Production and Operation Managements Advancement in Production Planning and Control Dr.Na GENG Prof.Zhibin JIANG Department of Industrial Engineering Management Shanghai Jiao Tong University
Production and Operation Managements Dr. Na GENG Prof. Zhibin JIANG Department of Industrial Engineering & Management Shanghai Jiao Tong University Advancement in Production Planning and Control
Content Optimized Production Planning Theory of Constraint (TOC) Advanced Planning System (APS) Mass Customization and its Production Planning 2 上浒充通大粤
Content Optimized Production Planning Theory of Constraint (TOC) Advanced Planning System (APS) Mass Customization and its Production Planning 2
Optimized Production Planning The most prevalent approach in the production planning is based on the concept of material requirement planning (MRP). √ The release time is obtained by shifting the expected output time back along the time scale by a period of the estimated average lead time; The release quantity is derived by dividing the expected output by the estimated average product yield. 上浒充通大粤
Optimized Production Planning The most prevalent approach in the production planning is based on the concept of material requirement planning (MRP). The release time is obtained by shifting the expected output time back along the time scale by a period of the estimated average lead time; The release quantity is derived by dividing the expected output by the estimated average product yield
Optimized Production Planning However,MRP-based methods have three major drawbacks: The lead time not only needs to be pre-specified but also is assumed to be static over the entire planning horizon; The capacity is assumed to be infinite,which means the derived production planning may not be realized; The production system is made nervous.Little adjustment in MPS changes the due date,requiring the recalculation of MRP 上浒充通大粤
Optimized Production Planning However, MRP-based methods have three major drawbacks: The lead time not only needs to be pre-specified but also is assumed to be static over the entire planning horizon; The capacity is assumed to be infinite, which means the derived production planning may not be realized; The production system is made nervous. Little adjustment in MPS changes the due date, requiring the recalculation of MRP
Optimized Production Planning -Introduction New methods need to be developed for production planning based on mathematical programming Time Dimension Space Dimension: .Corporate level planning:production planning .Shop floor level planning:production lot planning Mathematical programming based optimized Production Planning Commonly used in production planning: Linear Programming(LP)-the most widely used methods; Stochastic Programming (SP)-coping with the uncertainty 上泽充道大睾
Optimized Production Planning -Introduction New methods need to be developed for production planning based on mathematical programming Time Dimension Space Dimension: •Corporate level planning: production planning •Shop floor level planning: production lot planning Mathematical programming based optimized Production Planning Commonly used in production planning: Linear Programming (LP)- the most widely used methods; Stochastic Programming (SP)-coping with the uncertainty
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
Optimized Production Planning-Lp X7 is continuous: The barrels of milk is real Model Analysis: Features of LP:Linearity and Continuity: number The profit/kg of A1,A2 is Proportion:The contributions of constant,and the production Xi to objective function and quantity and time of A,A2 constraints are separately from one barrel of milk are proportional to xi. constant. The profit/kg of A,A,is Addition:The contributions of xi constant,and the production to objective function and quantity and time of A,A2 constraints are separately from one barrel of milk are independent of xi constant. 上济充通大粤
Optimized Production Planning -LP Model Analysis: Features of LP: Linearity and Continuity: Xi is continuous: The barrels of milk is real number Proportion: The contributions of xi to objective function and constraints are separately proportional to xi . Addition: The contributions of xi to objective function and constraints are separately independent of xj . The profit/ kg of A1, A2 is constant, and the production quantity and time of A1,A 2 from one barrel of milk are constant. The profit/ kg of A1, A2 is constant, and the production quantity and time of A1, A2 from one barrel of milk are constant
Optimized Production Planning-LP Conventional LP based production planning: A fixed upper bound is placed on production, assuming instantaneous production regardless of WIP level. Notations: i:Product index t:Period index X,,:Amount of product i produced in period t W:Amount of WIP of product i at the end of period t R:Amount of release for product i at the beginning of period t li:Amount of inventory for product i at the end of period t B:Amount of backorders for product i at the end of period t 上浒充通大粤
Optimized Production Planning -LP Conventional LP based production planning: A fixed upper bound is placed on production, assuming instantaneous production regardless of WIP level. Notations: i: Product index t: Period index Xit: Amount of product i produced in period t Wit: Amount of WIP of product i at the end of period t Rit: Amount of release for product i at the beginning of period t Iit: Amount of inventory for product i at the end of period t Bit: Amount of backorders for product i at the end of period t
