Basics of optimi z ation SU P P LY C H AIN AN ALYTIC S IN P YTH ON Aaren St u bber � eld S u ppl y Chain Anal y tics Mgr .
What is a s u ppl y chain A S u ppl y Chain consist of all parties in v ol v ed , directl y or indirectl y, in f u l � lling a c u stomer ’ s req u est . ¹ Incl u des : S u ppliers Internal Man u fact u ring O u tso u rced Logistics S u ppliers ( i . e . Third Part y S u ppliers ) 1 Chopra , S u nil , and Peter Meindl . _ S u ppl y Chain Management : Strateg y, Planning , and Operations ._ Pearson Prentice - Hall , 2007. SUPPLY CHAIN ANALYTICS IN PYTHON
What is a s u ppl y chain optimi z ation In v ol v es � nding the best path to achie v e an objecti v e based on constraints SUPPLY CHAIN ANALYTICS IN PYTHON
Crash co u rse in LP Linear Programing ( LP ) is a Po w erf u l Modeling Tool for Optimi z ation Optimi z ation method u sing a mathematical model w hose req u irements are linear relationships There are 3 Basic Components in LP : Decision Variables - w hat y o u can control Objecti v e F u nction - math e x pression that u ses v ariables to e x press goal Constraints - math e x pression that describe the limits of a sol u tions SUPPLY CHAIN ANALYTICS IN PYTHON
Introd u ctor y e x ample Use LP to decide on an e x ercise ro u tine to b u rn as man y calories as possible . P u sh u p R u nning Min u tes 0.2 per p u sh u p 10 per mile Calories 3 per p u sh u p 130 per mile Constraint - onl y 10 min u tes to e x ercise SUPPLY CHAIN ANALYTICS IN PYTHON
Basic components of an LP Decision Variables - What w e can control : N u mber of P u sh u ps & N u mber of Miles Ran Objecti v e F u nction - Math e x pression that u ses v ariables to e x press goal : Ma x (3 * N u mber of P u sh u ps + 130 * N u mber of Miles ) Constraints - Math e x pression that describe the limits of a sol u tions : 0.2 * N u mber of P u sh u ps + 10 * N u mber of Miles ≤ 10 N u mber of P u sh u ps ≥ 0 N u mber of Miles ≥ 0 SUPPLY CHAIN ANALYTICS IN PYTHON
E x ample sol u tion Optimal Sol u tion : 50 P u sh u ps 0 Miles Ran Calories B u rned : 150 SUPPLY CHAIN ANALYTICS IN PYTHON
LP v s IP v s MIP Terms Decision Variables Linear Programing ( LP ) Onl y Contin u o u s Integer Programing ( IP ) Onl y Discrete or Integers Mi x ed Integer Programing ( MIP ) Mi x of Contin u o u s and Discrete SUPPLY CHAIN ANALYTICS IN PYTHON
S u mmar y De � ned S u ppl y Chain Optimi z ation De � ned Linear Programing and Basic Components Decision Variables Objecti v e F u nction Constraints De � ned LP v s IP v s MIP SUPPLY CHAIN ANALYTICS IN PYTHON
Let ' s practice ! SU P P LY C H AIN AN ALYTIC S IN P YTH ON
Basics of P u LP modeling SU P P LY C H AIN AN ALYTIC S IN P YTH ON Aaren St u bber � eld S u ppl y Chain Anal y tics Mgr .
What is P u LP PuLP is a modeling frame w ork for Linear ( LP ) and Integer Programing ( IP ) problems w ri � en in P y thon Maintained b y COIN - OR Fo u ndation ( Comp u tational Infrastr u ct u re for Operations Research ) PuLP interfaces w ith Sol v ers CPLEX COIN Gurobi etc … SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling Cons u ltant for bo u tiq u e cake baker y that sell 2 t y pes of cakes 30 da y month There is : 1 o v en 2 bakers 1 packaging packer – onl y w orks 22 da y s SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling Di � erent reso u rce needs for the 2 t y pes of cakes : Cake A Cake B O v en 0.5 da y s 1 da y Bakers 1 da y 2.5 da y s Packers 1 da y 2 da y s . Cake A Cake B Pro � t $20.00 $40.00 SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling Objecti v e is to Ma x imi z e Pro � t Pro � t = 20* A + 40* B S u bject to : A ≥ 0 B ≥ 0 0.5 A + 1 B ≤ 30 1 A + 2.5 B ≤ 60 1 A + 2 B ≤ 22 SUPPLY CHAIN ANALYTICS IN PYTHON
Common modeling process for P u LP 1. Initiali z e Model 2. De � ne Decision Variables 3. De � ne the Objecti v e F u nction 4. De � ne the Constraints 5. Sol v e Model SUPPLY CHAIN ANALYTICS IN PYTHON
Initiali z ing model - LpProblem () LpProblem(name='NoName', sense=LpMinimize) name = Name of the problem u sed in the o u tp u t . lp � le , i . e . " M y LP Problem " sense = Ma x imi z e or minimi z e the objecti v e f u nction Minimi z e = LpMinimize ( defa u lt ) Ma x imi z e = LpMaximize SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling 1. Initiali z e Model from pulp import * # Initialize Class model = LpProblem("Maximize Bakery Profits", LpMaximize) SUPPLY CHAIN ANALYTICS IN PYTHON
