(400a) A Mixed-Integer Linear Programming Model for Optimizing the Scheduling and Assignment of Tank Farm Operations | AIChE

# (400a) A Mixed-Integer Linear Programming Model for Optimizing the Scheduling and Assignment of Tank Farm Operations

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## Authors

Carnegie Mellon University
Carnegie Mellon University
The Dow Chemical Company

Some chemical manufacturing sites ship finished products to customers using different modes of transportation (MOT) such as railcars, tank trucks, and pipelines. These MOTs are usually loaded from or connected to storage tanks. The set of storage tanks is known as a Tank Farm. All finished product has to be fed from the process into the storage tanks in the Tank Farm before being shipped to customers. This type of operation imposes the need for available storage space at all times in order to avoid unnecessary shut-downs of the upstream chemical process. When these shutdowns occur, they are said to be a result of storage tanks blocking the process. If the chemical process produces several products and each one requires dedicated tanks, the product-tank assignment and the processing schedule at the finishing lines determines how efficiently the storage space is used. An inefficient assignment of tanks or processing schedule can result in blocking the production of certain products even when there is plenty of available storage space in tanks assigned to other products. The problem outlined above is referred to in this work as the Tank Farm Operation Problem (TFOP).

This work presents a novel mixed-integer linear programming (MILP) formulation for the TFOP. The objective of the problem is to minimize blocking of the finished lines by obtaining an optimal schedule and an optimal allocation of storage resources. The scheduling part of the model is based on the Multi-operation Sequencing (MOS) model by Mouret et al. (2010). For scheduling purposes, there is a set of production orders that requires the processing of a certain amount of product in the finishing lines. Orders have a known release date and all are due at the end of the time horizon. The release date corresponds to the moment when a certain amount of an unfinished product becomes available for processing in the finishing lines. These lines can process the order immediately and feed the storage tanks, or delay the order for a while until there is available storage space. The main decisions in this problem are the tank-product assignment and the scheduling of processing orders.

The formulation is tested in three examples of different size and complexity. We solve a small example consisting of 2 lines, 3 products, and 5 tanks, spanning a two-week time horizon. This example illustrates the use of priority slots and the basic concept of multi-operation sequencing, where operations that can overlap are allowed to use the same priority slot. We solve two larger examples. In the first one, the system is extended to 8 products, 10 storage tanks, and 4 weeks; in the second one, the time horizon is further increased to cover 8 weeks. An important feature of the last example is that we consider a cyclic production schedule where inventory levels at the beginning and end of the time horizon have to be equal. The largest problem has 2,830 discrete variables, 36,011 continuous variables, and 87,745 constraints. Examples 1 and 2 are solved within optimality gap of 2% in less than 10 minutes of computations. However, Example 3 can only be solved within 6% of optimality after 7 CPU hours. An alternative for decreasing the computational complexity is considering unlimited storage in the cyclic schedule approach to determine the minimum storage space required to allocate all production.

The results point out to the possibility of incorporating the MILP model into a decision support system in combination a Discrete Event Simulation (DES) model of a tank farm, such as the one proposed by Sharda and Vazquez (2009).

References

Mouret S. I.E. Grossmann, and P. Pestiaux (2010).Time representations and mathematical models for process scheduling problems. Computers and Chemical Engineering, doi:10.1016/j.compchemeng.2010.07.007.

Sharda B., and A. Vazquez (2009). Evaluating Capacity and Expansion Opportunities at Tank Farm: A Decision Support System using Discrete Event Simulation. Winter Simulation Conference 2009, 2218 – 2224.