August 2012


 Résumé (opens in a new window)

 Statistics in a nutshell

  Research statement 

 Ongoing research


 List of journal publications

 Books, book chapters and proceedings

 Analysis of citations


 Doctoral Dissertation 

Early Years at Koç University

Recent Research Topics of Focus


During my doctoral study at Krannert Graduate School of Management of Purdue University I worked under the supervision of Prof. Kemal Altinkemer. My major degree was in management information systems (MIS) / optimization track and my minor was in Industrial Engineering. I committed myself to three independent research topics:

  1. Single-Item Dynamic Lot-Sizing with Immediate Lost Sales.

  2. Optimal Routing in Message Switched and Cell Relay Networks with Time Restrictions as Quality of Service Guarantees.

  3. Logistics of the Conversion from the "Brick-and-mortar" to "Click-and-mortar" Retailing Model:
    A Location-Routing Problem With Two Echelons and Two Types of Customers

The first topic was derived from my project in an MIS doctoral seminar class. I used dynamic programming techniques to solve a deterministic single-item lot-sizing problem that was incorporating lost sales and period dependent variable and fixed costs. Out of this research was born my ever first SCI journal paper [EJOR2003] which is the only such paper I published before coming to Koç University. It is also the one which received the highest number of citations to date both according to Scopus and Web of Science (see my citations report here). In this paper I coined the term conservation period used for the first time in the lot-sizing literature. It implies a period of the planning horizon in which the producer or supplier deliberately fails to meet customer's demand despite the availability of goods in the inventory.

The second topic was inspired by a previous study of Ph.D. advisor Kemal Altinkemer with his Ph.D. advisor Bezalel Gavish. In this research, I analyzed the problem of determining the primary routes used by two priority classes of messages or cells for each communicating origin—destination (O/D) pair
in message switched and Asynchronous Transfer Mode (ATM) networks. The networks are modeled as M/M/1 and Mx/D/1 priority queues with two priorities. The goal is to determine routes that satisfy time constraints for communicating pairs with high priority messages. These are taken as the Quality of Service (QoS) guarantees. No time constraints exist for the sessions in the second (low priority) class. The problem is formulated as an integer programming problem. The lower bounds on the optimal solution of the problem are obtained by Lagrangian Relaxation embedded in a subgradient optimization procedure. O/D time restrictions are handled through an Augmented Lagrangian Relaxation procedure. A heuristic method obtains a feasible routing plan satisfying time restrictions. This topic helped me master the Augmented Lagrangian Relaxation methodology, which I utilized also in my thesis problem, i.e., the third research topic. A working paper and a conference presentation by my advisor came out of this second research topic, but no paper was published in any journal.

The third research topic became later my Ph.D. thesis and gave rise to my only thesis paper [EJOR2008a] published in the European Journal of Operational Research in 2008. In my thesis I looked at the static cross-docking problem of a retailer that evolves from a traditional "bricks-and-mortar" business with physical facilities such as stores and warehouses into a hybrid "clicks-and-mortar" retailer with a virtual storefront on the Web. By engaging in e-commerce the retailer begins to serve online customers in addition to his traditional walk-in/drive-in customers. The orders of this new type of customers, i.e., the online orders can be delivered either from stores or directly from warehouses. The retailer is faced with the decision problem of which new Internet-enabled stores to open, which ones to close, and which ones to convert such that they too can process and deliver online orders. I modeled this problem as a two-echelon (3-tier) location-routing problem with time restrictions. While the distance between home and the nearest open store is used as a proxy measure for walk-in customers, a QoS guarantee for online customers is timely delivery of their orders.

I used Lagrangian Relaxation embedded in a subgradient optimization procedure as the main solution technique which decomposes the comprehensive problem into two subproblems. One of the subproblems is solved to optimality using Cplex, whereas an Augmented Lagrangian Relaxation is employed to solve the other one. To my knowledge, [EJOR2008a] is the first study in the literature that effectively integrates an augmented Lagrangian relaxation technique inside another Lagrangian relaxation algorithm.

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After joining Koç University in January 2003, I continued to work on the legacy of my doctoral research topics. The research of my thesis paper [EJOR2008a] was completed only in 2007.

