Python Script slowing down as it progresses?

10,723

Solution 1

This would be a good time to look at a profiler. You can profile the code to determine where time is being spent. It would appear likely that you issue is in the simulation code, but without being able to see that code the best help you're likely to get going to be vague.

Edit in light of added code:

You're doing a fair amount of copying of lists, which while not terribly expensive can consume a lot of time.

I agree the your code is probably unnecessarily confusing and would advise you to clean up the code. Changing the confusing names to meaningful ones may help you find where you're having a problem.

Finally, it may be the case that your simulation is simply computationally expensive. You might want to consider looking into a SciPy, Pandas, or some other Python mathematic package to get better performance and perhaps better tools for expressing the model you're simulating.

Solution 2

I experienced a similar problem with a Python 3.x script I wrote. The script randomly generated 1,000,000 (one million) JSON objects, writing them out to a file.

My problem was that the program was growing progressively slower as time proceeded. Here is a timestamp trace every 10,000 objects:

So far: Mar23-17:56:46:      0
So far: Mar23-17:56:48:  10000   ( 2 seconds)
So far: Mar23-17:56:50:  20000   ( 2 seconds)
So far: Mar23-17:56:55:  30000   ( 5 seconds)
So far: Mar23-17:57:01:  40000   ( 6 seconds)
So far: Mar23-17:57:09:  50000   ( 8 seconds)
So far: Mar23-17:57:18:  60000   ( 8 seconds)
So far: Mar23-17:57:29:  70000   (11 seconds)
So far: Mar23-17:57:42:  80000   (13 seconds)
So far: Mar23-17:57:56:  90000   (14 seconds)
So far: Mar23-17:58:13: 100000   (17 seconds)
So far: Mar23-17:58:30: 110000   (17 seconds)
So far: Mar23-17:58:51: 120000   (21 seconds)
So far: Mar23-17:59:12: 130000   (21 seconds)
So far: Mar23-17:59:35: 140000   (23 seconds)

As can be seen, the script takes progressively longer to generate groups of 10,000 records.

In my case it turned out to be the way I was generating unique ID numbers, each in the range of 10250000000000-10350000000000. To avoid regenerating the same ID twice, I stored a newly generated ID in a list, checking later that the ID does not exist in the list:

trekIdList = []

def GenerateRandomTrek ():
    global trekIdList

    while True:
        r = random.randint (10250000000000, 10350000000000)
        if not r in trekIdList:
            trekIdList.append (r)
            return r

The problem is that an unsorted list takes O(n) to search. As newly generated IDs are appended to the list, the time needed to traverse/search the list grows.

The solution was to switch to a dictionary (or map):

trekIdList = {}
. . .
def GenerateRandomTrek ():
    global trekIdList

    while True:
        r = random.randint (10250000000000, 10350000000000)
        if not r in trekIdList:
            trekIdList [r] = 1
            return r

The improvement was immediate:

So far: Mar23-18:11:30:      0
So far: Mar23-18:11:30:  10000
So far: Mar23-18:11:31:  20000
So far: Mar23-18:11:31:  30000
So far: Mar23-18:11:31:  40000
So far: Mar23-18:11:32:  50000
So far: Mar23-18:11:32:  60000
So far: Mar23-18:11:32:  70000
So far: Mar23-18:11:33:  80000
So far: Mar23-18:11:33:  90000
So far: Mar23-18:11:33: 100000
So far: Mar23-18:11:34: 110000
So far: Mar23-18:11:34: 120000
So far: Mar23-18:11:34: 130000
So far: Mar23-18:11:35: 140000

The reason is that accessing a value in a dictionary/map/hash is O(1).

Moral: When dealing with large numbers of items, use a dictionary/map or binary searching a sorted list rathen than an unordered list.

