# Logistics Models

These models and simulations have been tagged “Logistics”.

These models and simulations have been tagged “Logistics”.

Multi-echelon inventory optimization (sounds like a complicated phrase!) looks at the way we are placing the inventory buffers in the supply chain. The traditional practice has been to compute the safety stock looking at the lead times and the standard deviation of the demand at each node of the supply chain. The so called classical formula computes safety stock at each node as Safety Stock = Z value of the service level* standard deviation * square root (Lead time). Does it sound complicated? It is not. It is only saying, if you know how much of the variability is there from your average, keep some 'x' times of that variability so that you are well covered. It is just the maths in arriving at it that looks a bit daunting.

While we all computed safety stock with the above formula and maintained it at each node of the supply chain, the recent theory says, you can do better than that when you see the whole chain holistically.

Let us say your network is plant->stocking point-> Distributor-> Retailer. You can do the above safety stock computation for 95% service level at each of the nodes (classical way of doing it) or compute it holistically. This simulation is to demonstrate how multi-echelon provides better service level & lower inventory. The network has only one stocking point/one distributor/one retailer and the same demand & variability propagates up the supply chain. For a mean demand of 100 and standard deviation of 30 and a lead time of 1, the stock at each node works out to be 149 units (cycle stock + safety stock) for a 95% service level. You can start with 149 units at each level as per the classical formula and see the product shortage. Then, reduce the safety stock at the stocking point and the distributor levels to see the impact on the service level. If it does not get impacted, it means, you can actually manage with lesser inventory than your classical calculations.

That's what your multi-echelon inventory optimization calculations do. They reduce the inventory (compared to classical computations) without impacting your service levels.

Hint: Try with the safety stocks at distributor (SS_Distributor) and stocking point (SS_Stocking Point) as 149 each. Check the number of stock outs in the simulation. Now, increase the safety stock at the upper node (SS_stocking point) slowly upto 160. Correspondingly keep decreasing the safety stock at the distributor (SS_Distributor). You will see that for the same #stock outs, by increasing a little inventory at the upper node, you can reduce more inventory at the lower node.

Multi-echelon inventory optimization (sounds like a complicated phrase!) looks at the way we are placing the inventory buffers in the supply chain. The traditional practice has been to compute the safety stock looking at the lead times and the standard deviation of the demand at each node of the supply chain. The so called classical formula computes safety stock at each node as Safety Stock = Z value of the service level* standard deviation * square root (Lead time). Does it sound complicated? It is not. It is only saying, if you know how much of the variability is there from your average, keep some 'x' times of that variability so that you are well covered. It is just the maths in arriving at it that looks a bit daunting.

While we all computed safety stock with the above formula and maintained it at each node of the supply chain, the recent theory says, you can do better than that when you see the whole chain holistically.

Let us say your network is plant->stocking point-> Distributor-> Retailer. You can do the above safety stock computation for 95% service level at each of the nodes (classical way of doing it) or compute it holistically. This simulation is to demonstrate how multi-echelon provides better service level & lower inventory. The network has only one stocking point/one distributor/one retailer and the same demand & variability propagates up the supply chain. For a mean demand of 100 and standard deviation of 30 and a lead time of 1, the stock at each node works out to be 149 units (cycle stock + safety stock) for a 95% service level. You can start with 149 units at each level as per the classical formula and see the product shortage. Then, reduce the safety stock at the stocking point and the distributor levels to see the impact on the service level. If it does not get impacted, it means, you can actually manage with lesser inventory than your classical calculations.

That's what your multi-echelon inventory optimization calculations do. They reduce the inventory (compared to classical computations) without impacting your service levels.

Hint: Try with the safety stocks at distributor (SS_Distributor) and stocking point (SS_Stocking Point) as 149 each. Check the number of stock outs in the simulation. Now, increase the safety stock at the upper node (SS_stocking point) slowly upto 160. Correspondingly keep decreasing the safety stock at the distributor (SS_Distributor). You will see that for the same #stock outs, by increasing a little inventory at the upper node, you can reduce more inventory at the lower node.

Initially all of them are randomly spread geographically.

Then some Senders and Receivers randomly are willing to interact, and searching for the available carrier. All carriers have different radius of availability (suppose humans may walk maximum 6-10 km, car - 200-400 km, jet - over 10000). So the condition of deal is carrier containing receiver and sender within his radius of availability and who is free now.

Connections between inactive agents deteriorate with decay rate, after some time receiver and sender forget about each other and may form other connections in the system.

All agents have possibility to churn, and it is higher if they don't have any connections (any interest in the system)

Multi-echelon inventory optimization (sounds like a complicated phrase!) looks at the way we are placing the inventory buffers in the supply chain. The traditional practice has been to compute the safety stock looking at the lead times and the standard deviation of the demand at each node of the supply chain. The so called classical formula computes safety stock at each node as Safety Stock = Z value of the service level* standard deviation * square root (Lead time). Does it sound complicated? It is not. It is only saying, if you know how much of the variability is there from your average, keep some 'x' times of that variability so that you are well covered. It is just the maths in arriving at it that looks a bit daunting.

While we all computed safety stock with the above formula and maintained it at each node of the supply chain, the recent theory says, you can do better than that when you see the whole chain holistically.

Let us say your network is plant->stocking point-> Distributor-> Retailer. You can do the above safety stock computation for 95% service level at each of the nodes (classical way of doing it) or compute it holistically. This simulation is to demonstrate how multi-echelon provides better service level & lower inventory. The network has only one stocking point/one distributor/one retailer and the same demand & variability propagates up the supply chain. For a mean demand of 100 and standard deviation of 30 and a lead time of 1, the stock at each node works out to be 149 units (cycle stock + safety stock) for a 95% service level. You can start with 149 units at each level as per the classical formula and see the product shortage. Then, reduce the safety stock at the stocking point and the distributor levels to see the impact on the service level. If it does not get impacted, it means, you can actually manage with lesser inventory than your classical calculations.

That's what your multi-echelon inventory optimization calculations do. They reduce the inventory (compared to classical computations) without impacting your service levels.

Hint: Try with the safety stocks at distributor (SS_Distributor) and stocking point (SS_Stocking Point) as 149 each. Check the number of stock outs in the simulation. Now, increase the safety stock at the upper node (SS_stocking point) slowly upto 160. Correspondingly keep decreasing the safety stock at the distributor (SS_Distributor). You will see that for the same #stock outs, by increasing a little inventory at the upper node, you can reduce more inventory at the lower node.

Initially all of them are randomly spread geographically.

Then some Senders and Receivers randomly are willing to interact, and searching for the available carrier. All carriers have different radius of availability (suppose humans may walk maximum 6-10 km, car - 200-400 km, jet - over 10000). So the condition of deal is carrier containing receiver and sender within his radius of availability and who is free now.

Connections between inactive agents deteriorate with decay rate, after some time receiver and sender forget about each other and may form other connections in the system.

All agents have possibility to churn, and it is higher if they don't have any connections (any interest in the system)

Initially all of them are randomly spread geographically.

Then some Senders and Receivers randomly are willing to interact, and searching for the available carrier. All carriers have different radius of availability (suppose humans may walk maximum 6-10 km, car - 200-400 km, jet - over 10000). So the condition of deal is carrier containing receiver and sender within his radius of availability and who is free now.

Connections between inactive agents deteriorate with decay rate, after some time receiver and sender forget about each other and may form other connections in the system.

All agents have possibility to churn, and it is higher if they don't have any connections (any interest in the system)

Initially all of them are randomly spread geographically.