Supplier selection and order lot sizing modeling: A review

With globalization and the emergence of the extended enterprise of interdependent organizations, there has been a steady increase in the outsourcing of parts and services. This has led firms to give more importance to the purchasing function and its associated decisions. One of those decisions which impacts all firms’ areas is the supplier selection. Since the 1950s, several works have addressed this decision by treating different aspects and instances. In this paper, we extend previous survey papers by presenting a literature review that covers the entire purchasing process, considers both parts and services outsourcing activities, and covers internet-based procurement environments such as electronic marketplaces auctions. In view of its complexity, we will focus especially on the final selection stage that consists of determining the best mixture of vendors and allocating orders among them so as to satisfy different purchasing requirements. In addition, we will concentrate mainly on works that employ operations research and computational models. Thereby, we will analyze and expose the main decision's features, and propose different classifications of the published models.     

Improved algorithms for dynamic lot sizing problems with incremental discount

We develop improved algorithms for the dynamic lot sizing problems with incremental discount, where the procurement cost is a concave piecewise linear function with m sections and the holding cost is linear. We decompose the problem carefully and present a new dynamic programming formulation. By using geometric techniques, we show that when m is fixed, the problem can be solved in O(T?log?T) time, and further O(T) time if the procurement cost is stationary.     

Network-based optimization algorithms for the capacitated multi-item lot sizing problem

The capacitated, multi-item lot size problem is modeled as a fixed-charge single-commodity network flow problem. A branch and bound algorithm is developed which generally finds optimal solutions early in the search process. This property is exploited in developing heuristics that are based on the branch and bound scheme. Computational experience is discussed.     

A review of the current applications of genetic algorithms in assembly line balancing

Most of the problems involving the design and plan of manufacturing systems are combinatorial and NP-hard. A well-known manufacturing optimization problem is the assembly line balancing problem (ALBP). Due to the complexity of the problem, in recent years, a growing number of researchers have employed genetic algorithms. In this article, a survey has been conducted from the recent published literature on assembly line balancing including genetic algorithms. In particular, we have summarized the main specifications of the problems studied, the genetic algorithms suggested and the objective functions used in evaluating the performance of the genetic algorithms. Moreover, future research directions have been identified and are suggested.     

A math-heuristic Dantzig-Wolfe algorithm for capacitated lot sizing

The multi-item multi-period capacitated lot sizing problem with setups (CLST) is a well known optimization problem with wide applicability in real-world production planning problems. Based on a recently proposed Dantzig-Wolfe approach we present a novel math-heuristic algorithm for the CLST. The major contribution of this paper lies in the presentation of an algorithm that exploits exact techniques (Dantzig-Wolfe) in a metaheuristic fashion, in line with the novel trend of math-heuristic algorithms. To the best of the authors’ knowledge, it is the first time that such technique is employed within a metaheuristic framework, with the aim of tackling challenging instances in short computational time. Moreover, we provide reasoning that the approach may be beneficial when additional constraints like perishability constraints are added. This also constitutes an important extension when looking at it from the view of solution methods.     

A hybrid multi-population genetic algorithm applied to solve the multi-level capacitated lot sizing problem with backlogging

The present paper proposes a new hybrid multi-population genetic algorithm (HMPGA) as an approach to solve the multi-level capacitated lot sizing problem with backlogging. This method combines a multi-population based metaheuristic using fix-and-optimize heuristic and mathematical programming techniques. A total of four test sets from the MULTILSB (Multi-Item Lot-Sizing with Backlogging) library are solved and the results are compared with those reached by two other methods recently published. The results have shown that HMPGA had a better performance for most of the test sets solved, specially when longer computing time is given.     

A heuristic procedure for a single-item dynamic lot sizing problem

An O($\text{T}$) heuristic proceudre for a single-item dynamic lot sizing problem is introduced in this paper. The algorithm tries to establish the regeneration points of the problem whether either the production or the beginning inventory must be equal to zero. The proposed algorithm is very easy to implement and compares very favourably with the existing heuristic procedures.     

MRP lot sizing with multiple purchase discounts

Five MRP lot sizing models are modified to accommodate multiple purchase discounts and tested in an experiment involving different levels of requirements variability, discount attractiveness, and order cost. The testing of multiple purchase discounts is an extension of earlier research that compared MRP lot sizing models under a simplified discount structure involving a single price break [3, 4, 7]. The models tested here have either been implemented in some actual MRP systems or have been proposed as effective models by other researchers. Five hundred test problems were solved by each model, generating 2500 cost figures for comparison. The results indicate that an incremental version of part-period balancing and, to a lesser extent, the least unit cost method are the best models of those tested.     

