Optimized Production Planning-LP Common LP model: min(or max)z=f(x),x=(x,..x) s.t.8,(x)≤0，i=1,2,…m x:Decision variables; f(x):Objective function; g(x)<0:constraints. ▣Commonly used terms: Objective function,constraints,right-hand side,feasible region,feasible solution,optimal solution. Features of LP Linearity:the objective and all constraints can be expressed as a linear function of the decisions variables; Continuity:the decision variables should be continuous 上泽充道大睾
Optimized Production Planning - LP 1 (or ) ( ), ( , ) . . ( ) 0, 1, 2, T n i min max z f x x x x st g x i m Common LP model: x: Decision variables; f(x): Objective function; gi(x) 0: constraints. Commonly used terms: Objective function, constraints, right-hand side, feasible region, feasible solution, optimal solution. Features of LP Linearity: the objective and all constraints can be expressed as a linear function of the decisions variables; Continuity: the decision variables should be continuous
Optimized Production Planning-LP Example:Make the production planning of milk product One barrel of milk can be made into 3kg A by 12 hours or 4kg A2 by 8 hours.The profit of A and A2 are $24/kg and $16/kg, respectively.The supply of raw material,milk,is 50 barrels per day.Capacity is 480 hours per day and the production limit of A is 100kg at most. 1 barrel 3 kg A1 Profit:$24/kg 12 hours of milk 4 kgA2 →Profit:S16/kg 8 hours 50 barrels of milk/day,480 hours available/day,and 100kg A at most 上泽充道大睾
Optimized Production Planning -LP Example: Make the production planning of milk product One barrel of milk can be made into 3kg A1 by 12 hours or 4kg A2 by 8 hours. The profit of A1 and A 2 are $24/kg and $16/kg, respectively. The supply of raw material, milk, is 50 barrels per day. Capacity is 480 hours per day and the production limit of A1 is 100kg at most. 50 barrels of milk/ day, 480 hours available/day, and 100kg A1 at most 1 barrel of milk 12 hours 8 hours 3 kg A 1 4 kg A 2 Profit: $16/kg Profit: $24/kg
Optimized Production Planning-LP X1:barrels of milk x2:barrels of milk to Decision variables to produce A produce A2 Objective function Total profit/day M@xz=24*3x1+16*4x2 Raw material: x1+x2≤50 Work hours: 12x1+8x2≤480 Constraints Requirement 3x1≤100 constraints X1,x2≥0 上浒充通大粤
Optimized Production Planning -LP Decision variables x1: barrels of milk to produce A1 x2: barrels of milk to produce A 2 Constraints Raw material: 50 x1 x 2 Work hours: 12 x1 8 x 2 480 Requirement constraints 3 100 x 1 , 0 x1 x 2 Objective function Total profit/day: 1 2 Max z x x 24*3 16*4