Define decision v ariables - LpVariable () LpVariable(name, lowBound=None, upBound=None, cat='Continuous', e=None) name = Name of the v ariable u sed in the o u tp u t . lp � le lowBound = Lo w er bo u nd upBound = Upper bo u nd cat = The t y pe of v ariable this is Integer Binar y Contin u o u s ( defa u lt ) e = Used for col u mn based modeling SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling 1. Initiali z e Class 2. De � ne Variables # Define Decision Variables A = LpVariable('A', lowBound=0, cat='Integer') B = LpVariable('B', lowBound=0, cat='Integer') SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling 1. Initiali z e Class 2. De � ne Variables 3. De � ne Objecti v e F u nction # Define Objective Function model += 20 * A + 40 * B SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling 1. Initiali z e Class 2. De � ne Variables 3. De � ne Objecti v e F u nction 4. De � ne Constraints # Define Constraints model += 0.5 * A + 1 * B <= 30 model += 1 * A + 2.5 * B <= 60 model += 1 * A + 2 * B <= 22 SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling 1. Initiali z e Class 2. De � ne Variables 3. De � ne Objecti v e F u nction 4. De � ne Constraints 5. Sol v e Model # Solve Model model.solve() print("Produce {} Cake A".format(A.varValue)) print("Produce {} Cake B".format(B.varValue)) SUPPLY CHAIN ANALYTICS IN PYTHON
P u LP e x ample – reso u rce sched u ling from pulp import * # Define Constraints model += 0.5 * A + 1 * B <= 30 # Initialize Class model += 1 * A + 2.5 * B <= 60 model = LpProblem("Maximize Bakery Profits", model += 1 * A + 2 * B <= 22 LpMaximize) # Solve Model # Define Decision Variables model.solve() A = LpVariable('A', lowBound=0, print("Produce {} Cake A".format(A.varValue)) cat='Integer') print("Produce {} Cake B".format(B.varValue)) B = LpVariable('B', lowBound=0, cat='Integer') # Define Objective Function model += 20 * A + 40 * B SUPPLY CHAIN ANALYTICS IN PYTHON
S u mmar y P u LP is a P y thon LP / IP modeler Re v ie w ed 5 Steps of P u LP modeling process 1. Initiali z e Model 2. De � ne Decision Variables 3. De � ne the Objecti v e F u nction 4. De � ne the Constraints 5. Sol v e Model Completed Reso u rce Sched u ling E x ample SUPPLY CHAIN ANALYTICS IN PYTHON
Let ' s practice ! SU P P LY C H AIN AN ALYTIC S IN P YTH ON
Using lpS u m SU P P LY C H AIN AN ALYTIC S IN P YTH ON Aaren St u bber � eld S u ppl y Chain Anal y tics Mgr .
Mo v ing from simple to comple x Simple Baker y E x ample More Comple x Baker y E x ample # Define Decision Variables # Define Decision Variables A = LpVariable('A', lowBound=0, cat='Integer') A = LpVariable('A', lowBound=0, cat='Integer') B = LpVariable('B', lowBound=0, cat='Integer') B = LpVariable('B', lowBound=0, cat='Integer') C = LpVariable('C', lowBound=0, cat='Integer') D = LpVariable('D', lowBound=0, cat='Integer') E = LpVariable('E', lowBound=0, cat='Integer') F = LpVariable('F', lowBound=0, cat='Integer') SUPPLY CHAIN ANALYTICS IN PYTHON
Mo v ing from simple to comple x Objecti v e F u nction of Comple x Baker y E x ample # Define Objective Function model += 20*A + 40*B + 33*C + 14*D + 6*E + 60*F Need method to scale SUPPLY CHAIN ANALYTICS IN PYTHON
Using lpS u m () lpSum(vector) Therefore ... # Define Objective Function vector = A list of linear e x pressions model += 20*A + 40*B + 33*C + 14*D + 6*E + 60*F Eq u i v alent to ... # Define Objective Function var_list = [20*A, 40*B, 33*C, 14*D, 6*E, 60*F] model += lpSum(var_list) SUPPLY CHAIN ANALYTICS IN PYTHON
lpS u m w ith list comprehension # Define Objective Function cake_types = ["A", "B", "C", "D", "E", "F"] profit_by_cake = {"A":20, "B":40, "C":33, "D":14, "E":6, "F":60} var_dict = {"A":A, "B":B, "C":C, "D":D, "E":E, "F":F} model += lpSum([profit_by_cake[type] * var_dict[type] for type in cake_types]) SUPPLY CHAIN ANALYTICS IN PYTHON
S u mmar y Need w a y to s u m man y v ariables lpSum() Used in list comprehension SUPPLY CHAIN ANALYTICS IN PYTHON
Practice time ! SU P P LY C H AIN AN ALYTIC S IN P YTH ON
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