A review: accuracy optimization in clustering ensembles using genetic algorithms

The clustering ensemble has emerged as a prominent method for improving robustness, stability, and accuracy of unsupervised classification solutions. It combines multiple partitions generated by different clustering algorithms into a single clustering solution. Genetic algorithms are known as methods with high ability to solve optimization problems including clustering. To date, significant progress has been contributed to find consensus clustering that will yield better results than existing clustering. This paper presents a survey of genetic algorithms designed for clustering ensembles. It begins with the introduction of clustering ensembles and clustering ensemble algorithms. Subsequently, this paper describes a number of suggested genetic-guided clustering ensemble algorithms, in particular the genotypes, fitness functions, and genetic operations. Next, clustering accuracies among the genetic-guided clustering ensemble algorithms is compared. This paper concludes that using genetic algorithms in clustering ensemble improves the clustering accuracy and addresses open questions subject to future research.     

Capacitated lot sizing by using multi-chromosome crossover strategy

The capacitated lot sizing problem (CLSP) arises when, under capacity constraints, the decision maker has to determine the production schedule and lot sizes that will minimize the total costs involved. The costs considered in this article are order, inventory carrying, and labor costs. The fitness function for the chromosome is computed using these cost elements. Next, the chromosomes are partitioned into good and poor segments based on the individual product chromosomes. This information is later used during crossover operation and results in crossover among multiple chromosomes. Product chromosomes are grouped into three groups, group 1 (top X%), group 2 (next Y%), and group 3 (last Z%). Product chromosomes from Groups 1, 2 and 3 can only form pairs with chromosomes from group 1. Besides, different crossover and mutation probabilities are applied for each group. The results of the experimentation showed that the different strategies of the proposed approach produced much better results than the classical genetic algorithm. This article has been submitted to the Journal of Intelligent Manufacturing for publication.     

Hybrid methods for lot sizing on parallel machines

We consider the capacitated lot sizing problem with multiple items, setup time and unrelated parallel machines, and apply Dantzig–Wolfe decomposition to a strong reformulation of the problem. Unlike in the traditional approach where the linking constraints are the capacity constraints, we use the flow constraints, i.e. the demand constraints, as linking constraints. The aim of this approach is to obtain high quality lower bounds. We solve the master problem applying two solution methods that combine Lagrangian relaxation and Dantzig–Wolfe decomposition in a hybrid form. A primal heuristic, based on transfers of production quantities, is used to generate feasible solutions. Computational experiments using data sets from the literature are presented and show that the hybrid methods produce lower bounds of excellent quality and competitive upper bounds, when compared with the bounds produced by other methods from the literature and by a high-performance MIP software.     

遗传算法在结构优化中的应用

采用遗传算法求解桁架结构优化设计问题,建立了平面桁架结构优化的数学模型,应用改进的自适应遗传算法对其进行求解。为了加快遗传算法进化过程,本文采用精英选择与轮盘赌选择相结合的策略,鲁棒性更好,收敛速度更快,拥有较强的寻优能力。算例表明,该遗传算法可用于桁架结构的优化设计,优化速度快,效率高,优化结果更加可靠。     

Economic lot sizing in a production system with random demand

An extended economic production quantity model that copes with random demand is developed in this paper. A unique feature of the proposed study is the consideration of transient shortage during the production stage, which has not been explicitly analysed in existing literature. The considered costs include set-up cost for the batch production, inventory carrying cost during the production and depletion stages in one replenishment cycle, and shortage cost when demand cannot be satisfied from the shop floor immediately. Based on renewal reward process, a per-unit-time expected cost model is developed and analysed. Under some mild condition, it can be shown that the approximate cost function is convex. Computational experiments have demonstrated that the average reduction in total cost is significant when the proposed lot sizing policy is compared with those with deterministic demand.     

