Necati Aras

Optimal Prices and Trade-in Rebates for Durable, Remanufacturable Products

Most durable products have two distinct types of customers: first-time buyers and customers who already own the product, but are willing to replace it with a new one or purchase a second one. Firms usually adopt a price-discrimination policy by offering a trade-in rebate only to the replacement customers to hasten their purchase decisions. Any return flow of products induced by trade-in rebates has the potential to generate revenues through remanufacturing operations. In this paper, we study the optimal pricing/trade-in strategies for such durable, remanufacturable products. We focus on the scenario where the replacement customers are only interested in trade-ins. In this setting, we study three pricing schemes: (i) uniform price for all customers, (ii) age-independent price differentiation between new and replacement customers (i.e., constant rebate for replacement customers), and (iii) age-dependent price differentiation between new and replacement customers (i.e., age-dependent rebates for replacement customers). We characterize the roles that the durability of the product, the extent of return revenues, the age profile of existing products in the market, and the relative size of the two customer segments play in shaping the optimal prices and the amount of trade-in rebates offered. Throughout the paper we highlight the operational decisions that might influence the above factors, and we support our findings with real-life practices. In an extensive numerical study, we compare the profit potential of different pricing schemes and quantify the reward (penalty) associated with taking into account (ignoring) customer segmentation, the price-discrimination option, return revenues, and the age profile of existing products. On the basis of these results, we are able to identify the most favorable pricing strategy for the firm when faced with a particular market condition and discuss implications on the life-cycle pricing of durable, remanufacturable products.

The effect of categorizing returned products in remanufacturing

An increasing number of companies have been implementing comprehensive recycling and remanufacturing programs. These endeavors typically involve the operation of joint manufacturing and remanufacturing systems. One of the major challenges in managing such hybrid systems is the stochastic nature of product returns. In particular, there is significant variability in the condition of the returns. This paper presents an approach for assessing the impact of quality-based categorization of returned products. Through extensive numerical studies on a continuous-time Markov chain model, we show that incorporation of returned product quality in the remanufacturing and disposal decisions can lead to significant cost savings. We find that these savings are amplified as the return quality decreases, and as the return rate increases. We also show that prioritizing higher quality returns in remanufacturing is, in general, a better strategy.

Locating collection centers for incentive-dependent returns under a pick-up policy with capacitated vehicles

We address the problem of locating collection centers of a company that aims to collect used products from product holders. The remaining value in the used products that can be captured by recovery operations is the companys motivation for the collection operation. We assume that a pick-up strategy is in place according to which vehicles with limited capacity are dispatched from the collection centers to the locations of product holders to transport the returns. Each product holder has an inherent willingness to return, and makes the decision on the basis of the financial incentive offered by the company. The incentive depends on the condition of the returned item referred to as return type. We formulate a mixed-integer nonlinear facility location-allocation model to find both the optimal locations of a predetermined number of collection centers and the optimal incentive values for different return types. Since the problem is , we propose a heuristic method to solve medium and large-size instances. The main loop of the method is based on a tabu search method performed in the space of collection center locations. For each location set prescribed by tabu search, Nelder-Mead simplex search is called to obtain the best incentives and the corresponding net profit. We experiment with different quality profiles when there are two and three return types, and observe the effect of the uniform incentive policy (UIP) in which the same incentive is offered to product holders regardless of the quality of their returns. We conclude that the UIP is inferior to the quality-dependent incentive policy resulting in a higher profit loss when the proportion of lowest quality returns is relatively high.

The Kohonen network incorporating explicit statistics and its application to the travelling salesman problem

In this paper we introduce a new self-organizing neural network, the Kohonen Network Incorporating Explicit Statistics (KNIES) that is based on Kohonens Self-Organizing Map (SOM). The primary difference between the SOM and the KNIES is the fact that every iteration in the training phase includes two distinct modules-the attracting module and the dispersing module. As a result of the newly introduced dispersing module the neurons maintain the overall statistical properties of the data points. Thus, although in SOM the neurons individually find their places both statistically and topologically, in KNIES they collectively maintain their mean to be the mean of the data points, which they represent. Although the scheme as it is currently implemented maintains the mean as its invariant, the scheme can easily be generalized to maintain higher order central moments as invariants. The new scheme has been used to solve the Euclidean Travelling Salesman Problem (TSP). Experimental results for problems taken from TSPLIB [Reinelt, G. (1991). TSPLIB-A travelling salesman problem library. ORSA Journal on Computing, 3, pp. 376-384] indicate that it is a very accurate NN strategy for the TSP-probably the most accurate neural solutions available in the literature.

A two-echelon stochastic facility location model for humanitarian relief logistics

We develop a two-stage stochastic programming model for a humanitarian relief logistics problem where decisions are made for pre- and post-disaster rescue centers, the amount of relief items to be stocked at the pre-disaster rescue centers, the amount of relief item flows at each echelon, and the amount of relief item shortage. The objective is to minimize the total cost of facility location, inventory holding, transportation and shortage. The deterministic equivalent of the model is formulated as a mixed-integer linear programming model and solved by a heuristic method based on Lagrangean relaxation. Results on randomly generated test instances show that the proposed solution method exhibits good performance up to 25 scenarios. We also validate our model by calculating the value of the stochastic solution and the expected value of perfect information.

