To determine which option does not have access to the local supply of coal, we`ll analyze each option individually.

Option 1: TISCO, Jamshedpur

TISCO, also known as Tata Steel Limited, is located in Jamshedpur, Jharkhand, India. Jharkhand is rich in mineral resources, including coal. Jharia, a town in Jharkhand, is known for having one of the largest coal reserves in India. Therefore, it is highly likely that TISCO in Jamshedpur has access to a local supply of coal.

Option 2: VSL, Bhadravati

VSL stands for Visvesvaraya Iron and Steel Limited, located in Bhadravati, Karnataka, India. Bhadravati is not a significant coal-producing region. The major coalfields in Karnataka are located in the northern part of the state, near cities like Ballari and Raichur. As Bhadravati is not in proximity to these coal-rich areas, it is reasonable to assume that VSL does not have access to a local supply of coal.

Option 3: HSL, Durgapur

HSL stands for Hindustan Steelworks Construction Limited, situated in Durgapur, West Bengal, India. West Bengal has a few coalfields, such as Raniganj and Asansol, which are located in the western part of the state. Durgapur is relatively close to these coalfields. Therefore, it is likely that HSL in Durgapur has access to a local supply of coal.

Option 4: HSL, Bhilai

HSL, in this case, could refer to Hindustan Steel Limited or Heavy Engineering Corporation Ltd., but since Bhilai is mentioned, it is more likely that Hindustan Steel Limited (now known as Steel Authority of India Limited, Bhilai Steel Plant) is being referred to. Bhilai is located in the Durg district of Chhattisgarh, India. Chhattisgarh is known for its vast coal reserves, with major coalfields like Korba and Raigarh located in the state. Bhilai, being situated in Chhattisgarh, likely has access to a local supply of coal.

Based on the above analysis:

- Option 1 (TISCO, Jamshedpur) is likely to have access to a local supply of coal.

- Option 2 (VSL, Bhadravati) is unlikely to have access to a local supply of coal.

- Option 3 (HSL, Durgapur) is likely to have access to a local supply of coal.

- Option 4 (HSL, Bhilai) is likely to have access to a local supply of coal.

Therefore, the option that does not have access to a local supply of coal is Option 2: VSL, Bhadravati.