Haldun Süral

A review of hierarchical facility location models

In this study, we review the hierarchical facility location models. Although there have been a number of review papers on hierarchical facility problems, a comprehensive treatment of models has not been provided since the mid-80s. This review fills the gap in the literature. We first classify the hierarchical facility problems according to the features of systems studied, which are based on flow pattern, service availability at each level of the hierarchy, and spatial configuration of services in addition to the objectives to locate facilities. We then investigate the applications, mixed integer programming models, and solution methods presented for the problem. With an overview of the selected works, we consolidate the main results in the literature. Scope and purpose: Hierarchical systems have to decide about the locations of their interacting facilities within a multiple layer configuration. Although literature on hierarchical location decisions has grown, a review of hierarchical location models has not been published since 1986-1987. In this review, we consolidate the selected material in the literature, including more than 70 studies dated 1986 or later.

Locational analysis for regionalization of Turkish Red Crescent blood services

Abstract After a series of earthquakes in 1999, Turkish Red Crescent (TRC) has engaged in a restructuring for all of its activities, including the blood services. Our study on the blood management system had been started as part of this initiative to restructure the blood services and improve both their effectiveness and efficiency. In the current system of TRC, not much consideration has been given to how the locational decisions affect the performance of blood centers, stations and mobile units. In recent years, however, there has been much discussion regarding the regionalization of the blood management system in Turkey. In this study, we develop several mathematical models to solve the location–allocation decision problems in regionalization of blood services. We report our computational results, obtained by using real data, for TRC blood services. Statement of scope and purpose Regionalization of blood services has been implemented in many countries and found to be successful in resolving the management problems. In this study we formulate several mathematical problems to address the location–allocation aspects of regionalization of blood services of the Turkish Red Crescent Society.

A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem

We address a vendor-managed inventory-routing problem where a supplier (vendor) receives a given amount of a single product each period and distributes it to multiple retailers over a finite time horizon using a capacitated vehicle. Each retailer faces external dynamic demand and is controlled by a deterministic order-up-to level policy requiring that the supplier raise the retailers inventory level to a predetermined maximum in each replenishment. The problem is deciding on when and in what sequence to visit the retailers such that systemwide inventory holding and routing costs are minimized. We propose a branch-and-cut algorithm and a heuristic based on an a priori tour using a strong formulation. To the best of our knowledge, this study is the first to consider a strong formulation for the inventory replenishment part of inventory-routing problems. Computational results reveal that the new branch-and-cut algorithm and heuristic perform better than those noted in the literature.

Hubbing and routing in postal delivery systems

We consider the combined hubbing and routing problem in postal delivery systems and develop an iterative two-stage solution procedure for the problem. In the first stage, hub locations are determined and postal offices are multiply allocated to the hubs. The second stage gives the routes in hub regions that alter the distances between points used in the hub-location problem. The procedure then iterates between two stages by updating the distances used in hubbing in order to produce a route-compatible hub configuration. Computational experience is reported for the test problems taken from the literature. For a case study Turkish postal delivery system data are utilized. As the case study is applied on a road network, a final stage, seeking improvements based on special structures in the routed network, is appended to the two-stage solution procedure.

The Single-Vehicle Routing Problem with Unrestricted Backhauls

Suppose that a private carrier delivers to a set of customers and also has a number of (optional) backhaul opportunities. It wants to choose the best of these, depending on the revenue generated, and insert them in a revised tour. This will be at an expense of deviation from the original tour, because, here, deliveries need not precede backhauls. The problem is to find the mixed tour whose net cost is the lowest, selecting the most profitable backhauls subject to the overall capacity. We thus generalize several other vehicle routing problems with backhauls. A mixed-integer model is developed for the problem. It is based on Miller-Tucker-Zemlin subtour elimination constraints. We address several improvement techniques aimed at increasing computational tractability of the formulation. Computational results show that medium-sized problems can be solved optimally in a reasonable time by using a general-purpose commercial solver.

LAGRANGEAN RELAXATION BASED HEURISTICS FOR LOT SIZING WITH SETUP TIMES

We consider a lot sizing problem with setup times where the objective is to minimize the total inventory carrying cost only. The demand is dynamic over time and there is a single resource of limited capacity. We show that the approaches implemented in the literature for more general versions of the problem do not perform well in this case. We examine the Lagrangean relaxation (LR) of demand constraints in a strong reformulation of the problem. We then design a primal heuristic to generate upper bounds and combine it with the LR problem within a subgradient optimization procedure. We also develop a simple branch and bound heuristic to solve the problem. Computational results on test problems taken from the literature show that our relaxation procedure produces consistently better solutions than the previously developed heuristics in the literature.

Efes Beverage Group Makes Location and Distribution Decisions for its Malt Plants

We conducted a study for Efes Beverage Group to evaluate various sites as potential locations for new malt plants. We performed an economic analysis that showed the inferiority of some alternatives. To evaluate the remaining alternatives, we developed a mixed-integer-programming model that considers both the location of new malt plants and the distribution of barley and malt. It considers the long-run effects of the decisions and minimizes the present value of total costs. Sakarya, Izmir, and Ankara turned out to be the best locations for new malt plants. Efes is currently using the model for distribution decisions. Based on our results and new developments that occurred since then, top managers are currently debating where and when to locate the new malt plants.

Equivalence of the LP relaxations of two strong formulations for the capacitated lot-sizing problem with setup times

The multi-item Capacitated Lot-Sizing Problem (CLSP) has been widely studied in the literature due to its relevance to practice, such as its application in constructing a master production schedule. The problem becomes more realistic with the incorporation of setup times since they may use up significant amounts of the available resource capacity. In this paper, we present a proof to show the linear equivalence of the Shortest Path (SP) formulation and the Transportation Problem (TP) formulation for CLSP with setup costs and times. Our proof is based on a linear transformation from TP to SP and vice versa. In our proof, we explicitly consider the case when there is no demand for an item in a period, a case that is frequently observed in the real world and in test problems in the literature. The equivalence result in this paper has an impact on the choice of model formulation and the development of solution procedures.

On alternative mixed integer programming formulations and LP-based heuristics for lot-sizing with setup times

We address the multi-item, capacitated lot-sizing problem (CLSP) encountered in environments where demand is dynamic and to be met on time. Items compete for a limited capacity resource, which requires a setup for each lot of items to be produced causing unproductive time but no direct costs. The problem belongs to a class of problems that are difficult to solve. Even the feasibility problem becomes combinatorial when setup times are considered. This difficulty in reaching optimality and the practical relevance of CLSP make it important to design and analyse heuristics to find good solutions that can be implemented in practice. We consider certain mixed integer programming formulations of the problem and develop heuristics including a curtailed branch and bound, for rounding the setup variables in the LP solution of the tighter formulations. We report our computational results for a class of instances taken from literature.

The one-warehouse multi-retailer problem: reformulation, classification, and computational results

We consider the one-warehouse multi-retailer problem where a warehouse replenishes multiple retailers with deterministic dynamic demands over a horizon. The problem is to determine when and how much to order to the warehouse and retailers such that the total system-wide costs are minimized. We propose a new (combined transportation and shortest path based) integer programming reformulation for the problem in addition to the echelon stock and transportation based formulations in the literature. We analyze the strength of the LP relaxations of three formulations and show that the new formulation is stronger than others. We also show that the new and transportation based formulations are equivalent for the joint replenishment problem, where the warehouse is a crossdocking facility. We extend all formulations to the case with initial inventory at the warehouse and reveal the relation among their LP relaxations. We present our computational experiments with all formulations over a set of randomly generated test instances.