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DEGENERACY IN TRANSPORTATION PROBLEMS in Quantitative Techniques for management Tutorial 27 (This example is weird!)
Example from (Here) YouTube illustrates how to solve degeneracy in transportation problem.
Its explanation in pdf is here:
![Suppose we used least cost / vogel to get this feasible solution. Now our task is to find the optimal one using MODI method.](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fdd2cf7a3-4468-4e1c-b3f7-a10d07465a73%2FUntitled.png%3Ftable%3Dblock%26id%3De3334458-3506-48aa-9edf-992a88673c0e%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DUO3v1sqku1aJRPtnE_HmQqWOXu2KnNGGJI82Jt0XZtY?table=block&id=e3334458-3506-48aa-9edf-992a88673c0e&cache=v2)
When will we know the solution has degeneracy?
Step 1 of MODI: Check if there is a degeneracy.
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F53527ad1-f80c-49b3-8d55-e3afb8b2ffd7%2FUntitled.png%3Ftable%3Dblock%26id%3D23ecc0e2-f965-49ce-a051-aeb7c5aa8174%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3D6PD0KC4ug1bETNXMbAXar0fxM2PW0m-JMb74tuB6LP8?table=block&id=23ecc0e2-f965-49ce-a051-aeb7c5aa8174&cache=v2)
Now, we know there is a degeneracy. We want to find independent cells on which it can solve the problem.
What is independent cell?
Step 2 of MODI: Given there is a degeneracy, find independent cells on to solve the problem.
2 conditions:
- Unallocated cells that cannot form a closed loop
- Has the lowest value (e.g., cost)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F884440b0-2bb2-4dc9-874b-1ef2e2b157c4%2FUntitled.png%3Ftable%3Dblock%26id%3D83f6f4f9-99ec-4762-8313-6b375a16caa2%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DUVvfXU5x5duiNml-IEB-qqNv6ssZzHy15nvBhR_OEDw?table=block&id=83f6f4f9-99ec-4762-8313-6b375a16caa2&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F1cffb20b-da83-4425-a84c-2dd9d238c5d0%2FUntitled.png%3Ftable%3Dblock%26id%3Df2f23721-db3e-4ada-b16e-7006b32c0bbf%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DlhcVIYObI3EfaEOicEfL-4XBu3Z7Wwtc_rhzhduiUuY?table=block&id=f2f23721-db3e-4ada-b16e-7006b32c0bbf&cache=v2)
Step 3 of MODI: After confirming the independent cell, the degenerate issues is solved.
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F780378a7-1930-4c84-b4da-85c75e5d10bc%2FUntitled.png%3Ftable%3Dblock%26id%3D0afd9127-6007-41f0-b09e-7cff8d1f3b5a%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DW_TLggrPraoOP0moKYoUpSrjbGod0_nDQHV1u7oznCI?table=block&id=0afd9127-6007-41f0-b09e-7cff8d1f3b5a&cache=v2)
Step 4 we continue doing the MODI, until the optimality is reached.
Here is the solution:
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F97309205-8b0d-4a7a-8189-17184d2e4ace%2FUntitled.png%3Ftable%3Dblock%26id%3De0598e9a-e002-47bb-a341-4f712d025d88%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DaqjPyVzQ3-KxMs0j6VZsnFN0ZcVU-7yovdMOtlaAuXU?table=block&id=e0598e9a-e002-47bb-a341-4f712d025d88&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F15d94836-3521-4fea-a315-57d62342aeab%2FUntitled.png%3Ftable%3Dblock%26id%3Da8f39f68-6d33-4eb1-9a42-fecab6684495%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DoGZdzo08FSR8R1kuzf3gddaQS6hDZlYLSyMAT5I_R7o?table=block&id=a8f39f68-6d33-4eb1-9a42-fecab6684495&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F8ffc849f-454d-4b7d-84f2-b87182afd4db%2FUntitled.png%3Ftable%3Dblock%26id%3D84153bcd-20e3-4795-8bb7-e5281b5bb296%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DZMwIn9CE2wsanORtBFEauvhHO0mjyxp0V713jH0MHEs?table=block&id=84153bcd-20e3-4795-8bb7-e5281b5bb296&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F11eebc56-124a-4912-a64b-8ada4b1bd3ea%2FUntitled.png%3Ftable%3Dblock%26id%3Dcd805c5a-c5ec-47e6-93ea-46f9249f3173%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DY7Jp8VQEHqQeDTE0tjvNUclQQkFVbQfR9iGMkE08jkQ?table=block&id=cd805c5a-c5ec-47e6-93ea-46f9249f3173&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2Fa3016633-dee0-4ad5-8965-12a21d74e6d6%2FUntitled.png%3Ftable%3Dblock%26id%3Dac40009f-313f-463e-98bc-c6fc7cf2f148%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1725537600000%26signature%3DGq8s5WeO50Le8qvrAJCxw5d1_dB4T0Arrr6F26q8nVo?table=block&id=ac40009f-313f-463e-98bc-c6fc7cf2f148&cache=v2)
- Author:Jason Siu
- URL:https://jason-siu.com/article%2F5dc786ff-a242-4f53-91b7-505cc055b376
- Copyright:All articles in this blog, except for special statements, adopt BY-NC-SA agreement. Please indicate the source!
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