Research Topics:

• CAREER: A study of stochastic and robust integer programming: algorithms, computations and applications.
• Economic lot-sizing under uncertainty and stochastic integer programming
• Revenue management in logistics and distribution
• Container terminal operations with security inspection
• Inventory inaccuracy and cycle counting (finished)

CAREER: A study of stochastic and robust integer programming: Algorithms, computations and applications.

This project is supported by National Science Foundation under the award CMMI-0748204.

This project is just started and research progress will be posted here soon.

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Economic Lot-sizing under uncertainty and stochastic integer programming

This material is based upon work supported by the National Science Foundation under Grant No. CMMI-0700868. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

Strong formulations for stochastic lot-sizing problems
This research considers a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (l, S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (l, S) inequalities to a general class of valid inequalities, called the (Q, S) inequalities, and we establish necessary and sufficient conditions which guarantee that the (Q, S) inequalities are facet-defining. A separation heuristic for (Q, S) inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness of the (Q, S) inequalities as cuts.

Combining 0-1 inequalities
This research develops a framework for generating new valid inequalities by taking pair-wise combinations of valid inequalities for a set of 0-1 vectors. The approach easily extends to mixed 0-1 sets. The scheme is in general sequence-dependent. For some particular important cases, we identify combination sequences that lead to non-dominated inequalities. Finally, we demonstrate the framework for a number of important deterministic and stochastic integer programs and computational experiments show the efficiency of adding the new generated inequalities as cuts.

Cutting planes for multi-stage stochastic integer programs
This research addresses the problem of finding cutting planes for multi-stage stochastic integer programs. We give a general method for generating cutting planes for multi-stage stochastic integer programs based on combining inequalities that are valid for the individual scenarios. We apply the method to generate cuts for a stochastic version of a dynamic knapsack problem and to stochastic lot sizing problems. We give computational results which show that these new inequalities are very effective in a branch-and-cut algorithm.

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Collaborative research: Revenue management in Logistics and Distribution

This project is supported by National Science Foundation under the award IIP-0725843.

This project is just started and research progress will be posted here soon.

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Simulation and Optimization Studies on Berth Allocation with Inspection Operations

This project is supported by Department of Transportation. Joint work with Dr. Simin Pulat and the Ph.D. student Kang-Hung Yang

This project studies embedded simulation approaches for berth allocation problems with inspection operations, for which hard for current commercial simulation software to facilitate. An embedded simulation technique is first developed for the berth allocation problem with uncertain processing times. Two scheduling policies, a heuristic algorithm and First In First Out (FIFO) policy, are implemented through the embedded technique in the simulation model. Performance parameters such as queue length, average waiting time and total finishing time are evaluated to compare the performance of these two scheduling policies. Then, simulation experiments of different scenarios are executed to compare performances of the berth allocation problem with and without inspection between the heuristic algorithm and FIFO policy. The final simulation results indicate that for the berth allocation problem, if a proper scheduling policy is selected, for example an efficient heuristic algorithm, the system will perform better than the traditional FIFO approach.

We are currently investigating the mathematical insights of the problem.

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Inventory Inaccuracy and Cycle Counting

This project is supported by CELDi and joint work with Zhili Zhou, Dr. John J. Bartholdi III and Dr. Tieming Liu.

We study an inventory accuracy problem. In the warehousing management system, there are two types of inventory records. One is "physical inventory", which is the actual number of products in the warehouse. The other is "book inventory", which is the record in a computer. The discrepancy between these two records represents how inaccurate the inventory is. We provide a cycle counting policy deciding when and how to perform cycle counting. It performs much better than traditional ABC analysis according to our simulation results. Currently, we are implementing our policy to some industrial companies. Here is the detailed link to online software of Cycle Counting Scheduler.

Status: This project is completed and the copyright for the cycle counting scheduler has been applied. The working paper will be submitted soon.

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