Monday, February 17, 2014

Playing the Theory of Constraints game ..


   A chain is only as strong as its weakest link - Eliyahu Goldratt.

Theory of Constraints is a theoritical concept with loads of learning from the practical domain introduced by the Jewish Shop floor engineer cum manager Eliyahu Goldratt through his book "The Goal " in 1984 and made popular by him throughout the world.. 

Last year when we visited Titan Jewels in Hosur, Tamil Nadu, owners of the famous Tanishq brand, the SC manager was telling us how through Theory of Constraints and the consultancy offered by Eliyahu Goldratt himself to Tata Sons, Titan Jewels could increase its turnover from Rs 5000 crores to Rs 10,000 crores ( $ 2 billion) in a matter of four years and Tata Sons, their turnover from $ 65 billions to $ 100 billions plus, even beating IBM..

Brief description of the game is given here .. as played last year .. I do not know, we may be the only Bschool in the country to play this game, not even the IIMs .. It gives a clear visualisation to students of how inventory gets accumulated at some workstations in an assembly line and how tackling this workstation alone, instead of all the workstations together, will help improve the productivity of the line. 

On 15 Feb 2014, the second version of the game was played in the Operations class of 50 students (all initial stock only with the first workstation and none with the intermediate workstations) for 10 rounds by 9 assembly lines in the Operations class at Alliance University, Bangalore.

 Each of the first workstations of the nine assembly lines were given an initial stock of 30 units of inventory. The production at each of the five workstations in each of the assembly line ( or in other words the machines which were working at each station) was randomly chosen from 1 to 5. The production from each workstation was decided by a random number generator between 1 and 5. In the initial round, only the items passed from upstream stations were passed to downstream stations, while in later rounds, the inventory accumulated from earlier rounds were used if there was a difference between machines available at that workstation and inventory passed from upstream workstation.

Assumption :

It is assumed that each workstation has five machines and each machine part- processes units during a shift. If all machines are up in a workstation, it processes five parts, if only two machines are up it processes just two parts. these two parts now proceed to the next workstation for machine specific processing operations.

Mass Conservation Equations

The equation which guided movement of raw material from each work station was this :  
Items processed at each workstation i to workstation j (IP_i,j)= min(machines working at station i (M_i), items processed and passed from upstream station i-1 to i (IP_i-1,i). 

As the game progressed, each station started accumulating stock and thus the items dispatched from each work station to the succeeding workstation changed over passage of time. 

Items processed and passed from station i to station j (IP_i,j) = min ( machines working at station i (M_i) + WIP at station i, items processed and passed from upstream station i-1 to i (IP_i-1,i) + WIP at station i).

The game was played for ten rounds in the first phase. The data is given below.

Assembly line   Final O/P    Bottleneck Stn     Inv. bottleneck        Throughput rate
I                          19                 2                         16                     19/30 = 0.633
II                         17                 4                           5                     17/30 = 0.58
III                        18                2                            3                     18/30 = 0.6
IV                          -                -                     - ( no team)
V                         18                2                           19                    18/30 = 0.6
VI                        17                2                            3                     17/30 = 0.58
VII                       17                2                           6                      17/30 = 0.58
VIII                     14                4                            11                    14/30 = 0.47
IX                        16               4                             6                     16/30 = 0.53
X                         18               4                             9                     18/30 = 0.6


How the game is played : 

The game is played for three phases.

Assembly lines are created with 5 workstations in each. ie. if there are 30 students in the class, six assembly lines are setup. At the first workstation in each assembly line, initial RM inventory of 50 units is supplied. No other workstation in the assembly line is supplied any stock. The output from the last workstation is the throughput of the line. A record is kept of the inventory at each workstation at the end of each phase. ( the coloured tokens acting as inventory can be given to the first station as RM inventory if tokens are running short.)


A phase of the game is playing for 10 rounds. The bottle neck station is identified after each phase and the inventory accumulation there is removed completely/partial level ( the decision variable taken by the team members) at end of phase I. The game is continued after each phase with the same stock of WIP at all other stations retained as it is, is played for another two phases (with identification of bottleneck station and complete/partial removal of inventory accumulation at the bottleneck station at end of phase 2). The assembly line which gets the maximum throughput at the end of three phases is the winner.

The analysis of the game : - phase I.

Assembly line I had the highest throughput of 19 units with a throughput rate of 0.633 while lines III, V and X had a throughput of 18 each and throughput rate of 0.6.

The highest bottle neck at any workstation in any assembly line was observed as 19 and 16 on lines V and I respectively. Station 2 on line I and station 2 on line V had maximum accumulation of inventory, in other words these two stations had the least processing rate ( ie.  highest processing time). These are the bottleneck stations of lines I and V.

As per Eliyahu Goldratt's Theory of Constraints, we now have to turn our attention to the bottleneck stations (instead of concentrating on all the stations at the same time) and remove the bottle neck by way of better line balancing of machines, better maintained machines, techn, better training to workers , better quality of raw materials etc. etc.

After the initial bottle neck is removed ( bring the inventory to zero) continue the game for another ten rounds. Now another workstation may become the bottle neck.  Work to remove the bottleneck for this station also. As the bottle neck is removed we find the throughput rate also improves, which is the success of the assembly line. As time was limited, we could not play the game for another 10 rounds and hence could not demonstrate to the students how the average throughput rate (for two rounds) increases.

The final winner of the game is that assembly line which gets the maximum throughput after running the game for minimum thirty rounds, ie. three phases.

The uniformly distributed random number table between 1 and 5 is available here.. 

ge..

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