solution

A supplier for the chemical industry sells sulphuric acid to two customers. The supplier manages the stock levels (VMI) for both customers.
The setup looks like this:

The supplier has separate agreements with each customer regarding stock level interval. For Customer 1, the stock level must be between 8-25 m3. For Customer 2, the agreement is 5-17 m3. The distance D1 for Customer 1 is 100 km. The distance D2 for Customer 2 is also 100 km. The distance between the Customer 1 and Customer 2 is 50 km. The transport cost is assumed to be proportional to the distance. The truck loads 30 m3.
Assume that once a stock reaches its lower limit, a replenishment is ordered and delivered so that the stock level the next day will be increased with the delivered quantity.
Example: The current stock level is 9 m3. The usage rate is 5 m3/day and the lower limit is 5 m3. The top limit is 17 m3. Therefore, we want the stock level for the next day to be 17 m3. This means that we have to deliver (17 – 9) + 5 = 13 m3, since 5 m3 will be used during the same day as the delivery.
In the table below, the current situation is presented:

Customer 1 Customer 2
Storage level, day 1 V1 = 17 m3 V2 = 12 m3
Product usage rate 8 m3/day 5 m3/day

1. Assume Customer 1 manages their own inventory. Also assume that an order is triggered when the stock level falls below 8 + 8 = 16 m3 and that delivery takes place the next day. Disregard Customer 2 in questions 1-3.

Which day in the coming 10 days’ period is the first delivery needed?

2. During the coming 10 days’ peiod, how many deliveries are needed?

3. How many kilometers are needed in total for the coming 10 daysâ€™ deliveries?

4. Similarily to question 1-3 above, assume that Customer 2 manages their own inventory. Also assume that an order is triggered when the stock level is 5 + 5 = 10 m3 and that delivery takes place the next day. Disregard Customer 1.

How many kilometers are needed in total for the coming 10 daysâ€™ deliveries?

5. Assume that a Vendor Managed Inventory setup is used in questions 5-9

On which day in the coming 10 days’ period is the first delivery run needed?

6. How many kilometers will the truck have to drive to complete the first delivery run?

7. On which day in the coming 10 days’ period is the second delivery run needed?

8. How many delivery runs are needed in total?

9. How many kilometers will the truck have to drive in total to make the deliveries to Customer 1 and 2?

Customer 2 Customer 1 1-2 km D, V1 m Va m capacity 30 m3 Capacity 20 m3 D1 km Do km Truck capacity 30 m3 Supplier

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