An Integrated Strategy for a Production Planning and Warehouse Layout Problem: Modeling and Solution Approaches

We study a real-world production warehousing case, where the company always faces the challenge to find available space for their products and to manage the items in the warehouse. To resolve the problem, an integrated strategy that combines warehouse layout with the capacitated lot-sizing problem is presented, which have been traditionally treated separately in the existing literature. We develop a mixed integer linear programming model to formulate the integrated optimization problem with the objective of minimizing the total cost of production and warehouse operations. The problem with real data is a large-scale instance that is beyond the capability of optimization solvers. A novel Lagrangian relax-and-fix heuristic approach and its variants are proposed to solve the large-scale problem. The preliminary numerical results from the heuristic approaches are reported

Examining the LEED Rating System Using Inverse Optimization

The Leadership in Energy and Environmental Design (LEED) rating system is the most recognized green building certification program in North America. In order to be LEED certified, a building must earn a sufficient number of points, which are obtained through achieving certain credits or design elements. In LEED versions 1 and 2, each credit was worth one point. In version 3, the LEED system changed so that certain credits were worth more than one point. In this study, we develop an inverse optimization approach to examine how building designers intrinsically valued design elements in LEED version 2. Because of the change in the point system between version 2 and version 3, we aim to determine whether building designers actually valued each credit equally, and if not, whether their valuations matched the values in version 3. Due to the large dimensionality of the inverse optimization problem, we develop an approximation to improve tractability. We apply our method to 306 different LEED-certified buildings in the continental United States. We find that building designers did not value all credits equally and that other factors such as cost, building type, and size, and certification level play a role in how the credits are valued. Overall, inverse optimization may provide a new method to assess historical data and support the design of future versions of LEED.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant No. 385972-2010