Differential evolution to solve the lot size problem.

An Advanced Resource Planning model is presented to support optimal lot size decisions for performance improvement of a production system in terms of either delivery time or setup related costs. Based on a queueing network, a model is developed for a mix of multiple products following their own specific sequence of operations on one or more resources, while taking into account various sources of uncertainty, both in demand as well as in production characteristics. In addition, the model includes the impact of parallel servers and different time schedules in a multi-period planning setting. The corrupting influence of variabilities from rework and breakdown is explicitly modeled. As a major result, the differential evolution algorithm is able to find the optimal lead time as a function of the lot size. In this way, we add a conclusion on the debate on the convexity between lot size and lead time in a complex production environment. We show that differential evolution outperforms a steepest descent method in the search for the global optimal lot size. For problems of realistic size, we propose appropriate control parameters for the differential evolution in order to make its search process more efficient.Production planning; Lot sizing; Queueing networks; Differential evolution;

Reverse logistics network design: the impact of lead times and stochasticity

status: publishe

Differential evolution to solve the lot size problem

An Advanced Resource Planning model is presented to support optimal lot size decisions for performance improvement of a production system in terms of either delivery time or setup related costs. Based on a queueing network, a model is developed for a mix of multiple products following their own specific sequence of operations on one or more resources, while taking into account various sources of uncertainty, both in demand as well as in production characteristics. In addition, the model includes the impact of parallel servers and different time schedules in a multi-period planning setting. The corrupting influence of variabilities from rework and breakdown is explicitly modeled. As a major result, the differential evolution algorithm is able to find the optimal lead time as a function of the lot size. In this way, we add a conclusion on the debate on the convexity between lot size and lead time in a complex production environment. We show that differential evolution outperforms a steepest descent method in the search for the global optimal lot size. For problems of realistic size, we propose appropriate control parameters for the differential evolution in order to make its search process more efficient.status: publishe

A decision support system for the stochastic aggregate planning problem

An advanced decision support system is presented to answer aggregate planning questions regarding the trade-off between demand (product-mix) and supply (capacity) in a multi period stochastic setting. This tool improves the effectiveness and efficiency of sales and operation planning meetings by accounting for both revenues and costs that are relevant at the intermediate planning horizon. We develop a multi product, multi routing model, where a routing consists of a sequence of operations on different resources. Given customer demand in each time period, the model obtains the optimal production quantities in every period for each alternative routing, while explicitly taking into account the stochastic nature of both demand patterns and production lead times. This is the key difference between our approach and traditional aggregate planning models. At the same time, an optimal capacity level for each resource is obtained. We include trade-offs between level and chase strategies by charging costs for inventory, work-in-process, backorders, setups, regular time, overtime, etc. Outsourcing is considered as an alternative source with a stochastic lead time. The methodology builds upon a queueing network to estimate product’s lead time distribution and associated quoted lead time with a service level. More system improvements can be obtained by proper lot sizing. This model is a mixed integer non-linear programming problem. We show that the search process of the differential evolution algorithm is efficient to find stable results within acceptable time limits. A scenario analysis reveals interesting managerial insights.nrpages: 43status: publishe

www.elsevier.com/locate/cor Reverse logistics network design with stochastic lead times

This work is concerned with the efficient design of a reverse logistics network using an extended version of models currently found in the literature. Those traditional, basic models are formulated as mixed integer linear programs (MILP-model) and determine which facilities to open that minimize the investment, processing, transportation, disposal and penalty costs while supply, demand and capacity constraints are satisfied. However, we show that they can be improved when they are combined with a queueing model because it enables to account for (1) some dynamic aspects like lead time and inventory positions, and (2) the higher degree of uncertainty inherent to reverse logistics. Since this extension introduces nonlinear relationships, the problem is defined as a mixed integer nonlinear program (MINLP-model). Due to this additional complexity, the MINLP-model is presented for a single product-single-level network. Several examples are solved with a genetic algorithm based on the technique of differential evolution. � 2005 Published by Elsevier Ltd

Network and contract optimization for maintenance services and remanufacturing

Implementing comprehensive service contracts and sustainable supply chains are two recent trends that create the opportunity to develop maintenance contracts with an uptime guarantee for the customer and a remanufacturing process for removed parts. This involves management decisions on the design of the contract (price, uptime guarantee and overhaul interval) and the logistics network (facility locations, capacities and inventories with given service level). These two decision levels are interrelated: the number of contracts is a function of price and machine uptime, while this uptime is affected by the overhaul interval and network responsiveness. Steady-state queueing equations explicitly model the stochastic nature of the problem, e.g. the impact of resource utilization levels on lead time of the remanufacturing process. This approach results in a non-linear mixed integer model, which is solved by a differential evolution algorithm to find the maximum profit that simultaneously optimizes both problems. A real-life application reveals that price sensitivity is a critical determinant and that measures must be taken to tackle the problem of moral hazard.status: publishe

Optimization of a stochastic reverse logistics network with refurbishment and exchange options

Remanufacturing activities are gaining momentum in the manufacturing industry. Therefore, the need for optimized networks becomes more pressing. In this paper we take a profit maximization approach to simultaneously determine the optimal network and the delivery strategy to support remanufacturing services offered to customers. In order to set up a network, investment decisions have to be made concerning the number, locations and types of remanufacturing facilities. Additionally, appropriate capacity and inventory levels have to be set in order to guarantee a given service level. These network decisions are influenced by the way the remanufacturing services are offered by the manufacturing firm. We consider two possible service delivery strategies: the service provider can either make a quick exchange of the used part by a refurbished one or re-install the original part after remanufacturing it. The model described in this paper is applied to optimize the network and service delivery strategy at a worldwide manufacturer of construction, mining and industrial equipment.status: publishe