Solutions 1 and 92 are optimal with respect to economic value and water requirements, respectively. Our methodology produced robust solutions 74 achieving a tradeoff between these objectives. The robustness of our solutions (71-74, 100) is displayed in the robustness space (i.e., objective robustness versus feasibility robustness); in this space the implementation robust solutions shown in red dominate the efficient solutions when affected by uncertainty during implementation.

A solution is implementation-robust if it maintains close-to-optimality and close-to-feasibility when the values it prescribes change unpredictably at the time of implementation. Leon et.al (1994) performed pioneering work in scheduling robustness in computer-controlled manufacturing systems. Jornada and Leon (2016) developed a robust multi-objective linear programming methodology that reduces the size of the set of efficient solutions and apply the methodology to the electricity generation capacity expansion problem.

• Jornada, D. and V.J. Leon, "Biobjective robust optimization over the efficient set for Pareto set reduction," EJOR, 252, 573-586, 2016.
• LEON VJ, SD Wu and RH Storer, "Robustness Measures and Robust Scheduling," IIE Transactions, 26(5), 32-43, 1994.

We developed a framework for integrated diagnostics, maintenance planning, and operations scheduling for an electronics assembly line. In this project data collected from the production line and used to monitor the quality of the process using multivariate control charts, is also used as input of a maintenance diagnostics module that uses influence diagrams to identify the most probable cause of a quality problem. Once the cause of the maintenance problem is identified, a maintenance planning module generates the necessary tasks required to complete the maintenace task. Finally, an integrated maintenance and job scheduling module updates the production schedule.

• Jeong, I-J, V. J. Leon and J.R. Villalobos, "Integrated decision support system for diagnosis, maintenance planning and scheduling of manufacturing systems," IJPR, Vol. 45, No. 2, 267-285, 2007.
• Lee C.-Y. and V.J. Leon, "Machine scheduling with a rate-modifying activity," European Journal of Operational Research, 128, 119-128, 2001.

We developed search strategies find efficient solutions in a bicriteria solution space. In the animation, one search strategy sweeps the solution space depth-first, while another one searches breath-first.

Neighborhood search is an effective alternative for the solution of hard combinatorial problems that often appear in the management of operational systems. Examples of heuristic search include Genetic Algorithms, Problem-Space based search, Simulated Annealing, and Tabu-Search.

• Leon, V.J. and B. Ramamoorthy, “Strength and Adaptability of Problem-Space Based Neighborhoods for Resource-Constrained Scheduling,” OR Spektrum - Special Issue in Applied Local Search, Vol. 17, 173-182, 1995.

Optimization under partial information sharing allows multiple groups in an organization solve optimization problems and make decision with limited information sharing. These models allow solving optimization and decision problems by multiple decision makers with minimal information exchange between them. This may have potential applications in cyber-enabled manufacturing in continuosly evolving supply chains.

• Beier, E., Venkatachalam, S., Leon, V. J., & Ntaimo, L., "Nodal decomposition–coordination for stochastic programs with private information restrictions," IIE Transactions, 1-15, 2015.
• Chu, C.-L and V.J. Leon, "Scalable Methodology for Supply Chain Inventory Coordination with Private Information," EJOR, 195, 262-279, 2009.
• Jeong, I-J and V.J. Leon, "Decision making and cooperative interaction via coupling agents in organizationally distributed systems," IIE Transactions - Special Issue on Large Scale Optimization, 34, 789-802, 2002.

Sample articles

• Shin, H.J. and V.J. Leon, "Scheduling with Setup Times and Due-Dates in TFT-LCD Manufacturing," Int. J. Prod. Res., Vol. 42, No. 20, 4235-4248, 2004.
• Leon V.J. and B. Ramamoorthy, "An Adaptable Problem-Space Based Search Method for Flexible Flow Line Scheduling," IIE Transactions in Scheduling and Logistics, 29(2), 115-125, 1997.
• Leon, V.J., S.D. Wu and R.H. Storer, "Game-Theoretic Control Approach of Job Shops," International Journal of Production Research, 32(6), 1451-1476, 1994.
• Leon, V.J. and S.D. Wu, "On Scheduling with Ready-Times, Due-Dates and Vacations," Naval Research Logistics, 39(1), 53-64, 1992.

Supply-Chain and Logistics

• Chu, C.-L. and V.J. Leon, "Power-of-Two Single-Warehouse Multi-Buyer Inventory Coordination in Distributed Environments with Partial Information Sharing," International Journal or Production Economics, 111, 562-574, 2008.
• Chu, C.-L and V.J. Leon, "Single-Vendor Multi-Buyer Inventory Coordination: Global and Private Information Cases," EJOR, 191, 485-503, 2008.

Energy, Water and Environment Nexus

• Jornada, D. and V.J. Leon, "Robustness methodology to aid multiobjective decision making in the electricity generation capacity expansion problem to minimize cost and water withdrawal," Applied Energy, 162, 1089-1108, 2016.
• Capar, I., M. Kuby, V.J Leon and J. Tsai, "An Arc Cover-Path-Cover Formulation and Strategic Analysis for of Alternative-Fuel Station Locations, EJOR, 227, 142-151, 2013.