I authored alone another lot-sizing paper, namely [COR2007] which looks into the cost of customer goodwill loss in lot-sizing problems with immediate lost sales. As far as I know, it is the ever first paper that models the loss of customer goodwill as a reduction in the demand of the next period which is equal to a fraction of the unmet demand in the current period.

Provoked by the complexity of the research in my Ph.D. thesis, I ventured the vast area of vehicle routing problems (VRPs). Personally I find all sorts of combinatorial optimization problems in collection and distribution logistics irresistibly challenging. I worked with Zeynep Özyurt on an open-route vehicle routing problem (OVRP). Zeynep was my first MS student at Koç University, and I had recruited her actually to investigate compound Lagrangian relaxation methods for the uncapacitated single-echelon location routing problem (LRP). We wrote a book chapter from her thesis research, while the extracurricular work led to an effective tabu search application for an open vehicle routing problem with driver nodes and time deadlines. The findings of the latter research were first published in [OR2005b], later in [JORS2007]. Our paper [JORS2007] which was published in the Journal of the Operational Research Society is one of the earliest papers in the literature that tackles a time constrained OVRP.

My interest in modeling lost sales and customer selection in service systems prevailed also in my vehicle routing research. A peer-reviewed paper, namely [OR2005a] made its way into the edited book of the OR2005 conference held in Bremen in September 2005. This conference proceeding is the first article in the literature dealing with the net profit maximizing (selective) version of the classical capacitated VRP. We proposed a Clarke-Wright parallel savings-based heuristic involving an iterative marginal profit analysis (iMPA) to obtain good feasible solutions to the selective VRP with time deadlines.

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Reverse logistics attracted my attention in early 2006. I focused on facility location-allocation and vehicle routing problems which arise in the context of the collection of end-of-life (EOL) and end-of-use (EOU) products from dealers and customers. EOL/EOU products are utilized in remanufacturing, saving significant resources and thereby conserving the environment. The solution of this class of problems certainly requires combinatorial optimization skills merged with heuristic optimization techniques.

My research stream in reverse logistics can be scrutinized in two branches:

  1. Models involving facility location-allocation and pricing decisions for the acquisition (the buyback) of used products from customers (product holders).

  2. Models involving vehicle and inventory routing decisions along with the selection of customers to be included on the collection program.

The first branch gave birth to three journal papers and one IEEE proceeding as listed below:

In the above papers we approximated the inherent willingness of a customer to return his or her used product (this is, the probability of this event) with a uniform distribution over a certain range that is dependent on the quality of the product and the customer's reservation price for it. We analyzed both drop-off and pickup policies for the collecting company (either the remanufacturing company or a collection agency). In the latter policy, the company operates a homogeneous fleet of capacitated vehicles to pick up used products from customer sites. In the former policy, customers travel from their home addresses to the closest available collection center to drop off the used products in their possession and to claim their incentive (buyback price). Therefore, the proximity of the collection center is also a critical factor in making the difference between the customers who agree to participate in the collection campaign and the ones who decline to do so.

A distinguishing feature of the proposed models is that they all embrace multiple quality classes (types) of used products. The higher quality a used product, the higher reservation price set by its owner, thus the higher the incentive to be offered by the company. At the end of the day, the company has to apply quality differentiation when it announces the buyback prices (incentives) to the product holders.

The last two papers investigated two interrelated leader-follower games between the government and the company involved in product recovery. Since the company seeks only economic profitability, the collected amounts may not be aligned with the target collection ratio imposed by the government. In this case, the government may alleviate the under-collection issue through a subsidy paid to the company for each used product collected from customers. From the government’s perspective the problem is to find the minimum subsidy level while meeting the target collection ratio. This model is called the supportive model where the company itself is not bound by the minimum collection ratio target of the government. In the alternative legislative model the responsibility of the minimum collection ratio is on the shoulders of the company. However, the company requests a minimum profitability warranty from the government.


In the second branch of my reverse logistics studies I looked into the static collection of WEEE (waste electrical and electronic equipment) from equipment dealers and the periodic collection of waste vegetable oil from hospitals, hotels, restaurants, schools, etc. for biodiesel production. The former problem deals with a selective multi-depot vehicle routing problem involving minimum incentive payment decisions. The latter problem reckons with the accumulation of waste oil at source nodes. The amount of oil which is generated, but not collected at a given source is carried over from the current to the next period. Hence, this routing problem falls under the category of periodic inventory routing problems (PIRPs). While both problems feature customer selection, the outsourcing option is included only in the PIRP.

