# Modeling by Object-Driven Linear Elemental Relations: A by H.J. Greenberg

By H.J. Greenberg

Modeling through Object-Driven Linear Elemental family members (MODLER) is a working laptop or computer language for representing linear programming types, thoroughly cut loose circumstances outlined by means of info realizations. it's also representations of binary variables and logical constraints, which come up obviously in large-scale making plans and operational choice aid. the fundamental enter to MODLER is a version dossier, and its uncomplicated output is a matrix dossier that's in a typical (MPS) layout for many optimizers and for examine and RANDMOD. MODLER may also generate a syntax dossier for study to allow automated translation of actions and constraints into English for clever research aid. The publication is observed via a DOS model of MODLER on 3.5 inch diskettes and *A Laboratory guide for instructing Linear Programming* is out there upon request.

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**Sample text**

The for all interpretation is equivalent to a sum of terms, where the index of summation is over the set (jo) not fixed by the domain of the equation. Similarly, equation JOB(jo) leaves pe a free set, so X(pe, jo) is summed over pe. MODLER . Page 4-7 NAME ASSIGN Assignment of personnel to jobs SETS pe person jo job TABLES COST(pe,jo) cost to assign (pe) to (jo): 0/* BINARIES Note: the following generation condition suppresses unacceptable * assignments, defined by infinite cost * X(pe,jo) assigns (pe) to (jo): COST(pe,jo) <> * EQUATIONS COST = COST(pe,jo)*X(pe,jo) PER(pe) limits (pe) to perform 1 job = X(pe,jo) <= JOB(jo) requires (jo) to be performed = X(pe,jo) >= ENDATA Figure 4-2.

MeM,feFP SlmfTlmf A, ;"P,/ePL Cp/Ppi :s: s, for all TERM; Ct ;"P Ppi B/mf IpeP Y~pI- Tlmf Dmf ItePL Tlmf :s: ~ ci for alllePL; 0 for alllePt, meM,[eFP; 4nf for all meM,[eFP. where the variables, {PpI: peP,lePL} and {Tlmf lePt, meM,[eFP: Slmfis finite}, are non-negative. (The generation condition for T is not shown in figure 4-3, nor are the bounds. ) MODLER . Page 4-9 In figure 4-5, we display all of its data objects. The instantiation of tables _YIELDp, _DEMANDm and _DEMANDf, indicated in figure 4-4, occurs because these are implied tables.

A Model File for the Generalized Transportation Problem This version of the generalized transportation model illustrates some of the MODLER syntax. 001 was chosen arbitrarily to be a small positive value that constitutes a least value for each gain factor. We also limited the number of supply and demand regions to be no greater than 9 in each case by the range specification 1/9 for their parameters, M and N, respectively. If more than 9 regions are possible in an instance, the set names (i andj, respectively) need to have two characters, like SR and DR.