Overall problem implementation and execution

The model is programmed and solved in IBM ILOG CPLEX Optimization Studio 12.3 (code is provided in Appendix II), while data is read from and results, as stated before, are exported to Excel spreadsheets. It is interesting to note that IBM ILOG CPLEX Optimization Studio 12.3 cannot read arrays with more than two dimensions directly from Excel spreadsheets. Hence, in reading from these sheets in working with variables and parameters with higher dimensions e.g. RTtdf and Zhtdvs, they are read as tuples,

transformed to arrays, then used in calculations. The reverse process occurs in writing to spreadsheets for high dimension arrays; here the arrays are transformed to tuples then written to the spreadsheets.

It is discussed in Chapter 3 that solution algorithms are not the focus of this research since a solver is used for solving the model. But the reader might be interested to know that by looking at the help file of the solver it is understood that a branch-and-bound algorithm is the core of IBM ILOG CPLEX Studio 12.3 in solving the MIP problems. In brief, a branch-and-bound algorithm is a solution finding method for discrete optimization problems that divides the set of candidate solutions, also known as feasible solution space, into subsets and rejects the unrewarding subsets by using upper and lower estimated bounds of the problem objective function. The dividing and rejecting process and looking for the optimum solution in the remains of the feasible solution space in this algorithm continues until a solution is found that there is no better solution than that; that solution is the optimum one (Taha, 1992).

It has been previously discussed that the model is solved for a time period of two to three months. After the discussion in this section, which put different factors of the model into perspective, it can be understood why the planning period is relatively short. Factors, such as those that follow, make the far future too unpredictable for operational decision-making, hence having longer periods in that level of decision-making would not be rational. Reasons such as volatility in LNG spot prices which are important in decisions for spot sales, and the unpredictability of spot tanker chartering rates which needs to be considered in tanker assignment to uncommitted product, arbitrage and CIF/DES-LTC deliveries that are both taken to account in the objective function.

The accuracy and adoptability of operational decision-making is increasing by the rolling horizon process – Figure 4.2 – that is implemented in this type of planning in the LNG sector. In this process a period is planned but the plan is not totally executed, rather, after implementing a fraction of it, the problem planning span rolls forward (Figure 4.2) and a new period is planned. This means that of the two to three months that are

P a g e | 127 planned as a period, only a portion of it is executed. It is clear that the information available for planning, such as the spot prices and tankers available for spot chartering, after rolling the problem planning span forward, would be much more accurate than the information about the same days – the overlap in Figure 4.2 – in planning the previous period.

Figure 4.2 - The rolling horizon process

Usually two weeks to one month of the period planned is executed (Flower, 2011). But with unexpected/unpredictable events, such as reduction in LNG output of the Trains due to a failure, which affects the production rate of LNG PPh in equation number (3), a

technical problem with a fixed tanker, that influences equation number (12), a delay in the return of a fixed tanker from an assigned delivery due to bad weather, which concerns equation number (12), or a sharp change in spot prices in a market which may affect the LNG producer’s decision on uncommitted product sales, which involves equation number (2), the rolling horizon process may need to occur earlier. These incidents if they take place after the beginning of the implementation of the period planned and during the portion of the period that is executed, may need to be taken into account. But they are not considered in the planning of the period already executed as the LNG producer did not know about them at the time. Should the LNG producer think any of these are important during the planning process, then he stops the

implementation of the period planned on the day that any of these incidents occurs, considers the incident, plans a new period and executes the new plan. There is a chance that some of these incidents are not important in planning; for example, a fixed tanker that returns late and does not have a busy schedule and need not be dispatched for another delivery until after its delayed arrival, does not affect the period already planned and implemented. The LNG producer needs to consider unexpected/unpredictable incidents and decide whether they need to be taken into account or not.

Figure 4.3 puts the formulation, containing the objective function and constraints, along with the rolling horizon process, into perspective. The objective function and the set of constraints given the data read from Excel spreadsheets are built for the period studied. The set of constraints define the feasible solution space – the set of candid solutions – for the problem, and each of the constraints is essentially one of the borders of the feasible solution space. Having defined the feasible solution space the IBM ILOG CPLEX Optimization Studio 12.3 picks the best solution among the set of candidate solutions by minimizing the objective function using a branch-and-bound algorithm. The solution picked for a period includes decisions on uncommitted product (Xhtd), arbitrage (Zhtdvs)

and CIF/DES-LTC (Yhtd) deliveries along with the volume of LNG in the tank-farm at the

end of each day (Ih) that are meant to minimize the objective function (maximize the

revenue in uncommitted product sales and arbitrage, and minimize the tanker and tank- farm costs). After picking a solution for a specific period, in time the problem planning span rolls forward and the next period is planned by following the same procedure discussed in this paragraph.

With regards to the extent that producers can respond to changes in LTC demands it should be noted that if a negotiated change, in putting into practice by affects the

P a g e | 129 constraints, results in a situation where no feasible solution space can be defined, there is no solution that satisfies all the constraints, then the problem would be infeasible. In other words, such a change would not be possible. For example, if by changing the volume of deliveries to a LTC buyer there is need for a tanker to be loaded on a specific day in the production plant while all the berths on that day are occupied by tankers that are serving compulsory deliveries, this concerns equation (9), then such a change would not be possible, and the problem would be infeasible.

It should also be noted that the set of decisions made and executed in running the system in the last period (the solution picked for the last period) may affect the feasible solution space in the next period planned. For example, if a fixed tanker is dispatched to do a delivery in the last period and it is not back for the beginning of the new period, then in reading the data from Excel spreadsheets for the new period in which decisions made in the last period are considered, this unavailability is identified and taken into account. This unavailability is considered in equation (12) for the new period hence, affecting the feasible solution space for this period. In other words, the decisions made in the last period influence and limit the choice of decisions for the new period.

4.5. Concluding remarks

In this chapter an operational model for running an LNG production and distribution project is presented. The MIP model covers all types of LNG trades including: traditional LTCs (with CIF/DES and FOB deliveries), self-contracts (with CIF/DES deliveries) and spot sales for uncommitted product and in arbitrage (of CIF/DES deliveries in self-contracts and traditional LTC). It permits usage of both fixed and spot tankers for cargo delivery. One of the interesting features of the model is consideration of the time value of money

which, given the magnitude of the cash flows in the LNG business, can be important in decision-making.

Now that the model has been developed different aspects of the LNG business can be studied. This is the agenda for the next chapter where business characteristics such as arbitrage are studied and discussed.

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