F. Sibel Salman

A tabu search algorithm for order acceptance and scheduling

We consider a make-to-order production system, where limited production capacity and order delivery requirements necessitate selective acceptance of the orders. Since tardiness penalties cause loss of revenue, scheduling and order acceptance decisions must be taken jointly to maximize total revenue. We present a tabu search algorithm that solves the order acceptance and scheduling problem on a single machine with release dates and sequence dependent setup times. We analyze the performance of the tabu search algorithm on an extensive set of test instances with up to 100 orders and compare it with two heuristics from the literature. In the comparison, we report optimality gaps which are calculated with respect to bounds generated from a mixed integer programming formulation. The results show that the tabu search algorithm gives near optimal solutions that are significantly better compared to the solutions given by the two heuristics. Furthermore, the run time of the tabu search algorithm is very small, even for 100 orders. The success of the proposed heuristic largely depends on its capability to incorporate in its search acceptance and scheduling decisions simultaneously.

A mixed-integer programming approach to the clustering problem with an application in customer segmentation

Abstract This paper presents a mathematical programming based clustering approach that is applied to a digital platform company’s customer segmentation problem involving demographic and transactional attributes related to the customers. The clustering problem is formulated as a mixed-integer programming problem with the objective of minimizing the maximum cluster diameter among all clusters. In order to overcome issues related to computational complexity of the problem, we developed a heuristic approach that improves computational times dramatically without compromising from optimality in most of the cases that we tested. The performance of this approach is tested on a real problem. The analysis of our results indicates that our approach is computationally efficient and creates meaningful segmentation of data.

Approximation Algorithms for a Capacitated Network Design Problem

Abstract We study a capacitated network design problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support the flow at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (ρST + 2) where ρST is the performance ratio of any approximation algorithm for the minimum Steiner tree problem. When all sources have unit demand, the ratio improves to ρST + 1) and, in particular, to 2 when all nodes in the graph are sources.

Emergency facility location under random network damage

Damage to infrastructure, especially to highways and roads, adversely affects accessibility to disaster areas. Predicting accessibility to demand points from the supply points by a systematic model would lead to more effective emergency facility location decisions. To this effect, we model the spatial impact of the disaster on network links by random failures with dependency such that failure of a link induces failure of nearby links that are structurally more vulnerable. For each demand point, a set of alternative paths is generated from each potential supply point so that the shortest surviving path will be used for relief transportation after the disaster. The objective is to maximize the expected demand coverage within a specified distance over all possible network realizations. To overcome the computational difficulty caused by extremely large number of possible outcomes, we propose a tabu search heuristic that evaluates candidate solutions over a sample of network scenarios. The scenario generation algorithm that represents the proposed distance and vulnerability based failure model is the main contribution of our study. The tabu search algorithm is applied to Istanbul earthquake preparedness case with a detailed analysis comparing solutions found in no link failure, independent link failure, and dependent link failure cases. The results show that incorporating dependent link failures to the model improves the covered demand percentages significantly.

Assessing the reliability and the expected performance of a network under disaster risk

In a disaster situation, functionality of an infrastructure network is critical for effective emergency response. We evaluate several probabilistic measures of connectivity and expected travel time/distance between critical origin–destination pairs to assess the functionality of a given transportation network in case of a disaster. The input data include the most likely disaster scenarios as well as the probability that each link of the network fails under each scenario. Unlike most studies that assume independent link failures, we model dependency among link failures and propose a novel dependency model that incorporates the impact of the disaster on the network and at the same time yields tractable cases for the computation of the probabilistic measures. We develop algorithms for the computation of the measures and utilize a Monte Carlo simulation algorithm for the intractable cases. We present a case study of the Istanbul highway system under earthquake risk, and compare different dependency structures computationally.

