(Solved Homework): A supplier for the chemical industry sells sulphuric acid to two customers. The supplier manages the stock levels

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 days’ 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 days’ 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?

 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Opening Stock 17 25 25 25 25 25 25 25 25 25 Usage Stock 8 8 8 8 8 8 8 8 8 8 Closing Stock 9 17 17 17 17 17 17 17 17 17 Ordering Stock 16 8 8 8 8 8 8 8 8 8 Max Cap 25 25 25 25 25 25 25 25 25 25 Distance 100 100 100 100 100 100 100 100 100 100

The above table shows the stock and ordering quantity for customer -1 over 10 days period.

1. The first order will be the next day, i.e, Day-2 with quantity of 16.

This is because the for the day-1 the opening stock is 17 of which 8 is used during the day and remaining 9 will be for close. How ever, the closing stock of 9 is less than min ordering quantity of (8+8=16), hence order will be generated. The order quantity would be 25-9=17, this is because the volume must be 8-25m3.

2. For 10 days, 10 deliveried are required.

3. Considering only customer-1 for 10 deliveries with 100km each deliveries, a total of 1000km are needed.

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