Dynamic lot sizing and tool management in automated manufacturing systems

The overall aim of this study is to show that there is a critical interface between the lot sizing and tool management decisions, and these two problems cannot be viewed in isolation. We propose five alternative algorithms to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously. The first algorithm is an exact algorithm which finds the global optimum solution, and the others are heuristics equipped with a look-ahead mechanism to guarantee at least local optimality. The computational results indicate that the amount of improvement is statistically significant for a set of randomly generated problems. The magnitude of cost savings is dependent on the system parameters.Scope and purposeIn most of the studies on tool management, lot sizes are taken as a predetermined input while deciding on tool allocations and machining parameters. This might create empty feasible solution spaces and otherwise unnecessarily limit the number of alternatives possible for the tool management problem. In this study, we consider the integration of lot sizing and tool management problems to minimize total production cost for multiple periods under dynamic demand. By integrating these decisions we not only improve the overall solution, but also prevent any infeasibility that might occur for the tool management problem due to decisions made at the lot sizing level.     

Heuristic-based neural networks for stochastic dynamic lot sizing problem

Multi-period single-item lot sizing problem under stochastic environment has been tackled by few researchers and remains in need of further studies. It is mathematically intractable due to its complex structure. In this paper, an optimum lot-sizing policy based on minimum total relevant cost under price and demand uncertainties was studied by using various artificial neural networks trained with heuristic-based learning approaches; genetic algorithm (GA) and bee algorithm (BA). These combined approaches have been examined with three domain-specific costing heuristics comprising revised silver meal (RSM), revised least unit cost (RLUC), cost benefit (CB). It is concluded that the feed-forward neural network (FF-NN) model trained with BA outperforms the other models with better prediction results. In addition, RLUC is found the best operating domain-specific heuristic to calculate the total cost incurring of the lot-sizing problem. Hence, the best paired heuristics to help decision makers are suggested as RLUC and FF-NN trained with BA.     

The gambler's ruin problem, genetic algorithms, and the sizing of populations.

This paper presents a model to predict the convergence quality of genetic algorithms based on the size of the population. The model is based on an analogy between selection in GAs and one-dimensional random walks. Using the solution to a classic random walk problem-the gambler's ruin-the model naturally incorporates previous knowledge about the initial supply of building blocks (BBs) and correct selection of the best BB over its desired quality of the solution, as well as the problem size and difficulty. The accuracy of the model is verified with experiments using additively decomposable functions of varying difficulty. The paper demonstrates how to adjust the model to account for noise present in the fitness evaluation and for different tournament sizes.     

RFID localization algorithms and applications—a review

Object localization based on radio frequency identification (RFID) technology has promising potentials. By combining localization with its identification capability, existing applications can be enhanced and new applications can be developed for this technology. This paper starts with an overview introducing the available technologies for localization with a focus on radio frequency based technologies. The existing and potential applications of RFID localization in various industries are then summarized. Moreover, RFID localization algorithms are reviewed, which can be categorized into multilateration, Bayesian inference, nearest-neighbor, proximity, and kernel-based learning methods. Also, we present a localization case study using passive RFID technology, and it shows that objects can be successfully localized using either multilateration or Bayesian inference methods. The survey also discusses the challenges and future research on RFID localization.     

A review of genetic algorithms applied to training radial basis function networks

The problems associated with training feedforward artificial neural networks (ANNs) such as the multilayer perceptron (MLP) network and radial basis function (RBF) network have been well documented. The solutions to these problems have inspired a considerable amount of research, one particular area being the application of evolutionary search algorithms such as the genetic algorithm (GA). To date, the vast majority of GA solutions have been aimed at the MLP network. This paper begins with a brief overview of feedforward ANNs and GAs followed by a review of the current state of research in applying evolutionary techniques to training RBF networks.     

Multi-level lot sizing in material requirements planning: an empirical investigation

The research report in this paper was a result of a recent article by Yelle [8]. He reports computational results using all combinations of four single level heuristic lot sizing rules, which are applied sequentially to a two level problem in a Material Requirements Planning (MRP) environment. To test the impact of the different combinations of these lot sizing rules he employed six different demand patterns for the end-items which range from level demand to demand which is intermittent throughout the planning horizon. In our research we utilized the same data as Yelle and conducted a more extensive analysis by adding (a) two more recent and powerful single level heuristic rules, namely, the least unit cost heuristic and Silver and Meal's least-cost per period heuristic, (b) the very well known single level optimum method of Wagner-Whitin[7], and (c) a multi-level heuristic proposed recently by McLaren and Whybark [4]. The results show a significant improvement in many cases over the best solutions reported by Yelle.Further in this paper, we also provide a much simpler mathematical formulation of the multi-level lot sizing problem than found in the literature. This formulation was advantageously used to determine optimum solutions using IBM's Mathematical Programming System Extended (MPSX) to the aforementioned problems.