Halit Üster

Meta-heuristic approaches with memory and evolution for a multi-product production/distribution system design problem

We consider a multi-product two-stage production/distribution system design problem (PDSD) where a fixed number of capacitated distribution centers are to be located with respect to capacitated suppliers (plants) and retail locations (customers) while minimizing the total costs in the system. We present a mixed-integer problem formulation that facilitates the development of efficient heuristic procedures. We provide meta-heuristic procedures, including a population-based scatter search with path relinking and trajectory-based local and tabu search, for the solution of the problem. We also develop efficient construction heuristics and transshipment heuristics that are incorporated into the heuristic procedures for the solution of subproblems. We present extensive computational results that show the high performance of the solution approaches. We obtain smaller than 1.0% average optimality gaps with acceptable runtimes, even for relatively large problems. The computational results also demonstrate the effectiveness of the construction and transshipment heuristics that impact the solution quality and overall runtimes.

Tabu Search and Benders Decomposition Approaches for a Capacitated Closed-Loop Supply Chain Network Design Problem

We consider a network design problem in a multiproduct closed-loop supply chain setting consisting of remanufacturing facilities and finite-capacity manufacturing, distribution, and collection facilities that serve a set of retailers. We first present a mixed-integer linear program to determine the optimal locations of the collection centers and remanufacturing facilities along with the integrated forward and reverse flows such that the total cost of facility location, processing, and transportation associated with forward and reverse flows in the network is minimized. Second, we devise two tabu search heuristics---sequential and random neighborhood search procedures---in which we effectively combine search functions using move and exchange neighborhoods to improve efficiency in exploring the solution space. We also suggest a transshipment heuristic to quickly, but effectively, estimate the objective function value (goodness) of a feasible solution in the course of a tabu search. Third, we present a Benders decomposition solution approach that incorporates the tabu search heuristics as well as Benders cuts that are strengthened to facilitate faster convergence and improved computational efficiency, especially for large-scale instances. While the solutions using tabu search heuristics make the applicability of the Benders decomposition approach possible via providing initial upper bounds and facilitating the generation of good initial Benders cuts, the lower bounds obtained by the Benders approach computationally verify the high quality of the tabu search heuristic solutions. We present computational results illustrating the efficient performance of the solution algorithms in terms of both solution quality and time, especially for larger size problems.

Integrated warehouse location and inventory decisions in a three-tier distribution system

A three-tier distribution network which consists of a single supplier at a given location, a single intermediate warehouse whose location is to be determined, and multiple retailers at given locations is examined. The problem is the integration of warehouse location and inventory replenishment decisions with the objective of minimizing the system-wide transportation and inventory-related costs. The case where the inventory replenishment decisions are coordinated using a power-of-two policy is considered and a mathematical model for the simultaneous computation of the warehouse coordinates and coordinated replenishment policy parameters is developed. The analytical properties of the integrated location-inventory model are characterized and efficient solution methods that rely on these properties are developed. Computational results demonstrating the performance of the proposed heuristic methods and the potential practical impact of integrated decision making for location and inventory decisions are reported. These results indicate that the proposed methods are capable of effectively producing high-quality power-of-two solutions within 6% of the lower bound for the instances tested. The presented analysis is also useful for identifying: (i) the level of interaction between these two types of decisions that are treated separately in the traditional literature; and (ii) problem settings where the integrated location–inventory model offers significant cost savings.

Exact and heuristic algorithms for data-gathering cluster-based wireless sensor network design problem

Data-gathering wireless sensor networks (WSNs) are operated unattended over long time horizons to collect data in several applications such as those in climate monitoring and a variety of ecological studies. Typically, sensors have limited energy (e.g., an on-board battery) and are subject to the elements in the terrain. In-network operations, which largely involve periodically changing network flow decisions to prolong the network lifetime, are managed remotely, and the collected data are retrieved by a user via internet. In this paper, we study an integrated topology control and routing problem in cluster-based WSNs. To prolong network lifetime via efficient use of the limited energy at the sensors, we adopt a hierarchical network structure with multiple sinks at which the data collected by the sensors are gathered through the clusterheads (CHs). We consider a mixed-integer linear programming (MILP) model to optimally determine the sink and CH locations as well as the data flow in the network. Our model effectively utilizes both the position and the energy-level aspects of the sensors while selecting the CHs and avoids the highest-energy sensors or the sensors that are well-positioned sensors with respect to sinks being selected as CHs repeatedly in successive periods. For the solution of the MILP model, we develop an effective Benders decomposition (BD) approach that incorporates an upper bound heuristic algorithm, strengthened cuts, and an ε-optimal framework for accelerated convergence. Computational evidence demonstrates the efficiency of the BD approach and the heuristic in terms of solution quality and time.

