Manuel Mateo

Local search heuristics for the assembly line balancing problem with incompatibilities between tasks

This paper deals with the assembly line balancing problem considering incompatibilities between the tasks with the aim of: first minimizing the number of workstations, and then minimizing the cycle time for the minimum number of workstations. In order to solve the problem we propose the use of a greedy randomized adaptive search procedure obtained from the application of some classic heuristics based on priority rules, and a genetic algorithm that searches for the solution in the heuristic space. A computational experience is included to illustrate the performance of the proposed approach.

Different behaviour of a double branch-and-bound algorithm on Fm|prmu|Cmax and Fm|block|Cmax problems

In this paper we face the permutation flow-shop scheduling problem with a makespan objective function in two variants, with and without storage space between machines. We use an improved branch and bound algorithm, suitable for parallel computation, to solve these problems, and auxiliary heuristics to attain an initial good solution. The auxiliary heuristics proposed are built by two steps: in the first step a permutation is obtained; in the second step a local search procedure is applied. The improvement obtained by the local search procedure on NEH heuristic as first step is shown. Since the flow-shop scheduling problem with storage space is a relaxation of the problem without storage space, some elements and procedures developed for that problem can be used in both problems. In particular, some bounding procedures, for instance Nabeshima or Lageweg bounding schema, can be adapted. Moreover, the reversibility property holds on both problems. Consequently a double branch and bound algorithm can be applied simultaneously to the direct and the inverse instances. The same sets of data are submitted to heuristics and to the double branch-and-bound algorithm, LOMPEN, assuming first they are instances of flow-shop scheduling problem with storage space and later they are instances of flow-shop scheduling problem without storage space. The algorithms are coded in a similar way; therefore the behaviour and performance can be compared.

Analysis of the single-vehicle cyclic inventory routing problem

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, 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 maximised while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this article, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-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.

Planning production using mathematical programming: The case of a woodturning company

Herein we present a case of production planning in a woodturning company. The company wishes to plan the turning of various types of products of different radii in a set of parallel machines (lathes) and with the following principal conditions: for each type of product there is a minimum production lot size; some lathes cannot manufacture every type of product; the production capacity of a lathe depends on the lathe itself and the type of product to be manufactured; the products are classified into families according to radius; and there is an intra-family setup time (for manufacturing different products that have the same radius) and an inter-family setup time (for consecutively manufacturing products that have different radii), which is longer; part of the production can be subcontracted; each type of product can be manufactured on different lathes and/or subcontracted; and the operators can work overtime, during which additional time they can simultaneously operate multiple lathes. The goal is to meet the demand at minimum cost, which includes the cost of any overtime plus that of any subcontracting. The problem was modelled and solved by mixed-integer linear programming (MILP). The company considers the results to be satisfactory.

Application of genetic algorithms to assembly sequence planning with limited resources

Heuristic procedures based on priority rules are quite frequently used to solve the multiple resource-constrained project-scheduling problem (RCPSP), i.e. task programming with limited resources. The rules are based on the problem knowledge. Different local search procedures have been proposed in order to look for acceptable solutions in scheduling problems. In this work, local search procedures, that define the solution neighborhood based on greedy heuristics, are proposed to assign assembly operations to a fixed number of robots in a manufacturing cell. A genetic algorithm is used to generate the solution.

A combined inventory routing and game theory approach to solve a real-life distribution problem

In this paper, we discuss a solution approach combining inventory routing and game theory to optimise logistical costs in a real-life distribution system. The problem consists in developing a distribution plan to replenish inventory at each of the involved sales-points, and then clustering them in groups willing to cooperate and share parts of their stocks. The distribution strategy and clustering should be achieved in a way that minimises total distribution and inventory costs of the system. Clearly, cooperation inside each cluster increases the extra potential inventory to which each member of the cluster has access, without having to support the related cost. As a result, the service level that each of these sales-point may achieve would increase. This approach is implemented for a real-life supply chain. A part of obtained results are reported and discussed in the paper.

