Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

Vendor managedi nventory repleni shmenti s a busi ness practi cei n whi ch vendors moni tor thei r customers 'i nventori es, and deci de when and how muchi nventory should be repleni shed. Thei nventory rout i g problem addresses the coordi nati on of i ventory management and transportat ix . The abiS9 y to solve the i ventory routi ng problem contr i utes to the reali(S il of the potentiS sav i gs i i ventory and transportat ix costs brought about by vendor managedi nventory replen ix ment. Thei nventory routi ng problemi s hard, especi allyi f a large number of customersi si nvolved. We formulate thei nventory routi ng problem as a Markov deci si on process, and we propose approxi mati on methods to find good soluti ons wi th reasonable computati onal e#ort. Computati onal results are presented for thei nventory routi ng problem wi thdi rect deli veri es. # Supported by the National Science Foundation under grant DMI-9875400. The inventory routing problem (IRP) is one of the core problems that has to besUW ed when implementing the emergingbus#1HH practice called vendor managed inventory replenishment (VMI). VMI refers to the s tuation where the replenis ment of inventory at a number of locations is controlled by a central decis on maker (vendor). The centraldecisH n maker can be thes upplier and the inventory can be kept at independent cusU4#U, or the centraldecis5# maker can be a manager res ons41# for inventoryreplenis,fi3 t at a number of warehous es or retail outlets of thesW e company. Often the central decis on maker manages a fleet of vehicles that make the deliveries Inthis paper the centraldecisH3 maker is called thes,UD4HD and the inventory locations are referred to as the cus omers VMI di#ers from conventional inventory management in the following way. I...

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.

The inventory routing problem considered in this paper is concerned with the repeated distribution of a commodity, such as heating oil, over a long period of time to a large number of customers. The problem involves a central depot as well as various satellite facilities which the drivers can visit during their shift to refill their vehicles. The customers maintain a local inventory of the commodity. Their consumption varies daily and cannot be predicted deterministically. In case of a stockout, a direct delivery is made and a penalty cost is incurred. In this paper we present incremental cost approximations to be used in a rolling horizon framework for the problem of minimizing the total expected annual delivery costs.

informs ® doi 10.1287/trsc.1030.0054 © 2004 INFORMS In this paper, we present a solution approach for the inventory-routing problem. The inventory-routing problem is a variation of the vehicle-routing problem that arises in situations where a vendor has the ability to make decisions about the timing and sizing of deliveries, as well as the routing, with the restriction that customers are not allowed to run out of product. We develop a two-phase approach based on decomposing the set of decisions: A delivery schedule is created first, followed by the construction of a set of delivery routes. The first phase utilizes integer programming, whereas the second phase employs routing and scheduling heuristics. Our focus is on creating a solution methodology appropriate for large-scale real-life instances. Computational experiments demonstrating the effectiveness of our approach are presented. Key words: inventory routing; vehicle routing; insertion heuristics; clustering; integer programming

Vendor managed inventory replenishment is a business practice in which vendors monitor their customers’ inventories, and decide when and how much inventory should be replenished. The inventory routing problem addresses the coordination of inventory management and transportation. It needs to be solved to design a strategy that realizes the potential savings in inventory and transportation costs brought about by vendor managed inventory replenishment. The inventory routing problem is hard, especially if a large number of customers are involved. We formulate the inventory routing problem as a Markov decision process, and propose approximation methods to find good solutions with reasonable computational effort. Computational results are presented for the direct delivery inventory routing problem. 1

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

Abstract. GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution is found. While, in general, the construction phase of GRASP is a randomized greedy algorithm, other types of construction procedures have been proposed. Repeated applications of a construction procedure yields diverse starting solutions for the local search. This chapter gives an overview of GRASP describing its basic components and enhancements to the basic procedure, including reactive GRASP and intensification strategies. 1.

ABSTRACT: The single-vehicle cyclic inventory routing problem (SV − CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer that is selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each, and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximized while preventing stockouts at each of the selected customers. In this paper, the SV − CIRP is formulated as a mixed-integer program with a nonlinear objective function. After an efficient analysis of the problem, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of an insertion-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV −CIRP. KEYWORDS: Inventory-Routing, Nonlinear Mixed Integer Programming, Exact Algorithms. 1