An adaptive large neighborhood search algorithm for a selective and periodic inventory routing problem

We study a selective and periodic inventory routing problem (SPIRP) and develop an Adaptive Large Neighborhood Search (ALNS) algorithm for its solution. The problem concerns a biodiesel production facility collecting used vegetable oil from sources, such as restaurants, catering companies and hotels that produce waste vegetable oil in considerable amounts. The facility reuses the collected waste oil as raw material to produce biodiesel. It has to meet certain raw material requirements either from daily collection, or from its inventory, or by purchasing virgin oil. SPIRP involves decisions about which of the present source nodes to include in the collection program, and which periodic (weekly) routing schedule to repeat over an infinite planning horizon. The objective is to minimize the total collection, inventory and purchasing costs while meeting the raw material requirements and operational constraints. A single-commodity flow-based mixed integer linear programming (MILP) model was proposed for this problem in an earlier study. The model was solved with 25 source nodes on a 7-day cyclic planning horizon. In order to tackle larger instances, we develop an ALNS algorithm that is based on a rich neighborhood structure with 11 distinct moves tailored to this problem. We demonstrate the performance of the ALNS, and compare it with the MILP model on test instances containing up to 100 source nodes.

Selective and periodic inventory routing problem for waste vegetable oil collection

We consider a biodiesel production company that collects waste vegetable oil from source points that generate waste in large amounts. The company uses the collected waste as raw material for biodiesel production. The manager of this company needs to decide which of the present source points to include in the collection program, which of them to visit on each day, which periodic routing schedule to repeat over an infinite horizon and how many vehicles to operate such that the total collection, inventory and purchasing costs are minimized while the production requirements and operational constraints are met. For this selective and periodic inventory routing problem, we propose two different formulations, compare them and apply the better performing one on a real-world problem with 36 scenarios. We generate lower bounds using a partial linear relaxation model, and observe that the solutions obtained through our model are within 3.28% of optimality on the average. Several insights regarding the customer selection, routing and purchasing decisions are acquired with sensitivity analysis.

Analysis and network representation of hotspots in protein interfaces using minimum cut trees.

We propose a novel approach to analyze and visualize residue contact networks of protein interfaces by graph‐based algorithms using a minimum cut tree (mincut tree). Edges in the network are weighted according to an energy function derived from knowledge‐based potentials. The mincut tree, which is constructed from the weighted residue network, simplifies and summarizes the complex structure of the contact network by an efficient and informative representation. This representation offers a comprehensible view of critical residues and facilitates the inspection of their organization. We observed, on a nonredundant data set of 38 protein complexes with experimental hotspots that the highest degree node in the mincut tree usually corresponds to an experimental hotspot. Further, hotspots are found in a few paths in the mincut tree. In addition, we examine the organization of hotspots (hot regions) using an iterative clustering algorithm on two different case studies. We find that distinct hot regions are located on specific sites of the mincut tree and some critical residues hold these clusters together. Clustering of the interface residues provides information about the relation of hot regions with each other. Our new approach is useful at the molecular level for both identification of critical paths in the protein interfaces and extraction of hot regions by clustering of the interface residues. Proteins 2010.

Deployment of field hospitals in mass casualty incidents

We propose an analysis framework to determine the location and size of emergency service facilities to be established after a disaster to cope with the demand surge. We utilize a multi-period mixed integer programming (MIP) model that simultaneously optimizes capacity allocation and casualty transportation decisions in order to provide emergency transportation and medical care services to the largest number of casualties in shortest time. The objectives are to minimize the total travel and waiting time of casualties over the search-and-rescue period and the total cost of establishing new facilities. The model minimizes a weighted sum of these objectives subject to the availability of vehicles and service capacity at existing and new facilities in each period. We provide a detailed case study of a large-scale emergency due to an expected earthquake in Istanbul to demonstrate the two-level solution approach. Service requests over time and travel times are generated with respect to regional vulnerabilities and road network conditions. Solutions and sensitivity analysis reveal the resource needs and service performance to guide preparedness strategies.

Solving the Capacitated Local Access Network Design Problem

We propose an exact solution method for a routing and capacity installation problem in networks. Given an input graph, the problem is to route traffic from a set of source nodes to a sink node and to install transmission facilities on the edges of the graph to accommodate the flow at minimum cost. We give a branch-and-bound algorithm that solves relaxations obtained by approximating the noncontinuous cost function by its lower convex envelope. The approximations are refined by branching on the flow ranges on selected edges. Our computational experiments indicate that this method is effective in solving moderate-size problems and provides very good candidate solutions early in the branch-and-bound tree.