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10,723
Austin Wismer
Author by

Austin Wismer

Updated on June 14, 2022

Comments

  • Austin Wismer
    Austin Wismer almost 2 years

    I have a simulation running that has this basic structure:

    from time import time
    
    def CSV(*args):
        #write * args to .CSV file
        return
    
    def timeleft(a,L,period):
        print(#details on how long last period took, ETA#)
    
    for L in range(0,6,4):
        for a in range(1,100):
            timeA = time()
    
                for t in range(1,1000):
    
                    ## Manufacturer in Supply Chain ##
    
                    inventory_accounting_lists.append(#simple calculations#)
    
                        # Simulation to determine the optimal B-value (Basestock level)
    
                        for B in range(1,100):
                            for tau in range(1,1000):
                                    ## simple inventory accounting operations##
    
                    ## Distributor in Supply Chain ##
    
                    inventory_accounting_lists.append(#simple calculations#)
    
                        # Simulation to determine the optimal B-value (Basestock level)
    
                        for B in range(1,100):
                            for tau in range(1,1000):
                                    ## simple inventory accounting operations##
    
                    ## Wholesaler in Supply Chain ##
    
                    inventory_accounting_lists.append(#simple calculations#)
    
                        # Simulation to determine the optimal B-value (Basestock level)
    
                        for B in range(1,100):
                            for tau in range(1,1000):
                                    ## simple inventory accounting operations##
    
                    ## Retailer in Supply Chain ##
    
                    inventory_accounting_lists.append(#simple calculations#)
    
                        # Simulation to determine the optimal B-value (Basestock level)
    
                        for B in range(1,100):
                            for tau in range(1,1000):
                                    ## simple inventory accounting operations##
    
    
            CSV(Simulation_Results)
    
            timeB = time()
    
            timeleft(a,L,timeB-timeA)
    

    As the script continues, it seems to be getting slower and slower. Here is what it is for these values (and it increases linearly as a increases).

    • L = 0, a = 1: 1.15 minutes
    • L = 0, a = 99: 1.7 minutes
    • L = 2, a = 1: 2.7 minutes
    • L = 2, a = 99: 5.15 minutes
    • L = 4, a = 1: 4.5 minutes
    • L = 4, a = 15: 4.95 minutes (this is the latest value it has reached)

    Why would each iteration take longer? Each iteration of the loop essentially resets everything except for a master global list, which is being added to each time. However, loops inside each "period" aren't accessing this master list -- they are accessing the same local list every time.

    EDIT 1: I will post the simulation code here, in case anyone wants to wade through it, but I warn you, it is rather long, and the variable names are probably unnecessarily confusing.

    #########
    a = 0.01
    L = 0
    total = 1000
    sim = 500
    inv_cost = 1
    bl_cost = 4
    #########
    
    # Functions
    
    import random
    from time import time
    time0 = time()
    
    # function to report ETA etc.
    
    def timeleft(a,L,period_time):
        if L==0:
            periods_left = ((1-a)*100)-1+2*99
        if L==2:
            periods_left = ((1-a)*100)-1+99
        if L==4:
            periods_left = ((1-a)*100)-1+0*99
    
        minute_time = period_time/60
    
        minutes_left = (periods_left*period_time)/60
        hours_left = (periods_left*period_time)/3600
        percentage_complete = 100*((297-periods_left)/297)
    
        print("Time for last period = ","%.2f" % minute_time," minutes")
    
        print("%.2f" % percentage_complete,"% complete")
        if hours_left<1:
            print("%.2f" % minutes_left," minutes left")
        else:
            print("%.2f" % hours_left," hours left")
        print("")
        return
    
    def dcopy(inList):
        if isinstance(inList, list):
            return list( map(dcopy, inList) )
        return inList
    
    # Save values to .CSV file
    
    def CSV(a,L,I_STD_1,I_STD_2,I_STD_3,I_STD_4,O_STD_0,
            O_STD_1,O_STD_2,O_STD_3,O_STD_4):
    
        pass
    
    # Initialization
    
    # These are the global, master lists of data
    
    I_STD_1 = [[0],[0],[0]]
    I_STD_2 = [[0],[0],[0]]
    I_STD_3 = [[0],[0],[0]]
    I_STD_4 = [[0],[0],[0]]
    
    O_STD_0 = [[0],[0],[0]]
    O_STD_1 = [[0],[0],[0]]
    O_STD_2 = [[0],[0],[0]]
    O_STD_3 = [[0],[0],[0]]
    O_STD_4 = [[0],[0],[0]]
    
    for L in range(0,6,2):
    
        # These are local lists that are appended to at the end of every period
    
        I_STD_1_L = []
        I_STD_2_L = []
        I_STD_3_L = []
        I_STD_4_L = []
    
