Transshipments

The foregoing algebraic method can be generalized using optimization techniques. A particularly useful approach is the transshipment formulation (Papoulias and... 

Switzerland no verification of material and equipment of tank car At transshipment of hazardous substances, wrong substances contacted and reacted 6 1986 - 2000 USA... 

Zhang J (2005) Transshipment and its Impact on Supply Chain Members Performance. Management Science 51 (10) 1534-1539 Zhou T, Cheng S, Hua B (2000) Supply Chain Optimization of Continuous Process Industries with Sustainability Considerations. Computers Chemical Engineering 24 1151-1158... 

The increasing use of African countries for cocaine transshipment could be contributing to rising levels of cocaine use. In 2005, ten African countries reported an increase in cocaine use, up from 8 and 7 in 2004 and 2003 respectively. The number of African countries reporting stable cocaine markets remained unchanged in 2004 and 2005 (9 countries). Not a single African country reported a decline of cocaine use in 2004 or in... 

Europe as a whole accounted for about 6 per cent of global ephedrine seizures over the 2004-2005 period. Listed in order of importance, the following European countries reported seizures of methamphetamine precursors over the same period the Czech Republic, Greece, the Russian Federation, the UK, Bulgaria, Germany, Iceland, Romania, Hungary, Slovakia, the Ukraine, France, Norway and Latvia. In 2006, EUROPOL noted increased export, transshipment and diversion of ephedrine and pseudo-ephedrine to the European Union.24... 

Step 2. Formulate and solve the LP transshipment model of Papoulias and Grossmann (1983) for each period of operation to determine the minimum utility cost and pinch location for each period. 

Step 3. Formulate and solve the multiperiod MILP transshipment model of Floudas and Grossmann (1986) to determine a minimum set of stream matches for feasible operation in all the periods and the heat transferred in each match in each period. 

Step 5. Derive the multiperiod superstructure based upon the matches and heat transferred in each match predicted by the multiperiod MILP transshipment model. Formulate an NLP to optimize the superstructure (Floudas and Grossmann, 1987a) to give the HEN structure and exchanger sizes which minimize investment cost. 

Al) Energy balances on each hot process and utility stream in each temperature interval (TI) of the multiperiod MILP transshipment model. Each energy balance involves the residuals (heat cascaded) to and from the TI and the heat transferred in each stream match in the TI. 

By formulating and solving the multiperiod MILP transshipment model for these two periods of operation, the following set of matches is identified ... 

Target (i) without constraints on the matches was addressed via the feasibility table (Hohmann, 1971), the problem table analysis (Linnhoff and Flower, 1978a), and the T - Q diagram (Umeda et al., 1979). For unconstrained and constrained matches rigorous mathematical models were developed, namely the LP transportation model of Cerda et al. (1983), its improvement of the LP transshipment model of Papoulias and Grossmann (1983) and the modified transshipment model of Viswanathan and Evans (1987). 

Target (ii) was addressed rigorously by Cerda and Westerberg (1983) as a Mixed Integer Linear Programming MILP transportation model and by Papoulias and Grossmann (1983) as an MILP transshipment model. Both models determine the minimum number of matches given the minimum utility cost. 

The target of minimum utility cost in HENs can be formulated as a linear programming LP transshipment model which corresponds to a well known model in operations research (e.g., network problems). The transshipment model is used to determine the optimum network for transporting a commodity (e.g., a product) from sources (e.g., plants) to intermediate nodes (e.g., warehouses) and subsequently to destinations (e.g., markets). 

Papoulias and Grossmann (1983) drew the analogy between the transshipment model and the HEN, which is shown in Table 8.2. Using this analogy, heat is considered as a commodity which is transferred form the hot process streams and hot utilities to the cold process streams and cold utilities via the temperature intervals. The partitioning procedure discussed in the previous section allows only for feasible transfer of heat in each temperature interval (see also the remarks of section 8.3.1.3). 

Figure 8.4 shows pictorially the analogy between the transshipment model and the heat exchanger network. The nodes on the left indicate the sources while the nodes on the right denote the destinations. The intermediate nodes, shown as boxes, are the warehouses. The simple arrows denote the heat flow from sources to warehouses and from the warehouses to destinations, while the highlighted arrows denote the heat flow from one warehouse to the one immediately below. 

Having presented the pictorial representation of the transshipment model we can now state the basic idea for the minimum utility cost calculation. 

The basic idea of the minimum utility cost calculation via the transshipment representation is to (i) introduce variables for all potential heat flows (i.e., sources to warehouses, warehouses to destinations, warehouses to warehouses), (ii) write the overall energy balances around each warehouse, and (iii) write the mathematical model that minimizes the utility cost subject to the energy balance constraints. 

Then the transshipment model for minimum utility cost is... 

Remark 11 Cerda et al. (1983) first proposed the transportation model for the calculation of the minimum utility cost, and subsequently Papoulias and Grossmann (1983) presented the transshipment model PI which requires fewer variables and constraints than the transportation model. 

The temperature interval partitioning along with the transshipment representation is shown in Figure 8.6. Note that in Figure 8.6, we also indicate the heat loads provided by the hot process streams at each temperature intervals as well as the heat loads needed by the cold process streams at each temperature interval. Note also that the optimization variables are QS, QW, Ri, R2, and R3. 

This example is a modified version of illustration 8.3.2, and its data are shown in Table 8.3. Since we have two hot utilities and HP steam is the hottest hot utility we treat the intermediate hot utility (i.e., hot water) as a hot stream for the partitioning into temperature intervals. Then the pictorial representation of the transshipment model becomes (see Figure 8.7) ... 

In the previous section we discussed the minimum utility cost target and its formulation as an LP transshipment model. The solution of the LP transshipment model provides ... 

Papoulias and Grossmann (1983) proposed an MILP transshipment model for the formulation of the minimum number of matches target. This model is applied to each subnetwork of the HEN problem. 

The basic idea in the transshipment model for the minimum number of matches target is to model explicitly the potential heat exchange between all pairs of streams (excluding hot utilities to cold utilities) with respect to... 

Figure 8.8 Graphical representation of TJ - k for the MILP transshipment model...

The appropriate definition of the lower and upper bounds can have a profound effect on the computational effort of solving the model P2. In fact, the tighter the bounds, the less effort is required, even though the same solution can be obtained for arbitrarily large Uij. Finally, the nonnegativity and the top and bottom residual constraints are also linear. The variables are a mixed set of continuous and binary variables. Therefore, P2 corresponds to a mixed-integer linear programming MILP transshipment model. 

The MILP transshipment model P2 can be modified so as to correspond to a minimum utility cost calculation with restricted matches. The key modification steps are... 

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