Amaia Lusa

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.

A survey of the literature on the multiple or parallel assembly line balancing problem

This paper focuses on production systems that consist of multiple parallel assembly lines. The main literature contributions are briefly described and used to present a summary of the state of the art. The advantages and disadvantages of adopting multiple lines are discussed and the multiple assembly line balancing problem and its relevant characteristics are described. [Received 19 March 2007; Revised 3 July 2007; Accepted 3 September 2007]

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.

A variable neighbourhood search algorithm for the constrained task allocation problem

A variable neighbourhood search algorithm that employs new neighbourhoods is proposed for solving a task allocation problem whose main characteristics are: (i) each task requires a certain amount of resources and each processor has a capacity constraint which limits the total resource of the tasks that are assigned to it; (ii) the cost of solution includes fixed costs when using processors, task assignment costs, and communication costs between tasks assigned to different processors. A computational study shows that the algorithm performs well in terms of time and solution quality relative to other local search procedures that have been proposed.

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.

A detailed workforce planning model including non-linear dependence of capacity on the size of the staff and cash management

This paper introduces an original planning model which integrates production, human resources and cash management decisions, taking into account the consequences that decisions in one area may have on other areas and allowing all these areas to be coordinated. The most relevant characteristics of the planning problem are: (1) production capacity is a non-linear function of the size of the staff; (2) firing costs may depend on the worker who is fired; (3) working time is managed under a working time account (WTA) scheme, so positive balances must be paid to workers who leave the company; (4) there is a learning period for hired workers; and (5) cash management is included. A mixed integer linear program is designed to solve the problem. Despite the size and complexity of the model, it can be solved in a reasonable time. A numerical example, the main results of a computational experiment and a sensibility analysis illustrate the performance and benefits of the model.

Planning production and working time within an annualised hours scheme framework

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 organisations with flexibility; it enables a firm to adapt production capacity to fluctuations in demand. However, it can involve a worsening of the staff working conditions. To take this into account, the planning and scheduling of working time should comply with constraints derived from the law or from a collective bargaining agreement. Thus, new and more difficult working-time and production planning and scheduling problems are arising. This paper proposes two mixed-integer linear program models for solving the problem of planning the production, the working hours and the holiday weeks of the members of a human team operating in a multi-product process in which products are perishable, demand can be deferred and temporary workers are hired to stand in for employees. The results of a computational experiment are presented.

A manufacturing and remanufacturing aggregate planning model considering a non-linear supply function of recovered products

Abstract: This article addresses the joint aggregate planning of a system for manufacturing new units and remanufacturing used units to obtain items that are indistinguishable from the original product. A variety of used conditions are taken into account. A forecast of the number of items at the end of their useful life in each period is assumed to be available and the proportion of items that are returned is a non-linear function of the price paid for them. The case deals with products such as copiers, printers and scanners, and with containers that require a complex refilling process. A mathematical program is obtained whose constraints and objective function have non-linear terms that are linearised by means of piecewise functions. The solution of several instances is addressed and one example is examined in detail.

Planning working time accounts under demand uncertainty

Working time accounts (WTAs) are employer-oriented flexibility systems that have been applied in industry but could be used far more. WTAs enable capacity to be adapted to fluctuations in demand. The required capacity, which is needed to plan WTAs, usually depends on several factors. It is often impossible to reliably predict the required capacity or unrealistic to adjust it to a probability distribution. In some cases, a set of required-capacity scenarios can be determined, each with a related probability. This paper presents a multistage stochastic optimisation model that is robust (i.e., provides a solution that is feasible for any possible scenario) and minimises the expected total cost (which includes the cost of overtime and the cost of the capacity shortage).