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[Help-glpk] Constraint Construction

From: Alex Morelli
Subject: [Help-glpk] Constraint Construction
Date: Wed, 3 Aug 2011 21:41:11 +1000


I am struggling with the following and would appreciate any assistance:

I am constructing a model in an attempt to solve a location-allocation problem with multiple facilities (warehouses and plants) and multiple products.  I have prepared a feasible set of warehouse sites and identified the costs associated with deliveries to customers and deliveries from plants.

Some relevant statements --

param qty{(customer, product) in demand};

var whsales{warehouse in warehouses, (customer, product) in demand};

var whbin{warehouse in warehouses}, binary;

The following constraint is error free (not that I am sure of its relevance):

-- customer demand balancing

s.t. qty_cu{(customer, product) in demand}: sum{warehouse in warehouses} whsales[warehouse, customer, product] = qty[customer, product];

I do not know how to construct the constraint including the binary variable.

-- warehouse delivery balancing

s.t. qty_wh{(customer, product) in demand}: sum{customer in customers} whsales[warehouse, customer, product] <= whbin[warehouse] * sum{customer in customers} qty[customer, product];

This construction delivers the error "0-ary slice not allowed" - which i do not understand and could find no reference in "Modeling Language GNU MathProg, Language Reference", nor much that I could understand via internet search (which only gave be bug-glpk results).  I can see that the warehouse is not part of any domain following the <= sign, and have tried other options with no success.

I have been trying many options and have become very confused.

I have been referring to the Facilities Design chapter (Chapter 2) of "Production and Inventory Management" by Arnaldo C Hax and Dan Candea (Prentice-Hall 1984) for assistance with the lp formulation (spcifically for this instance p.24).

Regards, Alex
Alex Morelli


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