more-lp-formulations - More LP Formulations Chapters 5 and...

Unformatted text preview: More LP Formulations Chapters 5 and 7 McCarl and Spreen Types of Problem Joint Product Assembly Disassembly Assembly-Dissassembly Joint Product Wool and lamb Trees: Wood, sawdust Grain and straw Joint Products Problem Formulation Basic notation and the decision variable Let us denote the set of : the produced products : the production process possibities : the purchased inputs : the available resources Chapter 5: Joint Product Joint Product Let us define three fundamental decision variables as : the set of produced product, Sales,product : the set of production possibilities, Production,process : the set of purchased inputs, BuyInput,input The objective function: We want to maximize total profits across all of the possible productions. To do so, we need to know sale prices of the products, input purchase cost, inputs needed for different production processes, and any other production costs associated with production are needed. product pr prod o u duct ct SalePrice Sales ∑ The Objective Function is to Maximize input i input nput InputCost BuyInput- ∑ process proces process s OtherCost Production- ∑ 1) demand and supply balance for which quantity sold of each product is less than or equal to the quantity yielded by production. Constraints product produ proce , process ct ss process Pr- q oducti Sale o s 0 n ≤ ∑ 2)demand and supply balance for which quantity purchased of each fixed price input is greater than or equal to the quantity utilized by the production activities. process process input inp , proce ut ss BuyI r- 0 Produc n t n put io ≤ ∑ 3) resource availability constraint insuring that the quantity used of each fixed quantity input does not exceed the resource endowments resource, resou proces process pro s rce cess Production s b ≤ ∑ And non-negativity Algebra product pr prod o u duct ct SalePrice Sales ∑ input i input nput InputCost BuyInput- ∑ process proces process s OtherCost Production- ∑ product produ proce , process ct ss process Pr- q oducti Sale o s 0 n ≤ ∑ process process input inp , proce ut ss BuyI r- 0 Produc n t n put io ≤ ∑ resource, resou proces process pro s rce cess Production s b ≤ ∑ Max Subject to Two products produced: Wheat and wheat straw Three inputs: Land, fertilizer, seed Seven production processes possible, producing different amounts Of grain and straw and using different amounts of inputs Example: wheat production Information for each process Outputs and Inputs Per Acre Process 1 2 3 4 5 6 7 Wheat yield in bu. 30 50 65 75 80 80 75 Wheat straw yield/bales 10 17 22 26 29 31 32 Fertilizer use in Kg. 5 10 15 20 25 30 Seed in pounds 10 10 10 10 10 10 10 Land 1 1 1 1 1 1 1 Other information Wheat price = $4/bushel, wheat straw price =$0.5/bale Fertilizer = $2 per kg, Seed = $0.2/lb....
View Full Document