### Table 1: Relation of model (P ) with existing models

"... In PAGE 26: ... 5 Relation with existing literature The modeling framework presented in Sections 3 and 4 generalizes many of the models proposed in the literature (see also Appendix A). Table1 presents a classification of facility location problems. The table is not intended to provide an exhaustive review but rather to illustrate in which way this generalization occurs.... In PAGE 26: ... The table is not intended to provide an exhaustive review but rather to illustrate in which way this generalization occurs. Each column of Table1 represents one of nine criteria: type of planning horizon, type of objective function, number of commodities, number of facility levels in addition to the customer level, number of echelons to be located, consideration of relocation and inventory decisions, and finally, inclusion of capacity and budget constraints. As far as capacity constraints are concerned, one finds essentially three situations: the usual type of constraints, the possibility of expanding or reducing operating capacity, and modular capacities.... In PAGE 26: ... As far as capacity constraints are concerned, one finds essentially three situations: the usual type of constraints, the possibility of expanding or reducing operating capacity, and modular capacities. For each analytical study in Table1 which explicitly considers capacity constraints, we detail the corresponding case(s). Observing Table 1, one realizes that none of the existing models deals simultaneously with all the aspects considered in Sections 3 and 4.... In PAGE 26: ... For each analytical study in Table 1 which explicitly considers capacity constraints, we detail the corresponding case(s). Observing Table1 , one realizes that none of the existing models deals simultaneously with all the aspects considered in Sections 3 and 4. In particular, three elements are scarcely focused together in the literature, namely facility relocation, inventory opportunities and budget constraints.... In PAGE 26: ... Due to the fact that our modeling framework extends many existing models (cf. Ap- pendix A), solution procedures proposed in the papers listed in Table1 seem a reasonable starting point for developing analytical approaches to solve the new enlarged models. Even though the paper maintains a modeling rather than an algorithmic focus, we summarize next the approaches that have been developed to deal with simpler models.... In PAGE 36: ... Acknowledgements Special thanks are due to Sven-Hendrik Magotsch for his help in generating the random problems and implementing the various MIP formulations with the modeling language ILOG OPL Studio. Appendix A: Reduction to well known location prob- lems As mentioned in Section 1 (see also Table1 in Section 5), in a vast majority of the dynamic location literature, network design decisions are restricted to opening new facilities. Some authors also address the possibility of closing existing facilities (e.... ..."

### Table 1: Spatial Relations modelled in Relate Relation Type Explanation

### Table 1: Spatial Relations modelled in Relate Relation Type Explanation

### Table 3. De nition of relational model constructs

"... In PAGE 8: ...We de ne in Table3 how the basic relational data model can be represented in the HDM. Wetake the relational model to consist of relations, attributes (which maybenull), a primary key for each relation, and foreign keys.... ..."

### Table 3 Average errors relative to the model size

"... In PAGE 8: ...Re ( ) ( 100 % , , , , , , ngBox gionBoundi Face size ror PositionEr size Error z y x z y x z y x = (21) Note that in this case the error is computed separately along the x , y , and z directions. Table3 indicates that the average errors relative to the size of the model are negligible. Since the motion vectors are dense over the whole face, and their errors are small, visual artifacts are very difficult to perceive, even at high resolutions.... ..."

### Table 3 Average errors relative to the model size

"... In PAGE 8: ...Re ( ) ( 100 % , , , , , , ngBox gionBoundi Face size ror PositionEr size Error z y x z y x z y x = (21) Note that in this case the error is computed separately along the x , y , and z directions. Table3 indicates that the average errors relative to the size of the model are negligible. Since the motion vectors are dense over the whole face, and their errors are small, visual artifacts are very difficult to perceive, even at high resolutions.... ..."

### Table 2: Relating model components to decomposit

"... In PAGE 5: ...see Table2 . Both Tables 1 and 2 start from the explicit (visual) notion of model components.... In PAGE 5: ...articipation in activities (VI). They are expressed by arcs. Finally, Petri Nets foresee in an explicit mechanism for representing dynamics, through the firing of transitions (VII). Table2 makes clear how each diagramming technique builds on a subset of decomposition principles. The inclu- sion of specific decomposition principles may make it more or less fit for specific applications.... In PAGE 6: ...istinguishes between three elementary modalities, i.e., types of flow, for manufacturing systems: material flow information flow, and resources, see Table 3. For the mate- rial flow, further decomposition is realized by applying ba sic principles I-III, see Table2 . This is illustrated in Figure 2, which relates choice of entities to decomposition princi- ples (in italics).... ..."

### Table 1: Device attributes captured in the Relate model

2005

Cited by 4