Material Constraint Theory - Last Part

SOLUTION BY LINEAR PROGRAMMING

MANY TO MANY ALLOCATION PROBLEM





We can try to formulate the linear problem for this solution with different objective functions.

For current example, we can consider following three objective functions:
a. Maximize Profit and/or Priority
b. Maximize Total production Quantity
c. Minimize Total Delay [Cost / Time]


Problem Definition: • Parts to be produced are P1, P2 and P3. These are produced by operation 40, 50 and 60 respectively. • Illustration above shows the part requirement to produce each unit of these parts. For example, to produce one unit of P1, it requires one unit of Q10 and two units of Q20. • The available stock of Q10, Q20 and Q30 is 20, 35 and 29 respectively. • The need is to determine the quantity of parts P1, P2 and P3 to be produced in order to satisfy the stock constraint and achieve the objective function defined.

(I) MAXIMIZE PROFIT / PRIORITY




(II) MAXIMIZE TOTAL PRODUCTION QUANTITY



(III) MINIMIZE TOTAL DELAY [TIME/COST]





ONE TO MANY ALLOCATION PROBLEM

(I) MAXIMIZE PROFIT / PRIORITY



(II) MAXIMIZE TOTAL PRODUCTION QUANTITY

(III) MINIMIZE TOTAL DELAY [TIME/COST]

MANY TO ONE ALLOCATION PROBLEM


Let us take only one case here as this is simpler problem environment compare to other two. We can consider here the problem of maximizing total production quantity.


All above section gives a good overview of the problem related to stock limitation / constraints. It is logical to understand the problem first, domain requirements second and then apply the most practical solution, even I sometime(s) it is not the optimal solution.