        O_STD_0_L = []
        O_STD_1_L = []
        O_STD_2_L = []
        O_STD_3_L = []
        O_STD_4_L = []
    
        test = []
    
        for n in range(1,100):          # THIS is the start of the 99 value loop
    
            a = n/100
    
            print ("L=",L,", alpha=",a)
    
            # Initialization for each Period
    
            F_1 = [0,10]            # Forecast
            F_2 = [0,10]
            F_3 = [0,10]
            F_4 = [0,10]
    
            R_0 = [10]              # Items Received
            R_1 = [10]
            R_2 = [10]
            R_3 = [10]
            R_4 = [10]
    
            for i in range(L):
                R_1.append(10)
                R_2.append(10)
                R_3.append(10)
                R_4.append(10)
    
            I_1 = [10]              # Final Inventory
            I_2 = [10]
            I_3 = [10]
            I_4 = [10]
    
            IP_1 = [10+10*L]        # Inventory Position
            IP_2 = [10+10*L]
            IP_3 = [10+10*L]
            IP_4 = [10+10*L]
    
            O_1 = [10]              # Items Ordered
            O_2 = [10]
            O_3 = [10]
            O_4 = [10]
    
            BL_1 = [0]              # Backlog
            BL_2 = [0]
            BL_3 = [0]
            BL_4 = [0]
    
            OH_1 = [20]             # Items on Hand
            OH_2 = [20]
            OH_3 = [20]
            OH_4 = [20]
    
            OR_1 = [10]             # Order received from customer
            OR_2 = [10]
            OR_3 = [10]
            OR_4 = [10]
    
            Db_1 = [10]             # Running Average Demand
            Db_2 = [10]
            Db_3 = [10]
            Db_4 = [10]
    
            var_1 = [0]             # Running Variance in Demand
            var_2 = [0]
            var_3 = [0]
            var_4 = [0]
    
            B_1 = [IP_1[0]+10]      # Optimal Basestock
            B_2 = [IP_2[0]+10]
            B_3 = [IP_3[0]+10]
            B_4 = [IP_4[0]+10]
    
            D = [0,10]              # End constomer demand
    
            for i in range(total+1):
                D.append(9)
                D.append(12)
                D.append(8)
                D.append(11)
    
            period = [0]
    
            from time import time
            timeA = time()
    
            # 1000 time periods t
    
            for t in range(1,total+1):
    
                period.append(t)
    
    
                #### MANUFACTURER ####
    
                # Manufacturing order from previous time period put into production
                R_4.append(O_4[t-1])
    
                #recieve shipment from supplier, calculate items OH HAND
                if I_4[t-1]<0:
                    OH_4.append(R_4[t])
                else:
                    OH_4.append(I_4[t-1]+R_4[t])
    
                # Recieve and dispatch order, update Inventory and Backlog for time t
    
                if (O_3[t-1] + BL_4[t-1]) <= OH_4[t]:               # No Backlog
                    I_4.append(OH_4[t] - (O_3[t-1] + BL_4[t-1]))
                    BL_4.append(0)
                    R_3.append(O_3[t-1]+BL_4[t-1])
                else:
                    I_4.append(OH_4[t] - (O_3[t-1] + BL_4[t-1]))    # Backlogged
                    BL_4.append(-I_4[t])
                    R_3.append(OH_4[t])
    
                # Update Inventory Position
                IP_4.append(IP_4[t-1] + O_4[t-1] - O_3[t-1])
    
                # Use exponential smoothing to forecast future demand
                future_demand = (1-a)*F_4[t] + a*O_3[t-1]
                F_4.append(future_demand)
    
                # Calculate D_bar(t) and Var(t)
                Db_4.append((1/t)*sum(O_3[0:t]))
                s = 0
                for i in range(0,t):
                    s+=(O_3[i]-Db_4[t])**2
    
                if t==1:
                    var_4.append(0)                                 # var(1) = 0
                else:
                    var_4.append((1/(t-1))*s)
    
                # Simulation to determine B(t)
                S_BC_4 = [10000000000]*10
                Run_4 = [0]*10
                for B in range(10,500):
    
                    S_OH_4 = OH_4[:]
                    S_I_4 = I_4[:]
                    S_R_4 = R_4[:]
                    S_BL_4 = BL_4[:]
                    S_IP_4 = IP_4[:]
                    S_O_4 = O_4[:]
    
