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Parameters/Variables | Definitions |
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| The cost of supplying water to ith distributor from ith water-intake |
| The cost of transferring water to kth water-intake from (k-1)th water-intake in the horizontal supply chain |
| The water loss rate from (k-1)th to kth water-intake in the horizontal supply chain, and |
| The original pumping quantity from water source to the ith water-intake |
| The ordering amount of ith water-intake. |
| The fixed cost of water supply for the ith water-intake. |
| The fixed cost of water supply for the internal supplier, . |
| The fixed cost of water supply for the external supplier, . |
| The total fixed cost for the IBWT supplier is . |
| The wholesale price of water from internal to external supplier. |
| The retail price from the ith distributor to consumers, then . |
| The wholesale price from supplier to ith distributor, then . |
| The WGD effort for the ith water-intake, then . |
| The cost coefficient of the WGD effort. |
| The internal supplier’s bargaining power, . |
| The ith water-intake’s bargaining power, . |
| The possible maximum quantity of the water demand. |
| The price-elasticity of water demand, and satisfies . |
| The impact coefficient of WGD effort, and satisfies . |
| . |
| , the ith distributor’s “water stock factor”, then . |
| a random disturbance defined in the range with . |
| The ith distributor’s water demand, . |
| The mean value of . |
| The standard deviation of . |
| The probability density function (PDF) of . |
| The cumulative distribution function (CDF) of . |
| . |
note | , |
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