Francisco Saldanha-da-Gama

Facility location and supply chain management - A review

Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, a literature review of facility location models in the context of supply chain management is given. We identify basic features that such models must capture to support decision-making involved in strategic supply chain planning. In particular, the integration of location decisions with other decisions relevant to the design of a supply chain network is discussed. Furthermore, aspects related to the structure of the supply chain network, including those specific to reverse logistics, are also addressed. Significant contributions to the current state-of-the-art are surveyed taking into account numerous factors. Supply chain performance measures and optimization techniques are also reviewed. Applications of facility location models to supply chain network design ranging across various industries are presented. Finally, a list of issues requiring further research are highlighted.

Multi-period reverse logistics network design

The configuration of the reverse logistics network is a complex problem comprising the determination of the optimal sites and capacities of collection centers, inspection centers, remanufacturing facilities, and/or recycling plants. In this paper, we propose a profit maximization modeling framework for reverse logistics network design problems. We present a mixed-integer linear programming formulation that is flexible to incorporate most of the reverse network structures plausible in practice. In order to consider the possibility of making future adjustments in the network configuration to allow gradual changes in the network structure and in the capacities of the facilities, we consider a multi-period setting. We propose a multi-commodity formulation and use a reverse bill of materials in order to capture component commonality among different products and to have the flexibility to incorporate all plausible means in tackling product returns. The proposed general framework is justified by a case study in the context of reverse logistics network design for washing machines and tumble dryers in Germany. We conduct extensive parametric and scenario analysis to illustrate the potential benefits of using a dynamic model as opposed to its static counterpart, and also to derive a number of managerial insights.

Solving the variable size bin packing problem with discretized formulations

In this paper we study the use of a discretized formulation for solving the variable size bin packing problem (VSBPP). The VSBPP is a generalization of the bin packing problem where bins of different capacities (and different costs) are available for packing a set of items. The objective is to pack all the items minimizing the total cost associated with the bins. We start by presenting a straightforward integer programming formulation to the problem and later on, propose a less straightforward formulation obtained by using a so-called discretized model reformulation technique proposed for other problems (see [Gouveia L. A 2n constraint formulation for the capacitated minimal spanning tree problem. Operations Research 1995; 43:130-141; Gouveia L, Saldanha-da-Gama F. On the capacitated concentrator location problem: a reformulation by discretization. Computers and Operations Research 2006; 33:1242-1258]). New valid inequalities suggested by the variables of the discretized model are also proposed to strengthen the original linear relaxation bounds. Computational results (see Section 4) with up to 1000 items show that these valid inequalities not only enhance the linear programming relaxation bound but may also be extremely helpful when using a commercial package for solving optimally VSBPP.

The capacitated single-allocation hub location problem revisited: A note on a classical formulation

In this paper a well-known formulation for the capacitated single-allocation hub location problem is revisited. An example is presented showing that for some instances this formulation is incomplete. The reasons for the incompleteness are identified leading to the inclusion of an additional set of constraints. Computational experiments are performed showing that the new constraints also help to decrease the computational time required to solve the problem optimally.

On the capacitated concentrator location problem: a reformulation by discretization

In this paper, we present and discuss a discretized model for the two versions of the capacitated concentrator location problem: a simple version (SCCLP) and a version with modular capacities (MCCLP). We show that the linear programming relaxation of the discretized model is at least as good as the linear programming relaxation of conventional models for the two variations of the problem under study. A technique for deriving valid inequalities from the equations of the discretized model is also given. We will show that this technique provides inequalities that significantly enhance the linear programming bound of the discretized model. Our computational results show the advantage of the new models for obtaining the optimal integer solution for the two versions of the problem.

Comparing classical performance measures for a multi-period, two-echelon supply chain network design problem with sizing decisions

This paper addresses a new problem to design a two-echelon supply chain network over a multi-period horizon. Strategic decisions are subject to a given budget and concern the location of new facilities in the upper and intermediate echelons of the network as well as the installation of storage areas to handle different product families. A finite set of capacity levels for each product family is available at each potential location. Further decisions concern the quantities of products to be shipped through the network. Two mixed-integer linear programming models are proposed that differ in the type of performance measure that is adopted to design the supply chain. Under a cost minimization objective, the network configuration with the least total cost is to be determined. In contrast, under a profit maximization goal the aim is to design the network so as to maximize the difference between total revenue and total cost. In this case, it may not always be attractive to completely satisfy demand requirements. To investigate the implications that the choice of these performance measures have on network design, an extensive computational study is conducted with randomly generated instances that are solved using CPLEX.

