CHAPTER 3. DESIGN OF THE OPTIMAL INDUSTRIAL SYMBIOSIS SYSTEM TO IMPROVE BIOETHANOL PRODUCTION
3.4. Proposed methodology
3.4.1. LP model formulation for standalone plants
The LP formulation is developed for each plant when operating in standalone mode throughout the planning horizon. Equation 3.1 represents the objective function. Equation 3.2 – Equation 3.11 represent constraints for output products. Equation 3.12 – Equation 3.20 represent
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input product constraints and Equation 3.21 represents waste disposal constraint. All the products are classified into two categories: 1) Discrete and 2) Continuous. Discrete products are those products whose inventory can be stored and continuous products are those products that cannot be stored. Examples of continuous products include process steam, water and electricity.
The objective function Equation 3.1 for each individual plant is to maximize the profit of the entire planning horizon. This is obtained by subtracting the total operational cost from the total revenue obtained by selling output products to markets. The total operational cost includes input product purchase cost, production cost of output products, inventory holding cost, backorder cost, delay cost and waste disposal cost. The total revenue is calculated by 1(a) and 1(b) – 1(h) are used to obtain the different costs mentioned above.
SA
Zi
Max = 1(a) – 1(b) – 1(c) – 1(d) – 1(e) – 1(f) – 1(g) – 1(h) i (3.1)
The total revenue obtained by selling the final products and by-products to the market (1(a)) is calculated as follows:
The total production cost of the final products and by-products produced (1(b)) is calculated as follows:
1(b) = opi t
The total inventory holding cost for final products and by-products (1(c)) is calculated as follows:
The backorder cost of output products for the entire time period horizon (1(d)) is calculated as follows:
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The total cost of input products that are purchased over the entire time period horizon (1(e)) is calculated as follows:
1(e) = ipmktt i
The total cost of inventory held for input products (1(f)) is calculated as follows:
1(f) =
The total cost incurred when supplier fails to deliver input products in time (delay time) (1(g)) is calculated as follows:
The total disposal costs of waste (1(h)) is calculated as follows:
1(h) =
The LP model is subject to the following constraints:
Equation 3.2 – Equation 3.11 are the constraints for output products for each candidate plant for each time period.
Equation 3.2 is to constraint the amount of final products and by-products sold to the market to be always less than or equal to the demand of the market for any given time period.
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Equation 3.3 forces the amount of discrete final and by-products produced at each plant to be always greater than the total amount of products sold to the market for each time period.
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Equation 3.4 forces the amount of continuous final products and by-products produced to be always equal to the amount of products sold to market for each given time period.
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Equation 3.5 suggest that amount of final and by-products produced during any given time period is always less than the production capacity.
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Assumptions are made at times where combined production of certain products should be less than certain capacity limit. For example, at biorefinery plant, production of 2nd generation bioethanol such as corn stover, wheat straw and barley straw depends on the availability of bioethanol in nearby areas. So, combined production technology constraint is used and is given Equation 3.6. In such cases Equation 3.5 does not hold for those products.
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Equation 3.7 suggest that for discrete final and by-product, the inventory carried from the previous time period plus the amount produced should be equal to the amount sold plus the inventory carried to the next time period at any given time period.
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Equation 3.8 suggest that for continuous final and by-products, the amount produced should be equal to the amount sold in any given time period.
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Equation 3.9 calculates the amount of output product inventory held or backordered during each given time period. The inclusion of both inventory holding cost and backorder cost
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in objective function (Equation 3.1) enforces any one of inventory held or backordered to have value, but not both.
Equation 3.10 constraints inventory level of discrete products should be less than the holding capacity.
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Equation 3.11 suggest that the amount of by-products and waste products produced in any time period depends on the amount of final product produced in that time period and the rate of conversion when one unit of final product is produced.
Equation 3.12 – Equation 3.20 are the constraints for input products for each time period.
Equation 3.12 suggest that the amount of raw material and operational products purchased should be always less than the capacity that market can provide in any given time period. In the current problem, the capacity of input product that market can provide is assumed to be unlimited.
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Equation 3.13 suggest that for discrete raw materials and operational products, the amount of products purchased from market is always greater than or equal to the amount of input product used for any given time period.
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Equation 3.14 suggest that for continuous raw materials and operational products, the amount of products purchased from market should be equal to the amount of products used for each given time period.
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Equation 3.15 suggest that for discrete raw material and operational products, the inventory carried from the previous time period plus the amount purchased should be equal to the amount used plus the inventory carried to the next time period at any given time period.
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For continuous products, the amount of products purchased from market should be equal to the amount of products used in any given time period is given by Equation 3.16.
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Equation 3.17 is an inventory balancing constraint that enables to calculate amount of input product inventory held or delayed by supplier. Including both inventory holding cost and delay cost in objective function (Equation 3.1) enforces any one of the inventory held or delayed to have a value, but not both.
For discrete raw materials and operational products, the inventory level should be less than the holding capacity for each time period is given by Equation 3.18.
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Equation 3.19 suggests that the amount of raw materials and operational products used depends on the amount of final product produced and the unit final product conversion rate for any given time period.
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Assumptions are made to use combined technologies at plants. For example, CHP plant and cement plant often use co-combustion technology to reduce environmental impacts and to gain economic benefits. Such combined technology for input products is given by Equation 3.20. For such products, Equation 3.19 does not hold.
The amount of waste produced is equal to the amount of waste disposed for any given time period is given by Equation 3.21.
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