Aaron Luntala Nsakanda

Hybrid genetic approach for solving large-scale capacitated cell formation problems with multiple routings

We present a comprehensive model for designing a cellular manufacturing system. The model bridges several known problems in that it integrates the cell formation problem, the machine allocation problem, and the part routing problem. Multiple process plans for each part and multiple routing alternatives for each of those process plans are considered. The part demands can be satisfied from internal production or through outsourcing. Machines have limited capacities. We propose a solution methodology based on a combination of a genetic algorithm and large-scale optimization techniques. A computational study is conducted to evaluate the viability of our approach for solving large scale problems. A limited computational experiment involving smaller problems, that are special cases of our model, is also conducted to compare our solution approach with existing models.

Ensuring population diversity in genetic algorithms: A technical note with application to the cell formation problem

Abstract The entropy-based measure has been used in previous works to compute the population diversity in solving the cell formation problem with the genetic algorithm. Population diversity is crucial to the genetic algorithm’s ability to continue fruitful exploration as it may be used in choosing an initial population, in defining a stopping criterion, in evaluating the population convergence, and in making the search more efficient throughout the selection of crossover operators or the adjustment of various control parameters (e.g., crossover or mutation rate, population size). We show in this note that, when a non-ordinal chromosome representation corresponding to the allocation of machines to cells is used, the current way of measuring the population diversity is inaccurate. Consequently, it leads to wrong conclusions when, at various iterations, carrying out fruitful exploration or an efficient search of the solution space is guided by the perceived population diversity degree. An alternative approach based on computing the distance and the similarity between chromosomes is discussed.

Shortening cycle times in multi-product, capacitated production environments through quality level improvements and setup reduction

This paper addresses the issue of investing in reduced setup times and defect rates for a manufacturer of several products operating in a JIT environment. Production cycle times can be shortened by investing in setup time and defect rate reductions, respectively. The objective is to determine optimal levels of setup time and defect rate reductions along with the corresponding optimal levels of investments respectively, and the optimal production cycle time for each product. The problem is constrained by demand requirements, process improvement budget limitations, and manufacturing and warehousing capacity constraints. We consider the cases of product-specific quality improvements and joint-product quality improvements. A general nonlinear optimization models of these problems are formulated. A convex geometric programming approximation of these models is developed respectively, in order to solve them. The approximation can be made to any desired degree of accuracy. Our empirical findings provide insights into a number of managerial issues surrounding investment decisions in product-specific quality improvements and setup reductions due to a product redesign as well as in joint-product improvements due to a process redesign.

Large-scale capacitated part-routing in the presence of process and routing flexibilities and setup costs

We develop a Lagrangean relaxation-based heuristic procedure to generate a near-optimal solution to large-scale capacitated part-routing problems through a cellular manufacturing system with both routing flexibilities and setup times. Several alternate process plans exist for each product. Any given operation can be performed on alternate machines at different costs. The part demands can be satisfied from internal production or through outsourcing. The objective is to minimize the total material handling, production, outsourcing, and setup costs, subject to satisfying all the part demands and not exceeding any of the machine capacity limits. Our computational experiments show that large problems involving several thousand products and decision variables can be solved in a reasonable amount of computer time to within 1% of their optimal solutions. The proposed procedure is general enough to be applied directly or with slight modifications to real-life, industrial-sized problems.

Project crashing in the presence of general non-linear activity time reduction costs

In this paper, we are concerned with the project crashing problem. The functional form we consider for the crashing costs is a negative-exponential form of the amount of capital invested that captures most of the more realistic forms that have been proposed in the literature. We formulate a non-linear optimisation model of the resulting generalised crashing problem, and develop a convex geometric programming approximation of this model. The model can be readily extended to handle situations where it is desired to determine the minimum capital investment needed to crash activities so that the total project duration does not exceed a given time length. Numerical illustrations of the approach are provided.

An aggregate inventory-based model for predicting redemption and liability in loyalty reward programs industry

We propose a predictive model of redemption and liability to support short, medium, and long term planning and operational decision-making in Loyalty Reward Programs (LRPs). The proposed approach is an aggregate inventory model in which the liability of points is modeled as a stochastic process. An illustrative example is discussed as well as a real-life implementation of the approach to facilitate use and deployment considerations in the context of a frequent flyer program, an airline industry based LRP.

A stochastic linear programming modelling and solution approach for planning the supply of rewards in Loyalty Reward Programs

In this paper, we consider the problem of planning the supply of rewards in a Loyalty Reward Program (LRP). We formulate this problem as a two-stage stochastic linear program with simple recourse, and develop a new, sampling-based stochastic optimisation heuristic procedure for solving it. The proposed heuristic is general and can be applied in other contexts as well. Our computational experiments demonstrate the viability of the modelling and solution approaches for solving realistically-sized (large-scale) problems.

Planning the Supply of Rewards with Cooperative Promotion Considerations in Coalition Loyalty Programmes Management

Coalition loyalty programmes (CLPs) are owned and operated as for-profit enterprises. We consider the ordering decisions of rewards that arise in this context, under a general setting in which not only is the demand for rewards uncertain, but also the CLP firm offers bonus points, a very common cooperative promotion mechanism used in loyalty programmes. The rewards are acquired either at a wholesale ‘discounted’ cost or at a wholesale ‘non-discounted’ cost by the CLP firm from its multiple commercial partners and supplied to customers seeking to redeem their accumulated ‘reward points’, subject to commercial partners’ capacities for offering rewards, the firm’s overall budget for purchasing rewards, and its control policy on points liability. We formulate the problem as a stochastic linear programme with recourse and solve it using a sampling-based heuristic solution procedure previously discussed in the literature. We report on the managerial applicability of our model in dealing with the redemption budget spending resulting from changes in demand variability, changes in the redemption budget, and the control of liability levels within a reasonable range.

Rewards-supply planning under option contracts in managing coalition loyalty programmes

We examine the problem of planning the supply of rewards in coalition loyalty programmes considering that the buyer–supplier relationships with commercial partners are governed by option contracts rather than wholesale price contracts similar to what is commonly used in practice. We develop a two-stage stochastic linear programme model with simple recourse which considers uncertain demand requirements, limited reward purchasing budgets, multiple programme partners of various sizes, point-liability control targets and overall profitability. A sampling average approximation scheme is used to solve the model. Numerical experiments show that option contracts perform better than wholesale price contracts when redemption demand uncertainty is high and the number of redemption partners is large. The results also suggest that the common practice of increasing redemption capacities is not the most effective way to cope with demand uncertainties. Programmes that reduce redemption demand variability and/or create better contracting structures are more promising in improving points-liability, redemption budget spending and overall profitability than traditional approaches.

A Predictive Model of Redemption and Liability in Loyalty Reward Programs Industry

Loyalty reward programs (LRPs), initially developed as marketing programs to enhance customer retention, have now become an important part of customer-focused business strategies. With the growth in these programs, the complexities in their management and control have also increased. One of the challenges faced by LRPs managers is that of developing models to address various forecasting issues to support short, medium, and long term planning and operational decision-making. We propose in this paper a predictive model of redemption and liability in LRPs. The proposed approach is an aggregate inventory model in which the liability of points is modeled as a stochastic process. An illustrative example is discussed as well as a real-life implementation of the methodology to facilitate use and deployment considerations in the context of a frequent flyer program, an airline industry based LRP.