Production impact due to supply variations (Queueing Theory)

In this article, I will discuss about how to analyze production impact due to supply (or input) variations using simulation approach.

Consider the following scenarios: An iron ore receiving port takes in shipments and keep it in a holding area. Meanwhile, the ore is consumed by nearby processing plant. If the holding area is full, new shipment cannot unload. When it is empty, production is interrupted. Both situations are not desirable.

In Operation Research, this type of problem is categorized under Queueing Theory.

For the purpose of this discussion, we normalize the quantity into some arbitrary unit. Each shipment delivers a quantity of 1 unit.


Assumptions:

For simplicity, we will not include events due to, for example, failures of the conveyer system and the processing plant.

Shipment arrival variation can be described by Poisson process with λ = 5 shipments/day (or 0.2 day/shipments).

The holding area has a capacity of 20 units with 20% filled initially.

The plant processes the ore at the rate of 5 units/day, but it has a maximum processing rate of 6 units/day. It is designed to match the shipment arrival rate, and it does not fail in this example.

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Figure 1, Processing plant relies on non-continuous supply

The operator seeks to

1. Understand the utilization of the holding area.

2. Minimize the interruptions to processing plant (holding area becomes empty) and shipment operations (holding area is full).


A system model is created with the above requirements using AeROS software to simulated the scenario.

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Figure 2, Simple process flow model with varying input

The Shipment node in this scenario is configured to produce 1 unit with mean-time-between-arrival of 0.2 days.

The Holding Area node (a specialized node function as storage/buffer) with a capacity of 20 units. It takes in input from Shipment node and output to Process node simultaneously.

A 30-days simulation of 1000 executions is run.

The following shows the profile of a random execution.

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Figure 3, Tri-state plot. Process node (Plant) interrupted due to ore supply depletion

The following is the simulation results for storage node (Holding Area)

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Figure 4, Simulation results for Holding Area storage node

From the simulation results, over 30 days, on the average the Holding Area is

1. Full for 5.6 hours

2. Empty for 26.6 hours


Note that when the Holding Area is full, new shipment cannot unload. When it is empty, production is interrupted. Both situations may have cost implications.

In the above model, the Process node processes at 5 units/day. We did not account for the fact that it can process up to 6 units/day.

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Figure 5, Manage Process node production rate by controlling the Boost Node rate

In Figure 5, Boost node is turn-off (put to standby) so that the production rate is 5 units/day in normal operation. The Holding Area node is configured such that when its volume exceeds 50% of its capacity, it turns on Boost node, and Process node will receive 6 units/day as a result. Boost node is set to standby once the storage reduces to 25%.

A 30-days simulation of 1000 executions is run.

The following shows the profile of the last execution.

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Figure 6, Process node normally processes 5 units/day. If storage exceeds 50%, increases to 6 units/day

The following shows the simulation results for storage node (Holding Area)

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Figure 7, Simulation results for Holding Area storage node

From the simulation results, over 30 days, on the average the Holding Area is

1. Full for 0.17 hour, an improvement from 5.6 hours

2. Empty for 32.1 hours, getting worse compare to last configuration 26.6 hours


Reconfigure the flowrate of Boost and Main nodes to 2 and 4 units/day respectively, such that Process node produces 4 units/day in normal operation.

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Figure 8, Set the flowrates of Boost and Main nodes to 2 and 4 units/day respectively

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Figure 9, Simulation results for Holding Area storage node

From the simulation results, over 30 days, on the average the Holding Area is

1. Full for 0.5 hours

2. Empty for 3 hours


Through simulation method, we can setup different scenarios to determine the most desirable operating procedure.

This method is also useful for proof of concept during early design stage.


Conclusion

Using the Storage node construct in AeROS software, engineer can analyze production impact due to supply (or input) variations. This analysis provides an insight to the interaction among supply uncertainty, storage capacity and operating procedures.

Although this case study focuses on supply variations, one could add in nodes with maintenance properties in the system reliability model to further analyze the effect on productions.

With some imaginations, you could also extent the analyze to include demand variations.



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