Manuel Cardós

Branch and bound procedures for solving the Assembly Line Worker Assignment and Balancing Problem: Application to Sheltered Work centres for Disabled

In this paper a new problem called Assembly Line Worker Assignment and Balancing Problem (ALWABP) is introduced. This problem arises in those assembly lines where we have certain limited resources available (normally workers) in which the operation time for every task is different depending on who executes the task, and where there are also some task-worker incompatibilities defined. The problem consists of providing a simultaneous solution to a double assignment: (1) tasks to stations; and (2) available workers to stations. After defining the mathematical model for this problem, a basic Branch and Bound approach with three possible search strategies and different parameters is presented. We also propose the use of a Branch and Bound-based heuristic for large problems and analyse the behaviour of both exact and heuristic methods through experimental studies. Finally the implementation of these procedures in a Sheltered Work centre for Disabled-the real environment which has inspired this research-is described. In these centres the adoption of assembly lines provide many advantages, since the traditional division of work in single tasks may become a perfect tool for making certain worker disabilities invisible. Efficiently applying this configuration helps these centres to achieve their primary aim: growth in order to provide more jobs for more disabled people, but always considering the specific limitations that the disabled workers have. In this sense this paper shows one of the possible real applications where Operations Research can help not only to get economic and productive benefits but also certain social aims.

On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns

The primary goal of this paper is the development of a generalized method to compute the fill rate for any discrete demand distribution in a periodic review policy. The fill rate is defined as the fraction of demand that is satisfied directly from shelf. In the majority of related work, this service metric is computed by using what is known as the traditional approximation, which calculates the fill rate as the complement of the quotient between the expected unfulfilled demand and the expected demand per replenishment cycle, instead of focusing on the expected fraction of fulfilled demand. This paper shows the systematic underestimation of the fill rate when the traditional approximation is used, and revises both the foundations of the traditional approach and the definition of fill rate itself. As a result, this paper presents the following main contributions: (i) a new exact procedure to compute the traditional approximation for any discrete demand distribution; (ii) a more suitable definition of the fill rate in order to ignore those cycles without demand; and (iii) a new standard procedure to compute the fill rate that outperforms previous approaches, especially when the probability of zero demand is substantial. This paper focuses on the traditional periodic review, order up to level system under any uncorrelated, discrete and stationary demand pattern for the lost sales scenario.

An exact calculation of the cycle service level in a generalized periodic review system

This paper is focused on the exact calculation of the cycle service level for a generalized periodic review system accepting any discrete demand with a known probability function and any cycle service target. Previously, it was necessary to modify the definition of the cycle service level metric (also known as non stock out probability) so that it could be applied to these cases. The purpose of the proposed (R, S) system is to handle simultaneously fast-moving items, slow-moving items and intermittent or sporadic demand items any of them with high, medium or low cycle service targets.

EVITA: An Integral Evolutionary Methodology for the Inventory and Transportation Problem

The Inventory and Transportation Problem (ITP) can be seen as a generalisation of the Periodic Vehicle Routing Problem that takes into consideration the inventory costs, plus a set of delivery frequencies instead of a single delivery frequency for each shop. Additionally, the ITP can also be viewed as a generalisation of the Inventory Routing Problem to the multiproduct case. EVITA, standing for Evolutionary Inventory and Transportation Algorithm, is a two-level methodology designed to address this problem. The top level uses an evolutionary algorithm to obtain delivery patterns for each shop on a weekly basis so as to minimise the inventory costs, while the bottom level solves the Vehicle Routing Problem (VRP) for every day in order to obtain the transport costs associated to a particular set of patterns.

Effects on undershoots and lost sales on the cycle service level for periodic and continuous review policies

One of the most usual measures of customer service is the cycle service level (CSL) which indicates the specific probability of no stockout per replenishment cycle. This definition can be applied to any stock policy and demand pattern, given a known stock level at the beginning of the cycle. Some approximations have been used to compute this stock level in some scenarios not including undershoots or neglecting the probability of no demand during the cycle depending on the stock policy. However, in practice a number of different scenarios take place those basically depend on the market rules and the demand characteristics. A general approach is presented in this paper to compute the exact cycle service level in different scenarios for both periodic and continuous review policies. Additionally, this paper examines the deviations observed when the classical approximations are used. This paper is focused on uncorrelated, discrete and stationary demand with a known pattern.

