Albert Corominas

HEURISTICS AND EXACT ALGORITHMS FOR SOLVING THE MONDEN PROBLEM

Abstract Sequencing units on an assembly line in order to obtain a regular requirement of resources is a problem that can be modelled in a variety of ways. One of the most popular is known as the Monden problem, and the heuristic proposed to obtain a ‘satisfactory’ solution is called ‘goal-chasing’ ethod. In the paper the myopic behaviour of this heuristic is shown, and some improvements are proposed. An exact procedure, based on BDP, is also proposed. By relaxing the assumptions, the BDP procedure becomes a new, powerful heuristic. A sample of computational results is included.

Optimal manufacturing-remanufacturing policies in a lean production environment

This study analyses a production-management model that considers the possibility of implementing a reverse-logistics system for remanufacturing end-of-life products in a lean production environment (as opposed to models that use EOQ approaches). Decision variables are identified (including manufacturing and remanufacturing capacities and return rates and use rates for end-of-life products) and optimal policies are determined. Moreover, the structure of these optimal policies is analysed. The conclusion drawn is that, in many realistic scenarios, mixed policies (that is, with return rates and use rates strictly between 0 and 1) can be optimal. This conclusion is contrary to results published in earlier studies, which are based on more restrictive assumptions.

Response time variability

Response time variability is a new optimization problem with a broad range of applications and a distinctive number of theoretic flavour. The problem occurs whenever events, jobs, clients or products need to be sequenced so as to minimize the variability of time for which they wait for the next turn in obtaining the resources necessary for their advance. The problem has numerous real-life applications. We study its computational complexity, present efficiency, polynomial time algorithms for some cases, and the NP-hardness proof for a general problem. We propose a position exchange heuristic and apply it to improve the total response time variability of an initial sequence. The latter is the optimum bottleneck sequence, Webster or Jefferson sequence of the apportionment, or a random sequence. We report on computational experiments with the heuristic.

Rotational allocation of tasks to multifunctional workers in a service industry

This paper deals with the assignment of tasks to the members of the multi-functional staff (each worker is able to perform a given subset of types of tasks) of a work centre, during each period (e.g. 1 h) into which the planning horizon (e.g. 1 shift or 1 week) can be divided. For each type of task to perform, all workers who can perform the task do so at equal worker efficiencies. There are constraints that, if possible, should be respected. The objective is that the percentage of working time dedicated by each worker to each type of task be as close as possible to reference values. The problem is modelled as a sequence of assignments, in which appropriate values for the cost matrix depend on the results of the previous assignments. The obtained results are satisfactory: the solutions meet the constraints, the scheduled percentages steadily approach reference values and the calculation times are very short. Therefore, the work presented constitutes a potential tool for assigning tasks to multi-functional workers in the service industry.

Using MILP to plan annualised working hours

Annualising working hours (AH) is a means to achieve flexibility in the use of human resources in order to face the seasonal nature of the demand. MILP models are proposed to solve the problem of planning the staffs working hours with an annual horizon. The computational experience with the models leads to the conclusion that MILP is an appropriate way to deal with the problem in many real cases.

Planning Annualised Hours with a Finite Set of Weekly Working Hours and Joint Holidays

The need to adjust productive capacity to seasonal demand and the increasing flexibility in the distribution of annual working hours has given rise to new problems with respect to the organisation of staff working time. This paper presents a problem of planning annual working hours, in which the number of weekly working hours for any worker must belong to a previously agreed finite set and holiday weeks are the same for all the staff members. The problem is modelled and solved as a mixed integer linear program.

Assembly line balancing: general resource-constrained case

The problem of designing and balancing assembly lines has been widely studied in the literature. A recently introduced issue is the efficient use of constrained resources with specific assumptions, in which a task needs a resource type (A) or one of two resources (A ∨ B). This paper presents a more general resource-constrained case, in which each task needs resources that may be simple or multiple, alternative and/or concurrent: for instance, (3A), (A ∧ 4B ∧ 3C), (3A ∨ 2B ∨ C), (A ∧ B) ∨ (2C ∧ D) or (A ∨ B) ∧ (2C ∨ D). We also introduce an upper bound on the number of available resources. Finally, we present a computational experiment using the mathematical models that we develop, showing the instances that can be efficiently solved.

Using a MILP model to establish a framework for an annualised hours agreement

Abstract Production flexibility is essential for industrial companies that have to deal with seasonal demand. Human resources are one of the main sources of flexibility. Annualising working hours (i.e., the possibility of irregularly distributing the total number of working hours over the course of a year) is a tool that provides flexibility to organizations; it enables a firm to adapt production capacity to fluctuations in demand. However, it can imply a worsening of the staff’s working conditions. To take the human aspect into account, the planning and scheduling of working time should comply with constraints derived from the law or from a collective bargaining agreement. Furthermore, new and more difficult working-time planning and scheduling problems are arising. This paper proposes a mixed-integer linear program model to solve the problem of planning the production and the working hours of a human team that operates in a multi-product process. Solving the model for different settings provides the essential quantitative information to negotiate the best conditions of the annualised hours system (the elements to establish the trade-off between weekly flexibility and economic or working-time reduction compensation can be obtained). The results achieved in a computational experiment were very satisfactory.

Planning annualised hours with a finite set of weekly working hours and cross-trained workers

Abstract Annualising working hours (i.e., the possibility of irregularly distributing the total number of working hours over a year) permits companies to adapt capacity to fluctuations in demand, thus reducing overtime, temporary workers and inventory costs. Since annual hours can lead to a worsening of the staff’s working conditions, many laws and collective bargaining agreements contain constraints that affect the distribution of working time. This paper proposes a MILP model to solve an annualised working hours planning problem in which workers are considered to be cross-trained, and in which the number of weekly working hours must belong to a previously agreed finite set. A computational experiment demonstrates the effectiveness of the model.

Supply chains: what they are and the new problems they raise

The term ‘supply chain’ has been, perhaps surprisingly, highly successful since it was proposed. This paper discusses the material and theoretical roots from which the concept arises, as well as its content and implications. It focuses especially on the question of whether the term is useful only to, say, put old wine into new wineskins or responds to a very different reality from that we had a few decades ago. The latter poses new problems, some of which are pointed out, whose resolution requires new theoretical and computational tools. The obvious inadequacy of the term to describe the reality it refers to is emphasised. Some challenges, opportunities and switchpoints for the future of the supply chain are listed as well.