Chi-Tai Wang

A graph-pair representation and MIP-model-based heuristic for the unequal-area facility layout problem

The single-period unequal-area facility layout problem has been studied for several decades. Many solution approaches have been proposed. One approach models the problem as a mixed-integer program (MIP) in which binary (0/1) variables are used to prevent departments from overlapping with one another. Solving these MIPs is a difficult task-currently the largest problems that can be solved to optimality contain only 11 or 12 departments. Motivated by this situation, we developed a heuristic algorithm which utilizes a graph-pair representation technique to relax integer constraints. Our algorithm produces good solutions for problems considerably bigger than 12 departments. Moreover, our approach shows potentials in solving other layout problems such as multi-period or multi-floor.

IBM Blends Heuristics and Optimization to Plan Its Semiconductor Supply Chain

IBM uses operations research techniques to plan its enterprise semiconductor supply chain. The scale and complexity of this planning problem make developing robust supply chain optimization tools a challenge. Pure optimization methods are computationally infeasible, and fast heuristic methods alone generate poor results. Consequently, we developed a method that decomposes the problem by dividing the bills of materials product structure horizontally and vertically into complex and simple portions that are based on the major stages in semiconductor manufacturing and the choices of supply chain paths for building parts. The method then solves the complex portions with a mixed-integer program and the simple portions with fast heuristics that contain small embedded linear programs. A unique pegging algorithm, an explosion heuristic, and an implosion linear program enable coordination among these portions. The result is a unified production, shipping, and distribution plan with no evidence of the original decomposition. This method has helped IBM to improve its asset utilization, customer service, and inventory levels.

Optimized material requirements planning for semiconductor manufacturing

This paper describes a custom operational research algorithm, which is run nightly by IBM to create a material requirements plan for its semiconductor fabrication facility in Vermont, USA. To model alternative manufacturing processes and part substitutions, this application interweaves linear programming and heuristic methods to reap the benefits of each decision technology. At each level of the bills of materials supply chain with complex decision choices to be made, parallel linear programmes are invoked and their results are fed into a material requirements planning (MRP) heuristic, which processes parts through multiple iterations. The results from processing one level of the bills of materials supply chain are exploded to create demand for the next level and the interweaving of the two decision technologies continues. The algorithm creates recommended manufacturing releases and work-in-process priorities. These outputs point out opportunities for improvement in order to satisfy all demands on time. The output can be interpreted with well-known MRP assumptions.

The Ongoing Challenge: Creating an Enterprise-Wide Detailed Supply Chain Plan for Semiconductor and Package Operations

In the mid-1980s, Karl Kempf of Intel and Gary Sullivan of IBM independently proposed that planning, scheduling, and dispatch decisions across an enterprise’s demand-supply network were best viewed as a series of information flows and decision points organized in a hierarchy or set of decision tiers (Sullivan 1990). This remains the most powerful method to view supply chains in enterprises with complex activities. Recently, Kempf (2004) eloquently rephrased this approach in today’s supply chain terminology, and Sullivan (2005) added a second dimension based on supply chain activities to create a grid (Fig. 14.1) to classify decision support in demand-supply networks. The row dimension is decision tier and the column dimension is responsible unit. The area called global or enterprise-wide central planning falls within this grid.

Strategic capacity planning for light emitting diode (LED) supply chains across Taiwan and China

This paper describes a mixed-integer programming (MIP) model formulated for strategic capacity planning for light emitting diode (LED) makers of Taiwan, major companies in the global LED market. These firms have complex supply chains across Taiwan and China, and the region’s unique political and economic environment has created not only competitive advantages but also challenges in supply chain management: government regulations require that customer orders be accepted from Taiwan or China according to customer attributes; when conducting manufacturing, Taiwanese firms may need to transfer orders across national borders for reasons such as manufacturing technology (the required technology is available only at certain manufacturing facilities) or more efficient capacity utilization; and there are operations to be performed with specific processing requirements to follow, posing substantial challenges for planners. Motivated by the significance of these firms in the global market, we develop a MIP model with novel features to support their strategic capacity planning, covering demand and manufacturing-related decisions, including order acceptance and transfer, manufacturing starts, capacity expansion, and logistics. We illustrate the model’s performance using modified industry data in a numerical example; we also describe the potential impacts the model may create in industry applications.

The IBM advanced planning system for managing next generation demand-supply networks

IBM formed a team in the mid 1990s to develop a next generation demand-supply matching system. Using advanced heuristic algorithms and Linear Programming (LP), this team built a comprehensive system comprising solutions covering the complete spectrum of Supply Chain Planning (SCP). This systems cutting edge innovations and tremendous business impact have generated dozens of intellectual properties and earned major awards in operations research achievement for IBM. Since 2005, this system has also become a daily solver at Analog Devices, Inc. IBMs system fully supports a long term, incremental deployment of advanced SCP functions whenever needed with minimum effort required.

Incorporating contractual arrangements in production planning

The semiconductor supply chain is full of complexities outside of the traditional order, make/buy, and deliver process. One critical challenge occurs when part of a semiconductor fabricators capacity is allocated to produce wafers designed by and provided to fabless companies. In this situation, linked customer requirements are expressed simultaneously at both the semiconductor level of the supply chain and the finished goods level. As a result of the complex contractual relationships between the foundry and the fabless company, a new solution model and method is needed to determine a production plan. In our approach, two linear programming (LP) models are solved sequentially where the results of a first LP are post-processed into input for a second LP. We describe the application of this approach for two different types of contracts where the goal is maintaining as much common modeling as possible while ensuring the unique features of each contract are covered. For one type of contract, the first LP model determines the minimum quantities of wafers required to be released into the fab to meet the contractual obligation; these required starts are added as a constraint for the second LP model. For the other type of contract, the first LP determines production at one level of the bills of materials and feeds these outputs into a second LP that determines production for later stages of manufacture.

Enhancing mathematical programming models to account for demand priorities increasing as a function of delivery date

Linear and mixed integer programs are frequently used to allocate resources to support a prioritized statement of demands or needs. This paper describes how to enhance these mathematical programming formulations to reflect the dynamic relative importance of demands, namely the priorities of demands – relative to other objectives – increasing as a function of the time of demand fulfillment. We illustrate the modeling using data from a light-emitting diode manufacturer from Taiwan.

A graph-pair representation and MIP model based heuristic for the unequal-area facility layout problem

The single-period unequal-area facility layout problem has been studied for several decades. Many solution approaches have been proposed. One approach models the problem as a mixed-integer program (MIP) in which binary (0/1) variables are used to prevent departments from overlapping with one another. Solving these MIPs is a difficult task-currently the largest problems that can be solved to optimality contain only 11 or 12 departments. Motivated by this situation, we developed a heuristic algorithm which utilizes a graph-pair representation technique to relax integer constraints. Our algorithm produces good solutions for problems considerably bigger than 12 departments. Moreover, our approach shows potentials in solving other layout problems such as multi-period or multi-floor.