{ From user Lonnie, Model Production_allocatio at Wed, Sep 29, 2004 12:53 PM~~
}
Softwareversion 3.1.0


{ System Variables with non-default values: }
Windows := 2
Usetable := 0
Typechecking := 1
Checking := 1
Graphwindows := 9
Saveoptions := 2
Savevalues := 0
Webhelper := -1


{ Non-default Time SysVar value: }
Time := [0,1,2]
Title Time: Time
Description Time: Dynamic simulation periods are specified in Time's ~~
definition. This is usually a list of numbers or labels, typically in~~
 some unit of time (days, weeks, months, etc.).  Use the ÒDynamic()Ó ~~
function in your variables to perform dynamic simulation.

Model Production_allocatio
Title: Production allocation
Description: A demonstration of linear programming in Analytica Optim~~
izer.~
~
An integrated circuit manufacturer produces several different IC prod~~
ucts (chips).  Each chip is created by a sequence of processes, each ~~
carried out by a different machine.  Every chip must pass through eve~~
ry process, but the time required for each process depends on the pro~~
duct -- some products require a lot of time at Process1, while other ~~
require very little time there but more time at other processes.  The~~
 company's objective is to determine how much of each product to prod~~
uce so as to maximize profit without exceeding the capacity of each p~~
rocess.
Author: Lonnie Chrisman, Ph.D.~
Lumina Decision Systems
Date: Sat, Aug 28, 2004 11:18 AM
Saveauthor: Lonnie
Savedate: Wed, Sep 29, 2004 12:53 PM
Defaultsize: 48,24
Diagstate: 1,14,16,509,477,17
Windstate: 2,186,285,449,537
Fontstyle: Arial, 15
Fileinfo: 0,Model Production_allocatio,2,2,0,0,W:\Analytica\ExecDebug~~
\Example Models\Optimizer Examples\Optimal production allocation.ANA

Index Products
Title: Products
Description: The different products manufactured by the company.
Definition: ['Chip 1','Chip 2','Chip 3']
Nodelocation: 72,48,1
Nodesize: 48,24

Index Processes
Title: Processes
Description: The steps required to produce a product (of any type).  ~~
Each process is a separate resource with its own capacity constraints~~
.  A process can only work on a single product at any given time, but~~
 it is assumed that there is no setup time when switching from one pr~~
oduct type to another.
Definition: ['Process 1','Process 2','Process 3']
Nodelocation: 192,48,1
Nodesize: 48,24

Constant Process_output
Title: Process Output
Units: units / hr
Description: This table captures the number of units per hour of each~~
 type of product that each process can complete, when that process is~~
 dedicated only to that product type.
Definition: Table(Products,Processes)(~
15,12,7,~
7,4,6,~
10,8,5~
)
Nodelocation: 72,120,1
Nodesize: 48,24
Defnstate: 2,139,472,416,303,0,MIDM
Reformdef: [Products, Processes ]
Reformval: [Products, Processes ]

Constant Profit_per_unit_prod
Title: Profit per unit product
Units: $
Description: Marginal profit earned per sale of each product.
Definition: Table(Products)(~
300,700,600)
Nodelocation: 192,120,1
Nodesize: 48,24
Defnstate: 2,233,56,415,302,0,MIDM
Valuestate: 2,196,209,416,303,0,MIDM

Text Te1
Nodelocation: 135,89,-3
Nodesize: 122,79
Nodeinfo: 1,0,0,1,1,1,0,,1,

Variable Optimization_formula
Title: Optimization Formulation
Description: This defines the linear program used to solve for the op~~
timal production allocation.~

Definition: Lpdefine( Products, Processes, ~
objCoef : profit_per_unit_product, ~
lhs : Process_utilization, rhs : 1, ~
maximize:true, lb:0 )
Nodelocation: 192,232,1
Nodesize: 53,26
Windstate: 2,65,594,476,224
Valuestate: 2,104,114,416,303,0,MIDM

Objective Units_to_mfr_per_hou
Title: Units to Mfr per hour
Description: The result of optimization
Definition: LpSolution(Optimization_formula)
Nodelocation: 392,54,1
Nodesize: 48,24
Valuestate: 2,180,394,369,225,0,MIDM

Variable Process_utilization
Title: Process utilization
Definition: 1/Process_output
Nodelocation: 72,230,1
Nodesize: 48,24
Valuestate: 2,144,117,416,303,0,MIDM
Reformval: [Products, Processes ]

Objective Hourly_profit
Title: Hourly profit
Definition: LpOpt(optimization_formulation)
Nodelocation: 392,110,1
Nodesize: 48,24
Valuestate: 2,181,330,416,303,0,MIDM
Numberformat: 1,F,4,2,1,1

Variable Price_adjustment
Title: Price adjustment
Description: If the profit from a product does not exceed the opportu~~
nity cost from displacing the resources that could be used to make ot~~
her products, the optimal solution will be to make none of that produ~~
ct.  In that case, since zero units are being manufactured and sold a~~
nyway, the price for that product might as well be raised.  This valu~~
e is the minimum amount it would need to be raised in order to justif~~
y the use of production resources on that product.
Definition: -LpReducedCost( Optimization_formula )
Nodelocation: 392,174,1
Nodesize: 48,24
Windstate: 2,42,565,476,224
Valuestate: 2,83,370,416,303,0,MIDM

Variable Process_utilization1
Title: Process Utilization
Description: The percentage utilization of each process.  Any process~~
 with less than 100% utilization has extra capacity that isn't being ~~
utilized in the optimal solution.  Process with 100% utilization are ~~
essentially the bottlenecks to production.
Definition: 1-Lpslack( Optimization_formula )
Nodelocation: 392,230,1
Nodesize: 48,24
Valuestate: 2,238,32,416,303,0,MIDM
Numberformat: 1,%,4,1,0,0

Variable Solution_status
Title: Solution status
Definition: LpStatusText(optimization_formulation)
Nodelocation: 393,290,1
Nodesize: 48,24

Variable Value_of_process_cap
Title: Value of process capacity increase
Units: $/hr per 1%
Description: How much would it be worth if we could find a way to in~~
crease the total output of a process by a small amount?  This is capt~~
ured by the Shadow Price, which indicates how the objective function ~~
would change if the right-hand side (in this case, 100% capacity) wer~~
e changed by one unit.  The shadow price is really valid only over a ~~
small range in which the solution basis is unchanged, so here we expr~~
ess this as the value of a 1% change in capacity.
Definition: LpShadow( optimization_formula) / 100
Nodelocation: 392,376,1
Nodesize: 48,40
Windstate: 2,122,429,476,224
Valuestate: 2,184,387,416,303,0,MIDM
Numberformat: 1,F,4,2,0,1

Close Production_allocatio