A comparison of routing algorithms in a hybrid evolutionary tool for the Inventory and Transportation Problem

In this paper we propose new advances towards the development of a commercial tool to address the inventory and transportation problem, i.e. the problem of minimising both the transport and inventory costs of a retail chain that is supplied from a central warehouse. On the first level, we employ an evolutionary algorithm to evolve the delivery patterns for each shop. On a second level we obtain the delivery routes using two different algorithms: the bi-directional multistart sweep (daisy) algorithm and the daisy algorithm enhanced with local neighbourhood search. The experiments performed show that both methods can obtain acceptable results consistently and within a short timescale. The results are also of a lower cost than those obtained by other strategies employed in previous research, showing that employing a more efficient routing algorithm is effective in reducing costs, although for the cases studied the reduction is not significant. Furthermore, they confirm the interest of addressing the optimisation problem jointly, rather than minimising separately inventory and transport.

Configuring an evolutionary tool for the inventory and transportation problem

EVITA, standing for Evolutionary Inventory and TransportationAlgorithm, aims to be a commercial tool to addressthe problem of minimising both the transport and inventorycosts of a retail chain that is supplied from a centralwarehouse. In this paper we study different issues involvedin finding the appropriate settings for EVITA, so that itcan be employed by a non-expert user over wide range ofproblems.The aim is not to define a new algorithm for resolutionof the ITP, but to determine whether it is possible to finda set of input parameters that can provide good results ona wide range of problem configurations, hence eliminatingthe need for user adjustment once the tool is employed in acommercial setting.We focus on the influence of three parameters: the populationsize, the tournament size and the mutation probability.After extensive experimentation and statistical analysis weare able to find a good configuration for the three factors.

Design of a retail chain stocking up policy with a hybrid evolutionary algorithm

In this paper we address the joint problem of minimising both the transport and inventory costs of a retail chain that is supplied from a central warehouse. We propose a hybrid evolutionary algorithm where the delivery patterns are evolved for each shop, while the delivery routes are obtained employing the multistart sweep algorithm. The experiments performed show that this method can obtain acceptable results consistently and within a reasonable timescale. The results are also of a lower cost than those obtained by other strategies employed in previous research. Furthermore, they confirm the interest of addressing the optimisation problem jointly, rather than minimising separately inventory and transport.

On the estimation of on-hand stocks for base-stock policies and lost sales systems and its impact on service measures

This paper focuses on computing on-hand stock levels at the beginning of a replenishment cycle for a lost sales inventory system with periodic reviews and discrete demand. A base-stock policy is used for replenishments. The literature provides an Exact method which requires a huge computational effort, and two closed-form approximate methods that arise from the backordering case, the Non-stockout and the Bijvank & Johansen. In this paper we propose three new and closed-form approaches that explicitly consider the lost sales assumptions: the Adjusted Non-stockout, the Polar Opposite and the 1-Step methods. Existing and proposed methods are evaluated in terms of their accuracy when computing the cycle service level and the fill rate. In this sense, results show that the Bijvank & Johansen and 1-Step methods provide similar performance but present different behaviours in terms of under or over estimating service measures that have different implications on the design of stock policies.

On the Exact Calculation of the Fill Rate for Repairable Parts: Application to an Airline Company

This paper focuses on the improvement of inventory policies of repairable parts of the airline company Air Nostrum. The company uses the sales replacement policy to manage their repairable parts and the base stock is determined by means of an approximated expression of the fill rate assuming Poisson distributed demands. However, this paper shows that real data may not always be modelled with the Poisson distribution and the only exact method available in the literature fall into significant deviations when other discrete distribution is used. According to that, this paper derives an exact method to compute the fill rate in the presence of any stationary, discrete and i.i.d demand pattern for the policy the company uses. Illustrative examples show that deviations which arise from using approximate methods can lead to overestimate the fill rate so the inventory policy does not reach the target fill rate.