Material Constraint Theory Part V

(VI) PROBLEM ILLUSTRATION – ONE TO MANY ALLOCATION - Contd...

Problem A] Find out total feasible quantity of item ‘A’, which is available for production at particular time ‘t’. Consider here, WIP and Store stock as well. Say it is Q[A].

If Q[A] Σ D[ t ], Then there is no problem for inventory allocation, as sufficient quantity is available in stock to process succ_op, without violating constraints defined. Else, problem B] will be applicable.


Problem B] Find out inventory allocation rule, which assigns Q[A] to succ_op in an effective manner, without violating constraints and satisfying the objective function, as defined.

One can think of following parameters, basis on which derivation of allocation rule may be possible, mostly related to demand:
1] Current lot sizes of each of succ_op,
2] Demand on each of succ_op, over finite horizon T, {D20 / D30 / D40}
3] Weight of each item in succ_op, (weight may be defined as delay cost per unit or importance)
4] Propagated end item demand on each of succ_op.
5] Consumption ratio for each of succ_op.

Let us try to derive the effect of all stated parameters on allocation problem. For the Illustration, let us solve a simple problem, as given below:



Here
s = 5, S = 18, D10 = 8, QT10 = 12, Q’10 = 14. Total demand on op10 = 16+10+21 = 47
Qi = Lot size [planned production quantity of current operation i ],
Di = demand of items produced by succ_op i, over finite horizon T.

Problem A: Find out feasible quantity that can be used for production of operations 20, 30 & 40, without violating stock policy.
The algorithm as used earlier can also be applied here. Therefore,
Feasible quantity that can be assigned from stock can be calculated as:

Fq[ A ] = 14 + 10 – 8 – 5 = 11

Feasible quantity that can be assign from stock = 11
Total quantity available for allocation = 11 + 22 = 33

Problem B: Find out a good solution for allocation of available inventory for succ_op, based on criteria defined.

I] Allocate inventory proportionate to lot size quantity:
[Minimize variance]

Ratio of allocation --- op20 : op30 : op40 : : 16 : 10 : 21
Total amount available: 33



II] Allocate inventory proportionate to demand:
[Minimize shortage]

Ratio of allocation --- op20 : op30 : op40 : : 16 : 9 : 18
Total amount available: 33


III] Allocate inventory proportionate to penalty/delay cost:
[Minimize delay cost ]

Ratio of allocation --- op20 : op30 : op40 : : 4 : 3 : 2
Total amount available: 33



Though above problems do not represent common / generalized results, but one can observe that allocation of inventory based on delay cost shall yield a result with reduces total penalty or delay cost.

One has to identify the suitable objective function and then the allocation rule can be derived for the same.

Actually, after determining the feasible quantity that can be assigned at particular time t, one can determine numerous methods to allocate available inventory to all downstream consuming operations.

Different individual parameters can be identified as stated above, or one can derive combination of this parameter to find out the proportionate allocation to a particular operation.