Ignacio Castillo

Optimization of block layout design problems with unequal areas: A comparison of MILP and MINLP optimization methods

The block layout design problem with unequal areas, which was originally formulated by Armour and Buffa in the early 1960s, is a fundamental optimization problem encountered in many manufacturing and service organizations. In this paper, we present a new modelling framework for effectively finding global optimal solutions for the block layout design problem with unequal areas. The most fundamental aspect of the framework consists of an exact representation of the underlying area restrictions. Our computational results consistently yield optimal solutions on several well-known test problems from the published literature. Furthermore, different mixed-integer linear and mixed-integer nonlinear optimization methods are compared. Our study indicates that the new modeling framework together with simple constraints to avoid symmetric layout solutions can be successfully used to find optimal layout solutions; therefore, seriously challenging other optimization methods on this important class of hard, fundamental problems. The new modeling framework may easily be applied in the context of the process plant layout and piping design problems.

An ε-accurate model for optimal unequal-area block layout design

This paper proposes a mixed-integer linear programming model for the block layout design problem with unequal areas that satisfies the area recuirements with a given accuracy. The basic aspect of the model consists of an e-accurate representation of the underlying nonconvex and hyperbolic area restrictions using cutting planes. The use of such a representation of the area restrictions allow us to solve several challenging test problems to optimality with a guarantee that the final area of each department is within an e% error of the required area. Numerical results indicate that the proposed model seriously challenge other optimization approaches on this important class of hard, fundamental problems.

Workforce scheduling with multiple objectives

In workforce scheduling, the optimal schedule has traditionally been determined by minimizing the cost of labor subject to an acceptable service level, which is defined as the percentage of customers served within a predetermined time interval. We propose an alternative multidimensional paradigm, where cost minimization and service level maximization are considered simultaneously, together with other, complementary criteria. The ultimate goal of the proposed approach is to open a broader workforce scheduling paradigm that incorporates service quality into the analysis and provides the possibility to study the interaction between cost and service quality. Furthermore, the approach enables us to avoid strong assumptions. An example with real-world, empirical demand data is provided.

Formal modeling methodologies for control of manufacturing cells: Survey and comparison

Over the last two decades, several formal modeling methodologies have emerged. In the manufacturing cell control domain, these methodologies are directed toward integrating the requirements specification, the design, and the implementation of the cell controller into a consistent process, supported by efficient analysis and development tools. The search for a single methodology powerful enough to span all the stages of the development life cycle of a formal model capable of replacing existing non-formal practices, however, has proven more difficult than expected. This paper presents a survey of several formal modeling methodologies that have been used for manufacturing cell control. Furthermore, the methodologies are classified and compared based on their expressive power, their verification power, their level of abstraction, and their span in relation to the formal models development life cycle.

Unit load and material-handling considerations in facility layout design

The effectiveness of a layout design cannot be completely measured if the operational characteristics of the manufacturing system are ignored. There is, therefore, a need to develop integrated manufacturing system design models. In this paper, the integration of unit load and material-handling considerations in a facility layout design is presented. This integration is based on a stochastic model that captures the operational characteristics of the manufacturing system and a nonlinear mixed-integer program that incorporates a department formation and facility layout. The non-linear mixed-integer program is solved using a simulated annealing-based algorithm. Analytical results for different manufacturing system scenarios are presented and compared with results obtained using alternative QAP-type formulations. Based on our experiments and the characteristics of the different formulations, key observations are presented and discussed.

An extended distance-based facility layout problem

The distance-based facility layout problem with unequal-area departments has been studied by many researchers for over 30 years. Still, current approaches require certain assumptions that limit the type of solutions obtained. In this paper, we consider manufacturing systems in which replicates of the same machine type may exist in the facility, and propose an extended distance-based facility layout problem that concurrently determines the number and shape of the departments, the assignment of machines to departments, and the allocation of part flow volume to individual machines. A non-linear mixed-integer program that accurately captures the extended facility layout and part flow allocation problem, a decomposition approach that exploits the structure of the formulation using a heuristic solution procedure, as well as computational results that evaluate the proposed approach, are presented.

Integrating design and production planning considerations in multi-bay manufacturing facility layout

Abstract This paper develops a new mathematical model that integrates layout design and production planning to prescribe efficient multi-bay manufacturing facilities. The model addresses the need to distribute department replicas throughout the facility and extends the use of product and process requirements as problem parameters in order to increase process routing flexibility. In addition, the model allows for the consideration of practical material handling and production features such as alternate process routings, product flow production patterns, and department replica capacities. Computational results demonstrate that the run time required to solve our test problems is quite acceptable given the long-term nature of facility layout decisions. Moreover, comparative results indicate that department replication can reduce material movement significantly while maintaining the existing production capacity.

A framework for multi-objective facility layout design

Multi-objective meta-heuristic framework for the BLP.Integrating several recent advances in the layout design.More than one possible layout to implement depending on management preferences.Good starting point when faced with a decision about which layout to implement. The most commonly used metric for facility layout design in the academic literature is the flow-distance metric, a weighted average between the material transfer and the distance travelled. Researchers and practitioners, however, have recognized that other metrics are also important. Facility layout designs obtained using the flow-distance metric exclusively have been criticized because they completely ignore empty material transfer, which generally increases work-in-process and equipment costs. Therefore, facility layout design (block layout design in particular) based exclusively on the flow-distance metric is insufficient. In this paper, we present a framework that utilizes the recent advancements in the facility planning literature to generate block layout designs based on three objectives: flow-distance, average work-in-process, and the number of required material handling devices. Numerical experiments are conducted on a number of standard problems, and the tradeoffs between the different objectives are studied. Our study indicates that it is critical to pursue multi-objective analysis and optimization for the actual implementation of the layouts.

A spring-embedding approach for the facility layout problem

The facility layout problem is concerned with finding the most efficient arrangement of a given number of departments with unequal area requirements within a facility. The facility layout problem is a hard problem, and therefore, exact solution methods are only feasible for small or greatly restricted problems. In this paper, we propose a spring-embedding approach that unlike previous approaches results in a model that is convex. Numerical results demonstrating the potential of our model and the efficiency of our solution procedure are presented.

PRICING AND INVENTORY STRATEGIES FOR A TWO-STAGE DUAL-CHANNEL SUPPLY CHAIN

The Internet is becoming increasingly important as a sales channel. Thus, most large retail firms have adopted a multi-channel strategy that includes both web-based channels and pre-existing offline channels. In this paper, we consider joint pricing and inventory/production decision problems for members in a monopoly two-stage dual-channel retailer supply chain. For a dual-channel retailer, pricing in one channel will affect the demand in the other channel. This subsequently affects the retailers replenishment (ordering) decisions, which have an impact on the producers inventory/production plans and wholesale price decisions. It is clear then that pricing decisions and inventory/production decisions are interacting in each member of the supply chain and among the members in the chain as well. In this paper, we analyze joint pricing and inventory/production problems under three scenarios by incorporating intra-product line price interaction in the EOQ model. We show that a unique equilibrium exists under certain realistic conditions. We also provide numerical results that offer insights for pricing strategies for the dual-channel retailer supply chain and for product design for different channels.