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 difcult to solve. Even the feasibility problem becomes combinatorial when setup times are considered. This difculty in reaching optimality and the practical relevance of CLSP make it important to design and analyse heuristics to nd 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

Multi-item lot sizing problem with setup times

Ph.D. - Doctoral Progra

A polynomial algorithm for the earthwork allocation problem with borrow and waste site selection

In road construction projects, earthwork is planned together with horizontal and vertical alignments. This study focuses on earthwork operations that basically include cutting the hills and filling the holes on the road path. The candidate borrow and waste sites can also be used to obtain or heap earth when the available cut and fill amounts are not balanced or operating these sites reduces the total earthwork cost. Total earthwork cost contains the transportation cost and the overall cost related to opening the candidate sites. The problem is to determine which borrow and waste sites to operate, and the earth flows between cut, fill, waste, and borrow sites such that the total cost is minimized. It is shown that the problem is a generalization of the well-known lot-sizing problem. A fixed charge network flow problem formulation is presented, and a polynomial time dynamic programming algorithm is developed for solving the problem

Locating mobile facilities in railway construction management

The location problem with mobile facilities is motivated by a real-life railway construction project. In railway construction, (im)mobile concrete batching facilities are located to build viaducts and tunnels on a line over a planning horizon. The problem is to determine the number and types of facilities to be located, to schedule the movement of mobile facilities, and to make concrete production-allocation decisions, so that all requirements are satisfied, facility capacities are not violated, and the total cost is minimized. To the best of our knowledge, such a problem has not been studied in the literature before. Two mathematical models and a preprocessing heuristic are developed to solve the problem. Computational results on the real case study problem and randomly generated test problem instances show that locational decisions are important in construction management

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

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. (C) 2003 Wiley Periodicals, Inc

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

A single supplier-single retailer system with an order-up-to level inventory policy

We consider a two-level vendor-managed system in which external demand occurs only at a retailer and a supplier replenishes the retailer employing an order-up-to S policy over T periods. We present an O(T-3) algorithm to coordinate the system when S is known. We also show that S can be optimized in O(aT(3)) time for an input parameter a

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 retailer's 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