The following publications appeared hitherto from my reverse logistics research involving vehicle and inventory routing decisions:

In the first two works cited above, we developed a tabu search algorithm with strategic oscillation to solve the described multi-depot vehicle routing problem.

In the last one, we exclusively used the software industry's standard mixed-integer programming (MIP) solver Cplex 12.2 called from the mathematical modeling suite GAMS 23.6. We conducted a very extensive computational study to test the efficiency of two different MIP formulations enhanced with a variety of valid inequalities. To further tighten the lower bounds, we developed a partial linear relaxation scheme which is explained in the paper. All computer experiments with the two models were performed on real-world distance data extracted from Google Maps using its application programming interface (API). The cost data of two different vehicle models was also incorporated into the experiments. On the basis of the computational results, we were able to recommend one of the vehicle models over the other.

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As I also mention on the Ongoing Research page of this website, facility interdiction models in median and coverage type service networks appealed to me since 2007. I was introduced to this subject after reading the "online first" version of Scaparra and Church's paper (Comput Oper Res, 2008) about protection of critical infrastructure. In that paper which profoundly affected the direction of my research the protection of a limited number of facilities against a fixed number of interdictions by an attacker was modeled as a leader-follower game (also known as Stackelberg Game). A leader-follower game is equivalent to a bilevel programming problem (BPP) which is known to be an NP-hard optimization problem even when both the upper and the lower levels are linear.

Scaparra and Church (2008) were describing an intelligent search method implemented on a binary enumeration tree (BET) to solve the BPP. The problem involves binary decision variables both in the upper level (leader's problem) and in the lower level (follower's problem). As a future research direction, the paper was suggesting to impose a budget constraint on the number of protections and to consider capacity expansions at those facilities which survive interdictions. Following in the footsteps of the authors, this is exactly what I did in my first facility interdiction paper [CEJOR2010] published in Central European Journal of Operations Research in 2010. In that paper of mine I also showed that the Closest Assigment (CA) constraints proposed in Scaparra and Church are not sufficient alone, thus need to be complemented with a set of logical constraints. The logical constraints ensure feasible assignment of customers to the closest intact facilities when capacity expansion costs are also added to the attacker's objective function. 

This facility protection/interdiction paper paved the road to three further papers and one book chapter. My publication record in this subject is as follows as of August 26, 2012:

The book chapter and two of the papers examine a mixed-integer bilevel programming problem (MIBPP) which corresponds to the leader-follower game between a defender (system planner) and an attacker. The defender is the leader of the problem who decides--given a set of candidate locations--where to open service facilities. The protection mode of each opened facility (protected, hence immune to any attack, or unprotected, hence vulnerable in the event of an attack) is also decided by the defender. The pre-attack customer-facility assignments follow automatically according to CA constraints. When it is the turn of the attacker, he decides which r facilities to destroy beyond repair such that the total system cost is maximized. The total system cost is comprised of the sum of capacity expansion costs at non-interdicted facilities and the sum of post-attack demand-weighted traveling costs between all customers and their respective closest facilities surviving the attack.

My most recent paper in this research venue, namely [COR2014] captures an even smarter attacker who is capable of allocating his limited resources to the partial interdiction of capacitated facilities with only one thing in his mind: Inflicting the ever worst possible disruption on service delivery by  obliterating arbitrary fractions of capacities. This problem is also modeled as a MIBPP. However, this time the leader is the attacker, and there are continuous decision variables in the upper level problem, while the defender's problem (lower level problem) preserves its binary variables.

As can be seen in my accepted paper, I developed and tuned a sophisticated revised simplex search-based method which is applied as a stochastic multi-start algorithm. Actually, the method can be considered a matheuristic since an exact solution technique based on the Cplex solver is embedded in it to get the proven optimal solution of the lower level problem (defender's problem). The method compares quite well against a progressive grid search method (PGS) which requires enormous solution times when there exist more than nine facilities in the problem.

How I shall proceed to work on this challenging facility interdiction problem is explained on the Ongoing Research page.

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Last updated on 22-10-2014 by Deniz Aksen  ©2003-2012

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