Strategic Capacity Planning in KIOs: A Classification Scheme

This paper introduces the Strategic Capacity Planning problem in knowledge intensive organizations (KIOs) and proposes a classification scheme based on different characteristics such as the organization structure, the workforce characteristics, the capacity requirements, the capacity decisions or the evaluation criteria, among others. The classification, which gives rise to a high number of variants, is the first step towards a general solving methodology design and the developing of ad hoc solving procedures.

Note on the behaviour of an improvement heuristic on permutation and blocking flow-shop scheduling

This work deals with the permutation flow-shop scheduling problem with and without storage space between stages, where the performance criterion is the makespan. Many proposed procedures to solve these problems have an improvement phase based on the search in the pair-wise interchange neighbourhood. The authors have observed large plateaus in the solutions domain of these problems defined for this type of neighbourhood that make it difficult for the heuristics to search for a road to the optimum. An improvement heuristic is proposed, which uses two tools in order to evade these difficulties: a stochastic exploration of the neighbourhood (revolver) and a special consideration of ties. The improvement heuristic is applied, in conjunction with three adapted well-known heuristics in the literature, to the direct and inverse instances. The performance of the procedures was evaluated on nine generated sets of a thousand instances and on 90 instances from Taillard (1993). The obtained results recommend applying always the constructive heuristic procedures on the direct and inverse instance. The computational experience proves the effectiveness of the two tools implemented in the improvement phase.

A bi-objective parallel machine problem with eligibility, release dates and delivery times of the jobs

The scheduling of parallel machines is a well-known problem in many companies. Nevertheless, not always all the jobs can be manufactured in any machine and the eligibility appears. Based on a real-life problem, we present a model which has m parallel machines with different level of quality from the highest level for the first machine till the lowest level for the last machine. The set of jobs to be scheduled on these m parallel machines are also distributed among these m levels: one job from a level can be manufactured in a machine of the same or higher level but a penalty, depending on the level, appears when a job is manufactured in a machine different from the highest level i.e. different from the first machine. Besides, there are release dates and delivery times associated to each job. The tackled problem is bi-objective with the criteria: minimisation of the final date – i.e. the maximum for all the jobs of their completion time plus the delivery time – and the minimisation of the total penalty generated by the jobs. In a first step, we analyse the sub-problem of minimisation of the final date on a single machine for jobs with release dates and delivery times. Four heuristics and an improvement algorithm are proposed and compared on didactic examples and on a large set of instances. In a second step an algorithm is proposed to approximate the set of efficient solutions and the Pareto front of the bi-objective problem. This algorithm contains two phases: the first is a depth search phase and the second is a backtracking phase. The procedure is illustrated in detail on an instance with 20 jobs and 3 machines. Then extensive numerical experiments are realised on two different sets of instances, with 20, 30 and 50 jobs, 3 or 4 machines and various values of penalties. Except for the case of 50 jobs, the results are compared with the exact Pareto front.

Evaluation of the impact of strategic staff planning in a university using a MILP model

A mathematical model for optimising the strategic staff planning in universities is used to analyse the impact of different personnel and academic policies on the strategic staff plan, considering a preferable staff composition. The personnel policies are evaluated allowing or not the dismissals of permanent workers; the ratio of internal promotion for workers and the personnel budget. The academic policies are tested through the impact of different demand trends. Addressing the specificities of the university, the optimisation model considers not only economic criteria, i.e., personnel costs, but also other factors related to the fulfilment of the required service level and the achievement of a preferable workforce composition. Several computational scenarios are used, based on real data from the Universitat Politecnica de Catalunya (Barcelona, Spain). The results show the adjustment to the preferable workforce composition through the available mechanisms (dismissals, hiring and internal promotions). [Received 12 June 2015; Revised 24 November 2015; Revised 24 July 2016; Accepted 7 December 2016]