                    # Update O(t)(the period just before the simulation begins)
                    # using the B value for the simulation
                    if B - S_IP_4[t] > 0:              
                        S_O_4.append(B - S_IP_4[t])
                    else:
                        S_O_4.append(0)
    
                    c = 0
    
                    for i in range(t+1,t+sim+1):
    
                        S_R_4.append(S_O_4[i-1])
    
                        #simulate demand
                        demand = -1
                        while demand <0:
                            demand = random.normalvariate(F_4[t+1],(var_4[t])**(.5))
    
                        # Receive simulated shipment, calculate simulated items on hand
    
                        if S_I_4[i-1]<0:
                            S_OH_4.append(S_R_4[i])
                        else:
                            S_OH_4.append(S_I_4[i-1]+S_R_4[i])
    
                        # Receive and send order, update Inventory and Backlog (simulated)
    
                        owed = (demand + S_BL_4[i-1])
                        S_I_4.append(S_OH_4[i] - owed)
                        if owed <= S_OH_4[i]:                               # No Backlog
                            S_BL_4.append(0)
                            c += inv_cost*S_I_4[i]
                        else:
                            S_BL_4.append(-S_I_4[i])                        # Backlogged
                            c += bl_cost*S_BL_4[i]
    
                        # Update Inventory Position
                        S_IP_4.append(S_IP_4[i-1] + S_O_4[i-1] - demand)
    
                        # Update Order, Upstream member dispatches goods
                        if (B-S_IP_4[i]) > 0:
                            S_O_4.append(B - S_IP_4[i])
                        else:
                            S_O_4.append(0)
    
                    # Log Simulation costs for that B-value
                    S_BC_4.append(c)
    
                    # If the simulated costs are increasing, stop
                    if B>11:
                        dummy = []
    
                        for i in range(0,10):
                            dummy.append(S_BC_4[B-i]-S_BC_4[B-i-1])
                        Run_4.append(sum(dummy)/float(len(dummy)))
    
                        if Run_4[B-3] > 0 and B>20:
                            break
                    else:
                        Run_4.append(0)
    
                # Use minimum cost as new B(t)
                var = min((val, idx) for (idx, val) in enumerate(S_BC_4))
                optimal_B = var[1]
                B_4.append(optimal_B)
    
                # Calculate O(t)
                if B_4[t] - IP_4[t] > 0:
                    O_4.append(B_4[t] - IP_4[t])
                else:
                    O_4.append(0)
    
    
    
    
                #### DISTRIBUTOR ####
    
                #recieve shipment from supplier, calculate items OH HAND
                if I_3[t-1]<0:
                    OH_3.append(R_3[t])
                else:
                    OH_3.append(I_3[t-1]+R_3[t])
    
                # Recieve and dispatch order, update Inventory and Backlog for time t
    
                if (O_2[t-1] + BL_3[t-1]) <= OH_3[t]:               # No Backlog
                    I_3.append(OH_3[t] - (O_2[t-1] + BL_3[t-1]))
                    BL_3.append(0)
                    R_2.append(O_2[t-1]+BL_3[t-1])
                else:
                    I_3.append(OH_3[t] - (O_2[t-1] + BL_3[t-1]))    # Backlogged
                    BL_3.append(-I_3[t])
                    R_2.append(OH_3[t])
    
                # Update Inventory Position
                IP_3.append(IP_3[t-1] + O_3[t-1] - O_2[t-1])
    
                # Use exponential smoothing to forecast future demand
                future_demand = (1-a)*F_3[t] + a*O_2[t-1]
                F_3.append(future_demand)
    
                # Calculate D_bar(t) and Var(t)
                Db_3.append((1/t)*sum(O_2[0:t]))
                s = 0
                for i in range(0,t):
                    s+=(O_2[i]-Db_3[t])**2
    
                if t==1:
                    var_3.append(0)                                 # var(1) = 0
                else:
                    var_3.append((1/(t-1))*s)
    
                # Simulation to determine B(t)
                S_BC_3 = [10000000000]*10
                Run_3 = [0]*10
    
                for B in range(10,500):
                    S_OH_3 = OH_3[:]
                    S_I_3 = I_3[:]
                    S_R_3 = R_3[:]
                    S_BL_3 = BL_3[:]
                    S_IP_3 = IP_3[:]
                    S_O_3 = O_3[:]
    