Dynamic-demand capacitated facility location problems with and without relocation

We consider two multi-period dynamic-demand capacitated location problems. In the first problem, the facilities are allowed to be relocated in each period, whereas in the second they are kept at a fixed location determined at the beginning of the planning horizon. We provide Lagrangian Relaxation and Benders Decomposition algorithms, including an ϵ-optimal BD algorithm, for the solution for the first model and a Benders Decomposition algorithm for the second. For detailed analysis, we generate a wide variety of instances to test the performance of the algorithms by taking into account varying number of customer locations and time periods in the planning horizon as well as fixed cost structures and facility capacities. We observe that the efficiency of the solution algorithms depends on the input data structure, specifically the cost structures, the facility capacities (which, in turn, dictate the expected number of open facilities), and the variation in the total customer demand from period to period.

An Integrated Outbound Logistics Model for Frito-Lay: Coordinating Aggregate-Level Production and Distribution Decisions

In this paper, we describe research to improve Frito-Lays outbound supply chain activities by simultaneously optimizing its inventory and transportation decisions. Motivated by Frito-Lays practice, we first develop a mixed-integer programming formulation from which we develop a large-scale, integrated multiproduct inventory lot-sizing and vehicle-routing model with explicit (1) inventory holding costs, truck loading and dispatch costs, and mileage costs; (2) production, storage, and truck capacity limitations; and (3) direct (plant-to-store) and interplant (plant-to-plant) delivery considerations. Second, we present an iterative solution approach in which we decompose the problem into inventory and routing components. The results demonstrate the impact of direct deliveries on distribution costs and show that direct deliveries and efficient inventory and routing decisions can provide significant savings opportunities over two benchmark models, one of which represents the existing Frito-Lay system. We implemented our models using an application that allows strategy evaluation, analysis of output files, and technology transfer. This application was particularly useful in evaluating potential direct-delivery locations and inventory reductions throughout the supply chain.

Strategic network design for multi-zone truckload shipments

In recent years, the truckload trucking industry has faced a serious problem in retaining drivers. The primary reason for this problem is the very-long driver tour lengths that keep drivers on the road for extended time periods. In this paper, we present a mathematical model for a multi-zone dispatching method that addresses this issue. In addition to reducing driver tour lengths to desirable levels, the model captures important aspects of other practical problems via unique constraints that address the perspectives of both the truckload company and the customers. Using this model, we first provide insights into various aspects of the problem as well as the nature of the interaction among the problem components that pertain to these perspectives. We later develop a construction heuristic and a tabu search framework, which considers driver tour length constraints (a major determinant of driver turnover rate) to solve the model. We provide computational results illustrating the excellent performance of the proposed solution procedure.

Integrated Bioenergy Supply Chain Network Planning Problem

We consider planning and design of an extended supply chain for bioenergy networks i.e., networks for multibiomass as well as biofuel logistics in an integrated fashion while simultaneously addressing strategic and tactical decisions pertaining to location, production, inventory, and distribution in a multiperiod planning horizon setting. In our modeling, we also explicitly incorporate realistic operational parameters, including biomass deterioration rates and transportation economies of scale. For an efficient solution of our model, we suggest a Benders decomposition-based algorithm that can handle realistic size problems for design and analysis purposes. We implement the approach in a particular way using callback functions, in which the master problem is solved only once; we also develop surrogate constraints for enhanced lower bounds to obtain improved convergence especially for large instances. We provide computational results that demonstrate the efficiency of the solution approach on a wide-ranging set of problem instances. Furthermore, we develop a realistic case using data pertaining to the state of Texas and conduct an extensive analysis on the effects of varying input parameters on the design outcomes for a bioenergy supply chain network.

Formulation of confidence intervals for estimated actual distances

Abstract We devise a new method to calculate the confidence intervals for estimated actual distances. For that purpose, we first develop a prediction error related random variable which is both homoscedastic and normally distributed, and then we use this random variable to devise the confidence interval. Using this method, we develop confidence intervals for two distance predicting functions known as ordinary and weighted sums of order p . We also compare the prediction accuracy of these two distance functions using these confidence intervals and actual distance data from 17 geographical regions. We find that better confidence intervals for the estimated actual distances can be obtained with the weighted sum of order p than the ordinary sum of order p .

Application of a Weighted Sum of Order p to Distance Estimation

Distance functions are employed to estimate actual distances in a transportation network. The ℓbp-norm, which is a weighted sum of order p, is a generalization of the weighted ℓp-norm, a well-known distance-predicting function. We derive some mathematical properties of the new norm and of a goodness-of-fit criterion. These properties are used to develop computational procedures to determine the best-fitting parameter values of the ℓbp-norm for a transportation network. We apply the new norm to 17 geographic regions and find significant improvements in the accuracy of distance estimations over the weighted ℓp-norm.