Luis J. Zeballos

A constraint programming model for the scheduling of flexible manufacturing systems with machine and tool limitations

This contribution presents an integrated constraint programming (CP) model to tackle the problems of tool allocation, machine loading, part routing, and scheduling in a flexible manufacturing system (FMS). The formulation, which is able to take into account a variety of constraints found in industrial environments, as well as several objective functions, has been successfully applied to the solution of various case studies of different sizes. Though some of the problem instances have bigger sizes than the examples reported to date in literature, very good-quality solutions were reached in quite reasonable CPU times. This good computational performance is due to two essential characteristics of the proposed model. The most significant one is the use of two sets of two-index variables to capture manufacturing activities instead of having just one set of four indexes. Thus, dimensionality is greatly reduced. The other relevant feature is the fact that the model relies on an indirect representation of tool needs by means of tool types, thus avoiding the consideration of tool copies.

Multi-stage stochastic optimization of the design and planning of a Closed-Loop Supply Chain

Abstract This paper addresses the multi-period, multi-product Closed-Loop Supply Chain (CLSC) design and planning problem with uncertain levels in the amount of raw material and customer demands. In addition, several aspects of practical significance are taken into account, such as those related with the operational and environmental costs of different transportation modes, as well as capacity limits on production, distribution and storage. The considered SC is structured as a 10-layer network (5 forward plus 5 reverse). It is important to note that the structure incorporates most of the network nodes plausible in practice. The consideration of the multi-period setting leads to a multi-stage stochastic programming problem, which is handled by a mathematical model based on a multi-stage stochastic mixed-integer linear programming formulation. The objective is to minimize the total cost of facilities, including operational, purchasing, storage, transportation and emissions costs, while guaranteeing costumers demands and maximizing the amount of products returned from repairing and decomposition centers. Thus, the performance measure seeks to obtain low-cost solutions subjected to environmental concerns.

Optimum Design and Planning of Resilient and Uncertain Closed-Loop Supply Chains

Abstract The design and planning of efficient supply chains (SC) is a major challenge that increases when the return of products has to be accounted for, the so-called closed-loop supply chains (CLSC). In the present work the effect of disruptions and modifications in the operating conditions of CLSCs are investigated on the basis of a 2-stage scenario based model previously developed by the authors. Metrics derived from graph theory are used, along with more conventional economic and operational indices. A discussion on the results obtained is presented to assess how the design and planning of the CLSC respond to these challenges and how these metrics may contribute to this objective.

A Constraint Programming Approach to Tool Allocation and Resource Scheduling in FMS

A novel constraint programming (CP) formulation that addresses the scheduling problem associated to a class of Flexible Manufacturing System (FMS) is presented. It tackles the problem in a global way by considering the tool allocation, machine assignment, routing and scheduling decisions, altogether in the formulation. Moreover, it is able to take into account a variety of objective functions. The proposed approach proved to be computationally efficient. This is shown by discussing the results of different size problems

CLSC design with simultaneous consideration of product design for manufacturing and remanufacturing

Abstract This paper studies the network design for a multi-product, multi-echelon and multi-period closed-loop supply chain (CLSC) accounting for decisions on the manufacture of new products and remanufactured versions of the new products. It is important to note that the design for remanufacture is taken into account in order to facilitate the product remanufacture and, thus, assures products and/or components value over time. This work proposes a mathematical formulation to identify the optimal network and product design accounting for products life cycle while maximizing the total network profit. The developed approach determines a) the network design from a general network superstructure that includes raw material suppliers, factories, distribution centers, customer, collection centers, dismantlers, repairing centers, final disposal locations and dismantling centers, b) the design for new products and the design for remanufactured products, c) the selling prices for remanufactured products and d) the number of units of used products to be taken back. In addition, environmental aspects are addressed by modeling the CO 2 emissions. The effectiveness of the proposed formulation is shown using a case study from a European consumer goods company.

Chapter 16 - Managing Risk in the Design of Product and Closed-Loop Supply Chain Structure

Abstract This paper studies the network design for a multiproduct, multi-echelon, and multi-period closed-loop supply chain (CLSC) accounting for decisions on the products to produce (new and remanufactured) products and associated raw materials (new and recovered) to maximize the CLSC profit. Demands are classified in two types: first and second markets. While the first market is associated with clients who must be satisfied with new products, the second market is connected with customers who are interested in buying recycled products in good working condition at low prices. The general network structure includes raw material suppliers, factories, distribution centers, customer demands, recovery centers, recycle centers, final disposal locations, and redistribution centers. Uncertain raw material supplies and customer demands are considered. In addition, risk management related with critical uncertain parameters is performed. As a result, a two-stage stochastic linear programming approach is developed to investigate possible network improvements by using risk management in the addressed problems. With the objective of achieving risk-averse solutions, a multi-objective function based on the expected values and the conditional value at risk (CVaR) concept is applied to both revenues and costs. Thus, the formulation aims to find solutions with high economic and environmental benefits through the CLSC in a context with variable conditions. Environmental aspects are addressed by modeling the CO 2 network emissions. The effectiveness of the proposed two-stage stochastic formulation is shown using a realistic case study from a European consumer goods company. The advantages of using the approach considering the variability of the solutions are compared with the features of the results obtained considering a risk-neutral performance measure.

Risk measures in a multi-stage stochastic supply chain approach

This paper considers the optimal design and planning problem of a closed-loop supply chain (CLSC) where profit maximization is pursued while considering: adjustments in the network structure during the planning horizon providing flexibility to the network as well as uncertainty in supply and customer demands. A multi-stage stochastic framework is developed where the effects of the uncertainty are represented by means of discrete scenarios. With the objective of achieving more robust solutions, besides the expected profit, three other risk adverse objective functions are also considered: two based on the mean absolute deviation and another centered on the conditional value at risk (CVaR) concept. In contrast to other approaches, in this work the definition of CVaR is applied to both revenues and costs. The proposed framework is evaluated by means of several cases. The advantages of using risk adverse performance measures are explored. Thus, the characteristics of the solutions obtained with the stochastic approach considering the variability of the solutions are compared with the features of the solution obtained considering a risk neutral performance measure. Finally, a sensitivity study of the parameters associated with the objective function centered on the conditional value at risk concept is conducted.

New Scheduling Approach for Shared Resources and Mixed Storage Policies

Abstract We propose a new mixed-integer linear programming (MILP) model for scheduling automated wet-etching stations (AWS), which can be classified as a multistage batch plant with both zero-wait and local storage policies and featuring a robot for moving the wafer lots from one stage to the next. The novelty is the use of a slot-based approach for handling the processing tasks together with general precedence sequencing variables for dealing with the transportation tasks. The performance of the new continuous-time model is shown to be significantly better than a pure sequencing based formulation and a closely related hybrid model taken from the literature.

A CP method for the scheduling of multiproduct continuous plants with resource constraints

Abstract This contribution presents advances in relation to a prior Constraint Programming (CP) formulation that addresses the scheduling problem of a multiproduct plant that has continuous stages and a limited number of intermediate storage tanks. The proposed approach is able to handle production rates of intermediate products which can be greater or lower than the rates of their corresponding consumption campaigns. In addition, the formulation includes a domain specific search strategy which aims at speeding-up the solution process and making problem tractable. The search strategy focuses on those campaigns that seem to be more demanding in terms of storage and equipment requirements and, resorts to a domain reduction specific procedure. The proposed approach has rendered very good results for various test problems.