Solving the job-shop scheduling problem optimally by dynamic programming

Scheduling problems received substantial attention during the last decennia. The job-shop problem is a very important scheduling problem, which is NP-hard in the strong sense and with well-known benchmark instances of relatively small size which attest the practical difficulty in solving it. The literature on the job-shop scheduling problem includes several approximation and exact algorithms. So far, no algorithm is known which solves the job-shop scheduling problem optimally with a lower complexity than the exhaustive enumeration of all feasible solutions. We propose such an algorithm, based on the well-known Bellman equation designed by Held and Karp to find optimal sequences and which offers the best complexity to solve the Traveling Salesman Problem known to this date. For the TSP this means O ( n 2 2 n ) which is exponentially better than O ( n ! ) required to evaluate all feasible solutions. We reach similar results by first recovering the principle of optimality, which is not obtained for free in the case of the job-shop scheduling problem, and by performing a complexity analysis of the resulting algorithm. Our analysis is conservative but nevertheless exponentially better than brute force. We also show very promising results obtained from our implementation of this algorithm, which seem to indicate two things: firstly that there is room for improvement in the complexity analysis (we observe the generation of a number of solutions per state for the benchmark instances considered which is orders of magnitude lower than the bound we could devise) and secondly that the potential practical implications of this approach are at least as exciting as the theoretical ones, since we manage to solve some celebrated benchmark instances in processing times ranging from seconds to minutes.

Multi-period hub network design problems with modular capacities

In this paper, a modeling framework is proposed for multi-period hub location. The problems to be studied are extensions of classical hub location problems to the situation in which the hub network can be progressively built and its capacity gradually expanded over time. Both the single allocation and the multiple allocation cases are considered. For each case, a mixed-integer linear programming formulation is proposed and a set of valid inequalities is derived for enhancing the corresponding model. The results of a set of computational tests performed using the formulations proposed and their enhancements are reported. The value of the multi-period solution is discussed as a measure for evaluating the relevance of considering a multi-period model instead of a static counterpart.

Project scheduling with flexible resources: formulation and inequalities

In this paper, we study a variant of the resource-constrained project scheduling problem in which resources are flexible, i.e., each resource has several skills. Each activity in the project may need several resources for each required skill. We present a mixed-integer linear programming formulation for this problem. Several sets of additional inequalities are also proposed. Due to the fact that some of the above-mentioned inequalities require a valid upper bound to the problem, a heuristic procedure is proposed. Computational experience is reported based on randomly generated data, showing that for instances of reasonable size the proposed model enlarged with the additional inequalities can be solved efficiently.

The impact of fixed and variable costs in a multi-skill project scheduling problem: An empirical study

Abstract In this paper, we address a cost-oriented multi-skill project scheduling problem. The project consists on a set of activities such that, for some pairs, a start-to-start time dependency exists. The execution of each activity requires several skills. More than one resource of each skill may be required for processing an activity. A pull of multi-skilled resources is assumed. Costs are associated with resource usage and include fixed and variable costs. The former are incurred simply by using the resources; the latter depend on the final makespan of the project. For this problem, a mathematical programming modeling framework is proposed. The ‘natural’ model contains a non-linear objective function which, nonetheless, can be linearized at the expense of one additional set of continuous variables. The linearized model is enhanced using several sets of additional inequalities. The results of an extensive set of computational tests performed with the final model are reported. One major goal is to evaluate the possibility of using an off-the-shelf solver for tackling the problem. Another relevant goal is to understand the extent to which a cost-oriented objective influences the solutions obtained. Accordingly, we compare the solutions obtained using such objective with the solutions obtained using the traditional makespan minimization objective, often considered in project scheduling problems.