Why Models? State of world: Data (not information!) overload Reliance on computers Allocation of responsibility (must justify decisions) Decisions and numbers: Decisions are numbers –How many distribution centers do we need? –Capacity of new plant? –No. workers assigned to line? Decisions depend on numbers –Whether to introduce new product? –Make or buy? –Replace MRP with Kanban?

Why Models? (cont.) Data + Model = Information: Managers who don't understand models either: Abhor analysis, lose valuable information, or Put too much trust in analysis, are swayed by stacks of computer output

Goldratt Product Mix Problem Machines A,B,C,D Machines run 2400 min/week fixed expenses of $5000/week PQ

Modeling Goldratt Problem Formulation: Solution Approach: 1. Choose (feasible) production quantity of P (X p ) or Q (X q ). 2. Use remaining capacity to make other product. X p = weekly production of P, X q = weekly production of Q Weekly Profit Time on Machine A Time on Machine B Time on Machine C Time on Machine D Max Sales of P Max Sales of Q

Unit Profit Approach Make as much Q as possible because it is highest priced: 5 A B C,D A B

Bottleneck Ratio Approach Consider bottleneck: If we set X p =100, X q =50, we violate capacity constraint Profit/Unit of Bottleneck Resource ($/minute): X p : 45/15 = 3 X q : 60/30 = 2 so make as much P as possible (i.e., set X p =100, since this does not violate any of the capacity constraints): A B C D

Bottleneck Ratio Approach (cont.) Outcome: This turns out to be the best we can do. But will this approach always work? A B C,D

Modified Goldratt Problem Machines A,B,C,D Machines run 2400 min/week fixed expenses of $5000/week PQ D C C A B C B B A D $5$ Note: only minor changes to times.

Modeling Modified Goldratt Problem Formulation: Solution Approach: bottleneck method. Weekly Profit Time on Machine A Time on Machine B Time on Machine C Time on Machine D Max Sales of P Max Sales of Q

Bottleneck Solution Find Bottleneck: Note: Both B and D are bottlenecks! (Does this seem unrealistic in a world where line balancing is a way of life?) A B C D

Possible Solutions Make as much P as possible: A B C D

Possible Solutions (cont.) Make as much Q as possible: so make X q = 50 (can’t sell more than this) A B C D

Another Solution Make X p =73, X q =37: (Where in the heck did these come from? A model!) Conclusions: Modeling matters! Beware of simplistic solutions to complex problems! A B C D