                    # Update O(t)(the period just before the simulation begins)
                    # using the B value for the simulation
                    if B - S_IP_3[t] > 0:              
                        S_O_3.append(B - S_IP_3[t])
                    else:
                        S_O_3.append(0)
                    c = 0
                    for i in range(t+1,t+sim+1):
    
                        #simulate demand
                        demand = -1
                        while demand <0:
                            demand = random.normalvariate(F_3[t+1],(var_3[t])**(.5))
    
                        S_R_3.append(S_O_3[i-1])
    
                        # Receive simulated shipment, calculate simulated items on hand
                        if S_I_3[i-1]<0:
                            S_OH_3.append(S_R_3[i])
                        else:
                            S_OH_3.append(S_I_3[i-1]+S_R_3[i])
    
                        # Receive and send order, update Inventory and Backlog (simulated)
                        owed = (demand + S_BL_3[i-1])
                        S_I_3.append(S_OH_3[i] - owed)
                        if owed <= S_OH_3[i]:                               # No Backlog
                            S_BL_3.append(0)
                            c += inv_cost*S_I_3[i]
                        else:
                            S_BL_3.append(-S_I_3[i])                        # Backlogged
                            c += bl_cost*S_BL_3[i]
    
                        # Update Inventory Position
                        S_IP_3.append(S_IP_3[i-1] + S_O_3[i-1] - demand)
    
                        # Update Order, Upstream member dispatches goods
                        if (B-S_IP_3[i]) > 0:
                            S_O_3.append(B - S_IP_3[i])
                        else:
                            S_O_3.append(0)
    
                    # Log Simulation costs for that B-value
                    S_BC_3.append(c)
    
                    # If the simulated costs are increasing, stop
                    if B>11:
                        dummy = []
    
                        for i in range(0,10):
                            dummy.append(S_BC_3[B-i]-S_BC_3[B-i-1])
                        Run_3.append(sum(dummy)/float(len(dummy)))
    
                        if Run_3[B-3] > 0 and B>20:
                            break
                    else:
                        Run_3.append(0)
    
                # Use minimum cost as new B(t)
                var = min((val, idx) for (idx, val) in enumerate(S_BC_3))
                optimal_B = var[1]
                B_3.append(optimal_B)
    
                # Calculate O(t)
                if B_3[t] - IP_3[t] > 0:
                    O_3.append(B_3[t] - IP_3[t])
                else:
                    O_3.append(0)
    
    
    
                #### WHOLESALER ####
    
                #recieve shipment from supplier, calculate items OH HAND
                if I_2[t-1]<0:
                    OH_2.append(R_2[t])
                else:
                    OH_2.append(I_2[t-1]+R_2[t])
    
                # Recieve and dispatch order, update Inventory and Backlog for time t
    
                if (O_1[t-1] + BL_2[t-1]) <= OH_2[t]:               # No Backlog
                    I_2.append(OH_2[t] - (O_1[t-1] + BL_2[t-1]))
                    BL_2.append(0)
                    R_1.append(O_1[t-1]+BL_2[t-1])
    
                else:
                    I_2.append(OH_2[t] - (O_1[t-1] + BL_2[t-1]))    # Backlogged
                    BL_2.append(-I_2[t])
                    R_1.append(OH_2[t])
    
                # Update Inventory Position
                IP_2.append(IP_2[t-1] + O_2[t-1] - O_1[t-1])
    
                # Use exponential smoothing to forecast future demand
                future_demand = (1-a)*F_2[t] + a*O_1[t-1]
                F_2.append(future_demand)
    
                # Calculate D_bar(t) and Var(t)
                Db_2.append((1/t)*sum(O_1[0:t]))
                s = 0
                for i in range(0,t):
                    s+=(O_1[i]-Db_2[t])**2
    
                if t==1:
                    var_2.append(0)                                 # var(1) = 0
                else:
                    var_2.append((1/(t-1))*s)
    
                # Simulation to determine B(t)
                S_BC_2 = [10000000000]*10
                Run_2 = [0]*10
    
                for B in range(10,500):
                    S_OH_2 = OH_2[:]
                    S_I_2 = I_2[:]
                    S_R_2 = R_2[:]
                    S_BL_2 = BL_2[:]
                    S_IP_2 = IP_2[:]
                    S_O_2 = O_2[:]
    
                    # Update O(t)(the period just before the simulation begins)
                    # using the B value for the simulation
                    if B - S_IP_2[t] > 0:              
                        S_O_2.append(B - S_IP_2[t])
                    else:
                        S_O_2.append(0)
                    c = 0
    
                    for i in range(t+1,t+sim+1):
    
                        #simulate demand
                        demand = -1
                        while demand <0:
                            demand = random.normalvariate(F_2[t+1],(var_2[t])**(.5))
    
                        # Receive simulated shipment, calculate simulated items on hand
                        S_R_2.append(S_O_2[i-1])
    
                        if S_I_2[i-1]<0:
                            S_OH_2.append(S_R_2[i])
                        else:
                            S_OH_2.append(S_I_2[i-1]+S_R_2[i])
    
                        # Receive and send order, update Inventory and Backlog (simulated)
    
                        owed = (demand + S_BL_2[i-1])
                        S_I_2.append(S_OH_2[i] - owed)
                        if owed <= S_OH_2[i]:                               # No Backlog
                            S_BL_2.append(0)
                            c += inv_cost*S_I_2[i]
                        else:
                            S_BL_2.append(-S_I_2[i])                        # Backlogged
                            c += bl_cost*S_BL_2[i]
    
                        # Update Inventory Position
                        S_IP_2.append(S_IP_2[i-1] + S_O_2[i-1] - demand)
    
                        # Update Order, Upstream member dispatches goods
                        if (B-S_IP_2[i]) > 0:
                            S_O_2.append(B - S_IP_2[i])
                        else:
                            S_O_2.append(0)
    
                    # Log Simulation costs for that B-value
                    S_BC_2.append(c)
    
                    # If the simulated costs are increasing, stop
                    if B>11:
                        dummy = []
                        for i in range(0,10):
                            dummy.append(S_BC_2[B-i]-S_BC_2[B-i-1])
                        Run_2.append(sum(dummy)/float(len(dummy)))
    
                        if Run_2[B-3] > 0 and B>20:
                            break
                    else:
                        Run_2.append(0)
    
                # Use minimum cost as new B(t)
                var = min((val, idx) for (idx, val) in enumerate(S_BC_2))
                optimal_B = var[1]
                B_2.append(optimal_B)
    
                # Calculate O(t)
                if B_2[t] - IP_2[t] > 0:
                    O_2.append(B_2[t] - IP_2[t])
                else:
                    O_2.append(0)
    
    
    
    
    
                #### RETAILER ####
    
                #recieve shipment from supplier, calculate items OH HAND
                if I_1[t-1]<0:
                    OH_1.append(R_1[t])
                else:
                    OH_1.append(I_1[t-1]+R_1[t])
    
                # Recieve and dispatch order, update Inventory and Backlog for time t
    
                if (D[t] +BL_1[t-1]) <= OH_1[t]:              # No Backlog
                    I_1.append(OH_1[t] - (D[t] + BL_1[t-1]))
                    BL_1.append(0)
                    R_0.append(D[t]+BL_1[t-1])
                else:
                    I_1.append(OH_1[t] - (D[t] + BL_1[t-1]))  # Backlogged
                    BL_1.append(-I_1[t])
                    R_0.append(OH_1[t])
    
                # Update Inventory Position
                IP_1.append(IP_1[t-1] + O_1[t-1] - D[t])
    
                # Use exponential smoothing to forecast future demand
                future_demand = (1-a)*F_1[t] + a*D[t]
                F_1.append(future_demand)
    
                # Calculate D_bar(t) and Var(t)
                Db_1.append((1/t)*sum(D[1:t+1]))
                s = 0
                for i in range(1,t+1):
                    s+=(D[i]-Db_1[t])**2
    
                if t==1:                                            # Var(1) = 0
                    var_1.append(0)
                else:
                    var_1.append((1/(t-1))*s)
    
                # Simulation to determine B(t)
                S_BC_1 = [10000000000]*10
                Run_1 = [0]*10
                for B in range(10,500):
                    S_OH_1 = OH_1[:]
                    S_I_1 = I_1[:]
                    S_R_1 = R_1[:]
                    S_BL_1 = BL_1[:]
                    S_IP_1 = IP_1[:]
                    S_O_1 = O_1[:]
    
                    # Update O(t)(the period just before the simulation begins)
                    # using the B value for the simulation
                    if B - S_IP_1[t] > 0:              
                        S_O_1.append(B - S_IP_1[t])
                    else:
                        S_O_1.append(0)
    
                    c=0
                    for i in range(t+1,t+sim+1):
    
                        #simulate demand
                        demand = -1
                        while demand <0:
                            demand = random.normalvariate(F_1[t+1],(var_1[t])**(.5))
    
                        S_R_1.append(S_O_1[i-1])
    
                        # Receive simulated shipment, calculate simulated items on hand
                        if S_I_1[i-1]<0:
                            S_OH_1.append(S_R_1[i])
                        else:
                            S_OH_1.append(S_I_1[i-1]+S_R_1[i])
    
                        # Receive and send order, update Inventory and Backlog (simulated)
                        owed = (demand + S_BL_1[i-1])
                        S_I_1.append(S_OH_1[i] - owed)
                        if owed <= S_OH_1[i]:                               # No Backlog
                            S_BL_1.append(0)
                            c += inv_cost*S_I_1[i]
                        else:
                            S_BL_1.append(-S_I_1[i])                        # Backlogged
                            c += bl_cost*S_BL_1[i]
    
                        # Update Inventory Position
                        S_IP_1.append(S_IP_1[i-1] + S_O_1[i-1] - demand)
    
                        # Update Order, Upstream member dispatches goods
                        if (B-S_IP_1[i]) > 0:
                            S_O_1.append(B - S_IP_1[i])
                        else:
                            S_O_1.append(0)
    
                    # Log Simulation costs for that B-value
                    S_BC_1.append(c)
    
                    # If the simulated costs are increasing, stop
                    if B>11:
                        dummy = []
                        for i in range(0,10):
                            dummy.append(S_BC_1[B-i]-S_BC_1[B-i-1])
                        Run_1.append(sum(dummy)/float(len(dummy)))
    
                        if Run_1[B-3] > 0 and B>20:
                            break
                    else:
                        Run_1.append(0)
    
                # Use minimum as your new B(t)
                var = min((val, idx) for (idx, val) in enumerate(S_BC_1))
                optimal_B = var[1]
                B_1.append(optimal_B)
    
                # Calculate O(t)
                if B_1[t] - IP_1[t] > 0:
                    O_1.append(B_1[t] - IP_1[t])
                else:
                    O_1.append(0)
    
    
            ### Calculate the Standard Devation of the last half of time periods ###
    
            def STD(numbers):
                k = len(numbers)
                mean = sum(numbers) / k
                SD = (sum([dev*dev for dev in [x-mean for x in numbers]])/(k-1))**.5
                return SD
    
            start = (total//2)+1
    
            # Only use the last half of the time periods to calculate the standard deviation
    
            I_STD_1_L.append(STD(I_1[start:]))
            I_STD_2_L.append(STD(I_2[start:]))
            I_STD_3_L.append(STD(I_3[start:]))
            I_STD_4_L.append(STD(I_4[start:]))
    
            O_STD_0_L.append(STD(D[start:]))
            O_STD_1_L.append(STD(O_1[start:]))
            O_STD_2_L.append(STD(O_2[start:]))
            O_STD_3_L.append(STD(O_3[start:]))
            O_STD_4_L.append(STD(O_4[start:]))
    
            from time import time
            timeB = time()
    
            timeleft(a,L,timeB-timeA)
    
            I_STD_1[L//2] = I_STD_1_L[:]
            I_STD_2[L//2] = I_STD_2_L[:]
            I_STD_3[L//2] = I_STD_3_L[:]
            I_STD_4[L//2] = I_STD_4_L[:]
    
            O_STD_0[L//2] = O_STD_0_L[:]
            O_STD_1[L//2] = O_STD_1_L[:]
            O_STD_2[L//2] = O_STD_2_L[:]
            O_STD_3[L//2] = O_STD_3_L[:]
            O_STD_4[L//2] = O_STD_4_L[:]
    
            CSV(a,L,I_STD_1,I_STD_2,I_STD_3,I_STD_4,O_STD_0,
                O_STD_1,O_STD_2,O_STD_3,O_STD_4)
    
    
    from time import time
    timeE = time()
    
    print("Run Time: ",(timeE-time0)/3600," hours")