Binary integer programming formulation and heuristics for differentiated coverage in heterogeneous sensor networks

Coverage is a fundamental task in sensor networks. We consider the minimum cost point coverage problem and formulate a binary integer linear programming model for effective sensor placement on a grid-structured sensor field when there are multiple types of sensors with varying sensing quality and price. The formulation is general and can be adapted to handle situations where sensing is perfect, imperfect or uncertain, and the coverage requirements are differentiated. Unfortunately, the new model suffers from the intractability of the binary integer programming formulations. We therefore suggest approximation algorithms and heuristics. Computational results indicate that the heuristic based on Lagrangean relaxation outperforms the others in terms of solution quality.

Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution

We are concerned with a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at predetermined candidate sites. We employ Huffs gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find the optimal solution of this model, we convert it into an equivalent one-level mixed-integer nonlinear program so that it can be solved by global optimization methods. Apart from reporting computational results obtained on a set of randomly generated instances, we also compute the benefit the leader firm derives from anticipating the competitors reaction of adjusting the attractiveness levels of its facilities. The results on the test instances indicate that the benefit is 58.33% on the average.

Wireless sensor network lifetime maximization by optimal sensor deployment, activity scheduling, data routing and sink mobility

The longevity of Wireless Sensor Networks (WSNs) is a crucial concern that significantly influences their applicability in a specific context. Most of the related literature focuses on communication protocols aiming to reduce the energy consumption which would eventually lead to longer network lifetimes. On the other hand, a limited number of studies concentrate on providing a unifying frame to investigate the integrated effect of the important WSN design decisions such as sensor places, activity schedules, data routes, trajectory of the mobile sink(s), along with the tactical level decisions including the data propagation protocols. However, a monolithic mathematical optimization model with a practically applicable, efficient, and accurate solution method is still missing. In this study, we first provide a mathematical model which integrates WSN design decisions on sensor places, activity schedules, data routes, trajectory of the mobile sink(s) and then present two heuristic methods for the solution of the model. We demonstrate the efficiency and accuracy of the heuristics on several randomly generated problem instances on the basis of extensive numerical experiments.

A bilevel fixed charge location model for facilities under imminent attack

We investigate a bilevel fixed charge facility location problem for a system planner (the defender) who has to provide public service to customers. The defender cannot dictate customer-facility assignments since the customers pick their facility of choice according to its proximity. Thus, each facility must have sufficient capacity installed to accommodate all customers for whom it is the closest one. Facilities can be opened either in the protected or unprotected mode. Protection immunizes against an attacker who is capable of destroying at most r unprotected facilities in the worst-case scenario. Partial protection or interdiction is not possible. The defender selects facility sites from m candidate locations which have different costs. The attacker is assumed to know the unprotected facilities with certainty. He makes his interdiction plan so as to maximize the total post-attack cost incurred by the defender. If a facility has been interdicted, its customers are reallocated to the closest available facilities making capacity expansion necessary. The problem is formulated as a static Stackelberg game between the defender (leader) and the attacker (follower). Two solution methods are proposed. The first is a tabu search heuristic where a hash function calculates and records the hash values of all visited solutions for the purpose of avoiding cycling. The second is a sequential method in which the location and protection decisions are separated. Both methods are tested on 60 randomly generated instances in which m ranges from 10 to 30, and r varies between 1 and 3. The solutions are further validated by means of an exhaustive search algorithm. Test results show that the defenders facility opening plan is sensitive to the protection and distance costs. Highlights? We investigate a bilevel fixed charge facility location problem for a system planner (the defender) who has to provide public service to customers by opening facilities at candidate locations. ? Facilities can be opened either in the protected or unprotected mode. Protection immunizes against an attacker who is capable of destroying at most r unprotected facilities in the worst-case scenario. Partial protection or interdiction is not possible. ? The problem is formulated as a static Stackelberg game between the defender (leader) and the attacker (follower). ? Two solution methods are proposed. The first is a tabu search heuristic where a hash function calculates and records the hash values of all visited solutions for the purpose of avoiding cycling. The second is a sequential method in which the location and protection decisions are separated. ? The produced solutions are validated by means of an exhaustive search algorithm.

The budget constrained r-interdiction median problem with capacity expansion

In this article, we elaborate on a budget constrained extension of the r-interdiction median problem with fortification (RIMF). The objective in the RIMF is to find the optimal allocation of protection resources to a given service system consisting of p facilities so that the disruptive effects of r possible attacks to the system are minimized. The defender of the system needs to fortify q facilities of the present system to offset the worst-case loss of r non-fortified facilities due to an interdiction in which the attacker’s objective is to cause the maximum possible disruption in the service level of the system. The defender-attacker relationship fits a bilevel integer programming (BIP) formulation where the defender and attacker take on the respective roles of the leader and the follower. We adopt this BIP formulation and augment it with a budget constraint instead of a predetermined number of facilities to be fortified. In addition, we also assume that each facility has a flexible service capacity, which can be expanded at a unit cost to accommodate the demand of customers who were serviced by some other interdicted facility before the attack. First, we provide a discrete optimization model for this new facility protection planning scenario with a novel set of closest assignment constraints. Then, to tackle this BIP problem we use an implicit enumeration algorithm performed on a binary tree. For each node representing a different fortification scheme, the attacker’s problem is solved to optimality using Cplex 11. We report computational results obtained on a test bed of 96 randomly generated instances. The article concludes with suggestions for future research.