The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NP-hard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2-exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3-exchange or 4-exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very large-scale neighborhood search algorithms give consistently better solutions compared the popular 2-exchange neighborhood algorithms considering both the solution time and solution accuracy.

Vendor managed resupply is an emerging trend in logistics and refers to situations in which a supplier manages the inventory replenishment of its customers. Vendors save on distribution cost by being able to better coordinate deliveries to di erent customers, and customers do not have to dedicate resources to inventory management. We present and discuss the inventory routing problem. The inventory routing problem captures the basic characteristics of situations where vendor managed resupply may be used, and methodologies developed for its solution could become building blocks for logistics planning systems.

This work is motivated by the need to solve the inventory routing problem when implementing a business practice called vendor managed inventory replenishment (VMI). With VMI, vendors monitor their customers ’ inventories, and decide when and how much inventory should be replenished at each customer. The inventory routing problem attempts to coordinate inventory replenishment and transportation in such a way that the cost is minimized over the long run. We formulate a Markov decision process model of the stochastic inventory routing problem, and propose approximation methods to find good solutions with reasonable computational effort. We indicate how the proposed approach can be used for other Markov decision processes involving the control of multiple resources. ∗ Supported by the National Science Foundation under grant DMI-9875400.

This paper reviews recent work on integrated analysis of production-distribution systems, and identifies important areas where further research is needed. By integrated analysis we understand analysis performed on models that integrate decisions of different production and distribution functions for a simultaneous optimization. We review work that explicitly considers the transportation system in the analysis, since we are interested in the following questions: (i) How have logistics aspects been included in the integrated analysis? and (ii) What competitive advantages, if any, have been obtained from the integration of the distribution function to other production functions within a company and among different companies? In our review we also mention whether the work has been done at the strategic level, i.e. if it concerns the design of the distribution system, or at the tactical level, i.e. if it concerns optimization problems for which the characteristics of the distribution system are provided.

The capacitated arc routing problem (CARP) has attracted much attention during the last few years due to its wide applications in real life. Since CARP is NP-hard and exact methods are only applicable to small instances, heuristic and metaheuristic methods are widely adopted when solving CARP. In this paper, we propose a memetic algorithm, namely memetic algorithm with extended neighborhood search (MAENS), for CARP. MAENS is distinct from existing approaches in the utilization of a novel local search operator, namely Merge-Split (MS). The MS operator is capable of searching using large step sizes, and thus has the potential to search the solution space more efficiently and is less likely to be trapped in local optima. Experimental results show that MAENS is superior to a number of state-of-the-art algorithms, and the advanced performance of MAENS is mainly due to the MS operator. The application of the MS operator is not limited to MAENS. It can be easily generalized to other approaches.

The typical inventory routing problem deals with the repeated distribution of a single product from a single facility with an unlimited supply to a set of customers that can all be reached with out-and-back trips. Unfortunately, this is not always the reality. We introduce the inventory routing problem with continuous moves to study two important real-life complexities: limited product availabilities at facilities and customers that cannot be served using out-and-back tours. We need to design delivery tours spanning several days, covering huge geographic areas, and involving product pickups at different facilities. We develop an innovative randomized greedy algorithm, which includes linear programming based postprocessing technology, and we demonstrate its effectiveness in an extensive computational study. 1

In this paper, we study the distribution network design problem integrating transportation and infinite horizon multi-echelon inventory cost function. We consider the trade o# between inventory cost, direct shipment cost and facility location cost in such system. The problem is to determine how many warehouses to set up, where to locate them, how to serve the retailers using these warehouses, and to determine the optimal inventory policies for the warehouses and retailers. The objective is to minimize the total multi-echelon inventory, transportation and facility location costs. To the best of our knowledge, none of the papers in the area of distribution network design has explicitly addressed the issues of 2-echelon inventory cost function arising from co-ordination of replenishment activities between the warehouses and the retailers. We structure this problem as a set-partitioning integer-programming model. The pricing problem that arises from the column generation algorithm gives rise to a new class of submodular function minimization problem. We show that this pricing problem can be solved in O(n log n) time, where n is the number of retailers. Computational results show that large distribution network design problem can be solved e#ciently via this approach. 1 1