop two inventory models. In the first model it is assumed that all the requirements are supplied by only one source, whereas in the second, two suppliers are available. We use sensitivity analysis to determine the situations in which each sourcing policy is the most economic. We then study a real case from the European pharmaceutical industry to demonstrate the applicability and effectiveness of the proposed models. Finally, more promising directions are suggested for future research. Key words: Order splitting, Deteriorating items, Stochastic lead time, Optimal ordering policy. URL:

9 Title: Simultaneous coordination of capacity building and price decisions in a decentralized supply chain Authors: Y. PEZESHKI, A. BABOLI, M. R. AKBARI JOKAR Journal: International Journal of Advanced Manufacturing Technology (ISI Web of Science), (2013) 64: , Impact factor: 1,205 Abstract: In this paper we investigate the simultaneous coordination of price and capacitybuilding decisions in a dyadic supply chain. This problem is a combination of capacity reservation problem and pricing problem. While coordination of supply chain with stochastic demand and fixed prices, has received much attention in the literature, price-dependent and stochastic demand has been less considered. We study the latter case where a price-setting retailer faces a linear decreasing demand with respect to price. To capture the uncertainty of the demand we add a stochastic variable to the demand function. In addition, we incorporate production rate and inventory cost on the supplier side. We propose Revenue Sharing Reservation Contract with Penalty (RSRP) as a coordination mechanism to align the price and capacity decisions. We then extend the model to include multiple retailers which are geographically dispersed. We next conduct a comprehensive numerical example with an extensive sensitivity analysis to understand the behavior and robustness of the supply chain under a RSRP, and finally, we draw some managerial implications. Key words: Supply chain coordination, contract, price-dependent demand, capacity building URL:

10 Title: A replenishment policy for perishable products with non-linear holding cost under stochastic supply lead time Authors: Z. SAZVAR, A. BABOLI, M. R. AKBARI JOKAR Journal: International Journal of Advanced Manufacturing Technology (ISI Web of Science), (2013) 64: Impact factor: 1,205 Abstract: The development and application of inventory models for deteriorating items is one of the main concerns of subject matter experts. The inventory models developed in this field have focused mainly on supply chains under the assumption of constant lead time. In this study, we develop an inventory model for a main class of deteriorating items, namely perishable products, under stochastic lead time assumption. The inventory system is modelled as a continuous review system (r, Q). Demand rate per unit time is assumed to be constant over an infinite planning horizon and the shortages could be backordered completely. For modeling the deterioration process, a non-linear holding cost is considered. Taking into account the stochastic lead time as well as a non-linear holding cost makes the mathematical model more complicated. We customize the proposed model for a uniform distribution function that could be tractable to solve optimally by means of an exact approach. We then solve an example taken from the literature to demonstrate the applicability and effectiveness of the proposed model. Finally, by doing several sensitivity analyses for the key parameters of the model, some managerial insights are proposed. Key words: Supply chain management, Inventory control, Replenishment policy, Perishable products, Non-linear holding cost, Stochastic lead time. URL:

11 Title: Reliable design of a forward/reverse logistics network under uncertainty: A robust-m/m/c queuing model Authors: B. VAHDANI, R. TAVAKKOLI-MOGHADDAM, M. MODARRES, A. BABOLI, Journal: Transportation Research Part E (ISI Web of Science) 48 (2012) , Impact factor: 2,272 Abstract: This paper presents a novel model for designing a reliable network of facilities in closed-loop supply chain under uncertainty. For this purpose, a bi-objective mathematical programming formulation is developed which minimizes the total costs and the expected transportation costs after failures of facilities of a logistics network. To solve the model, a new hybrid solution methodology is introduced by combining robust optimization approach, queuing theory and fuzzy multi-objective programming. Computational experiments are provided for a number of test problems using a realistic network instance. Key words: Closed-loop supply chain (CLSC); Reliability; Robust optimization; Queuing theory; Fuzzy multi-objective programming URL:

12 Title: Reliable design of a closed loop supply chain network under uncertainty: An interval fuzzy possibilistic chance-constrained model Authors: B. VAHDANI, R. TAVAKKOLI-MOGHADDAM, F. JOLAI, A. BABOLI, Journal: Engineering Optimization (ISI Web of Science), (2012), Vol. 45, No. 6, , Impact factor: 0,962 Abstract: This paper seeks to offer a systematic approach to establishing a reliable network of facilities in closed loop supply chains (CLSCs) under uncertainties. Facilities that are located in this paper concurrently satisfy both traditional objective functions together with reliability considerations in CLSC network designs. To attack this problem, a novel mathematical model is developed that integrates the network design decisions in both forward and reverse supply chain networks. The model also utilizes an effective reliability approach to find a robust network design. In order to make the results of this paper more realistic, a CLSC for a case study in iron and steel industry has been explored. The considered CLSC is multi-echelon, multi-facility, multiproduct and also multi-supplier. Furthermore, multiple facilities exist in the reverse logistics network leading to high complexities. Since the collection centers play an important role in this network, the reliability concept of these facilities is taken into consideration. To solve the proposed model, a novel interactive hybrid solution methodology is developed by combining a number of efficient solution approaches from the recent literature. The proposed solution methodology is a bi-objective interval fuzzy possibilistic chance-constraint mixed integer linear programming (BOIFPCCMILP). Finally, the computational experiments are provided to demonstrate the applicability and suitability of the proposed model in supply chain environment and also help decision makers facilitate their analyses. Key words: Closed loop supply chain; Network design; Reliability; Interval programming; Fuzzy possibilistic; Chance-constrained programming URL:

13 Title: Solving a group layout design model of a dynamic cellular manufacturing system with alternative process routings, lot splitting and flexible reconfiguration by simulated annealing Authors: R. KIA, A. BABOLI, N. JAVADIAN, R. TAVAKKOLI-MOGHADDAM, M. KAZEMI, J. KHORRAMI Journal: Computers & Operations Research (ISI Web of Science), 39 (2012) , Impact factor: 1,909 Abstract: This paper presents a novel mixed-integer non-linear programming model for the layout design of a dynamic cellular manufacturing system (DCMS). In a dynamic environment, the product mix and part demands are varying during a multi-period planning horizon. As a result, the best cell configuration for one period may not be efficient for successive periods, and thus it necessitates reconfigurations. Three major and interrelated decisions are involved in the design of a CMS; namely cell formation (CF), group layout (GL) and group scheduling (GS). A novel aspect of this model is concurrently making the CF and GL decisions in a dynamic environment. The proposed model integrating the CF and GL decisions can be used by researchers and practitioners to design GL in practical and dynamic cell formation problems. Another compromising aspect of this model is the utilization of multi-rows layout to locate machines in the cells configured with flexible shapes. Such a DCMS model with an extensive coverage of important manufacturing features has not been proposed before and incorporates several design features including alternate process routings, operation sequence, processing time, production volume of parts, purchasing machine, duplicate machines, machine capacity, lot splitting, intra-cell layout, inter-cell layout, multi-rows layout of equal area facilities, and flexible reconfiguration. The objective of the integrated model is to minimize the total costs of intra and inter-cell material handling, machine relocation, purchasing new machines, machine overhead and machine processing. Linearization procedures are used to transform the presented non-linear programming model into a linearized formulation. Two numerical examples taken from the literature are solved by the Lingo software using a branch-and bound method to illustrate the performance of this model. An efficient simulated annealing (SA) algorithm with elaborately-designed solution representation and neighborhood generation is extended to solve the proposed model because of its NP-hardness. It is then tested using several problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison with the Lingo software. The obtained results show that the proposed SA is able to find the nearoptimal solutions in computational time, approximately 100 times less than Lingo. Also, the computational results show that the proposed model to some extent overcomes common disadvantages in the existing dynamic cell formation models that have not yet considered layout problems. Key words: Dynamic cellular manufacturing systems; Mixed-integer non-linear programming; Group layout; Multi-rows layout; Flexible reconfiguration; Simulated annealing. URL:

14 Title: A replenishment policy based on joint optimization in a downstream pharmaceutical supply chain: Centralized vs. decentralized replenishment Authors: A. BABOLI, J. FONDREVELLE, R. TAVAKKOLI-MOGHADDAM, Ali MEHRABI Journal: International Journal of Advanced Manufacturing Technology, (ISI Web of Science), (2011), 57: , Impact factor: 1,205 Abstract: This paper considers a number of problems in a pharmaceutical downstream supply chain under specific constraints related to pharmaceutical products (e.g., their expiry date and regulations) and to inventory control (e.g., low prices of products, gift products or prices near zero, shortages prohibited but excess inventory allowed). As traditional models of inventory control and replenishment cannot optimize the total cost of the system, it is very important to consider the transportation cost as well. In this paper, we take into account some of these constraints and propose two models for multi-product replenishment policies, namely centralized and decentralized models. We seek to identify the best quantity and period of replenishment of products for a joint optimization of inventory and transportation costs. The proposed models can be applied to a specific family of products with a stable demand and high turnover rate, low prices (or gift products for some of them) and without any shortage. These two models are compared and the global approach is illustrated by a numerical example taken from a real-case study. Key words: Supply chain; Replenishment policy; Inventory control; Transportation; Pharmaceutical case. URL:

15 Title: A multi-objective stochastic productiondistribution planning problem in an uncertain supply chain considering risk and workers productivity Authors: S. M. J. MIRZAPOUR AL-E-HASHEM, A. BABOLI, S. J. SADJADI, and M.B. ARYANEZHAD, Journal: Mathematical Problems in Engineering, (ISI Web of Science), (2011), Article ID , 14 pages, doi: /2011/406398, Impact factor: 1,383 Abstract: In this paper a multi-objective two stage stochastic programming model is proposed to deal with a multi-period multi-product multi-site production-distribution planning problem for a midterm planning horizon. The proposed model considers two stage decision variables; the variables related to the supplying and producing decisions and the variables related to the distribution decisions. Also our proposed model involves majority of supply chain cost parameters such as transportation cost, inventory holding cost, shortage cost, production cost. Moreover some respects as lead time, outsourcing, employment, dismissal, workers productivity and training are considered. Due to the uncertain nature of the supply chain, it is assumed that cost parameters and demand fluctuations are random variables and follow from a pre-defined probability distribution. To develop a robust stochastic model, an additional objective functions is added to the traditional production-distribution planning problem. So, our multi-objective model includes (i) the minimization of the expected total cost of supply chain, (ii) the minimization of the variance of the total cost of supply chain and (iii) the maximization of the workers productivity through training courses that could be held during the planning horizon. Then, the proposed model is solved applying a hybrid algorithm that is a combination of Monte Carlo sampling method, modified ε-constraint method and L-shaped method. Finally, a numerical example is solved to demonstrate the validity of the model as well as the efficiency of the hybrid algorithm. Key words: production-distribution planning, productivity, ε-constraint method URL:

16 Title: A comprehensive mathematical model for the design of a dynamic cellular manufacturing system integrated with production planning and several manufacturing attributes Authors: F. KHAKSAR-HAGHANI, R. KIA, N. JAVADIAN, R. TAVAKKOLI- MOGHADDAM, A. BABOLI, Journal: International Journal of Industrial Engineering & Production Research, 22(3), 2011, pp Abstract: This paper presents a novel mixed-integer non-linear programming model for the design of a dynamic cellular manufacturing system (DCMS) based on production planning (PP) decisions and several manufacturing attributes. Such an integrated DCMS model with an extensive coverage of important design features has not been proposed yet and incorporates several manufacturing attributes including alternative process routings, operation sequence, processing time, production volume of parts, purchasing machine, duplicate machines, machine depot, machine capacity, lot splitting, material flow conservation equations, inflation coefficient, cell workload balancing, budget constraints for cell construction and machine procurement, varying number of formed cells, worker capacity, holding inventories and backorders, outsourcing part-operations, warehouse capacity, and cell reconfiguration. The objective of the integrated model is to minimize the total costs of cell construction, cell unemployment, machine overhead and machine processing, part-operations setup and production, outsourcing, backorders, inventory holding, material handling between system and warehouse, intra-cell and inter-cell movements, purchasing new machines, and machine relocation/installation/uninstallation. A comprehensive numerical example taken from the literature is solved by the Lingo software to illustrate the performance of the proposed model in handling the PP decisions and to investigate the incorporated manufacturing attributes in an integrated DCMS. Key words: Dynamic cellular manufacturing systems, Mixed-integer non-linear programming, Production planning, Manufacturing attributes. URL:

17 Title: Statistical distribution of the savings induced by sharing demand information in a two-company Beer Game Authors: T. MOYAUX, A. BABOLI, Journal: Production Planning and Control (ISI Web of Science), (2010), pages , Impact factor: 0,600 Abstract: Information sharing (IS) incurs savings that are statistically distributed in supply chains, i.e., companies do not all draw the same benefits from IS. This paper investigates this distribution which causes different inventory and backorder levels to exist, depending on both the position in the supply chain and the IS policy of every company. Our companies may use one of three replenishment policies: (α) no IS, (β) slow IS and (γ) instantaneous IS. Our results show that IS induces savings due to lower inventory and backorder levels, and that the speed of IS increases these savings. We also discuss the goal of replenishment policies in the Beer Game: keeping inventories close to their target levels, in addition to the traditional minimisation of logistic costs. Finally, the Nash equilibria show that companies have incentives to use IS because such collaboration saves money. Key words: Statistical distribution of savings; replenishment policy; information sharing; game theory; Nash equilibrium URL: