Shortfall, production

Prior to the discovery of plentihil suppHes of natural gas, and depending on the definition of the resources (1), there were plans to accommodate any shortfalls in gas supply from soHd fossil fuels and from gaseous resources by the conversion of hydrocarbon (petroleum) Hquids to lower molecular weight gaseous products. 

Uranium production in 1992 of 36,246 t U was only about 63% of world reactor requirements of 57,182 t U the remainder, 20,950 t U, was met from inventory drawdown. The worldwide production shortfall has developed since 1990 when production exceeded reactor requirements by about 1000 t U (27). 

Supply Projections. Additional supphes are expected to be necessary to meet the projected production shortfall. A significant contribution is likely to come from uranium production centers such as Eastern Europe and Asia, which are not included in the capabihty projections (27). The remaining shortfall between fresh production and reactor requirements is expected to be filled by several alternative sources, including excess inventory drawdown. These shortfalls could also be met by the utili2ation of low cost resources that could become available as a result of technical developments or pohcy changes, production from either low or higher cost resources not identified in production capabihty projections, recycled material such as spent fuel, and low enriched uranium converted from the high enriched uranium (HEU) found in warheads (28). 

Once all technical and pohtical problems are resolved, reactor-grade uranium produced from HEU warhead material could contribute significantly to meeting the anticipated fresh uranium production shortfall. This source, however, is not expected to have a significant impact until the year 2000 or later. The discovery of new low cost resources is not expected to make a significant contribution to production until after the year 2005 because of the very low level of uranium exploration and the relatively long lead times required to develop new production centers (29). 

In addition to conventional petroleum (qv) and heavy cmde oil, there remains another subclass of petroleum, one that offers to provide some rehef to potential shortfalls in the future supply of Hquid fuels and other products. This subclass is the bitumen found in tar sand deposits (1,2). Tar sands, also known as oil sands and bituminous sands, are sand deposits impregnated with dense, viscous petroleum. Tar sands are found throughout the world, often in the same geographical areas as conventional petroleum. 

The United States is largely self-sufficient with respect to copper, meeting any shortfall by imports. AustraHa and the CIS consume most of their production on the domestic market. Japan and Western Europe import substantial quantities of copper in the form of concentrates, bHster, and refined copper. World mine, smelter, and refining capacities in 1989 are given in Table 6. Copper industries in Chile, Pern, Zaire, and Zambia are nationalized. 

From the above discussion, it follows that the quality and conformance to tolerance of the product characteristics should be designed in and not left to the process engineer and quality engineer to increase to the required level. In order to do this, designers need to be aware of potential problems and shortfalls in the capability of their designs. They therefore need a technique which estimates process capability and quantifies design risks. 

It comes to the fore when new design of buildings, plant, equipment or production processes is being considered. It is at this stage that the right specification must be made. Any shortfall in the thickness or error in the type and application details will prove costly to rectify at a later data. 

Birewar and Grossmann (1990a) proposed a model for the simultaneous determination of the best production goals and the best allocation of tasks to the equipment units. They incorporated inventory costs into the objective function. To keep commitments that have been made at the stage of production planning, a penalty PNu) was incurred in the objective function for not meeting the commitments for product i in interval r as a linear function in terms of the shortfalls SFn) ... 

Wood has been used by mankind for millennia because of its excellent material properties. Although the use of timber in some markets has decreased, the consumption of timber overall continues to rise. Projections have been made until the middle of the 21st century that in most cases show a rise in demand for timber (in all but low economic growth models) and an increase in production (Figure 1.7) (Brooks etal., 1996). There is, however, concern that the supply of timber for industrial purposes may not be able to match demand. For example, Bowyer etal. (2003), note that there will be a shortfall in the amount of forest area providing industrial timber by the year 2100, due to the rise in human population during this time (Table 1.4). 

Compensating slack variables accounting for shortfall and/or surplus in production are introduced in the stochastic constraints with the following results (i) inequality constraints are replaced with equality constraints (ii) numerical feasibility of the stochastic constraints can be ensured for all events and (iii) penalties for feasibility violations can be added to the objective function. Since a probability can be assigned to each realization of the stochastic parameter vector (i.e., to each scenario), the probability of feasible operation can be measured. In this... 

It is desirable to demonstrate that the proposed stochastic formulations provide robust results. According to Mulvey, Vanderbei, and Zenios (1995), a robust solution remains close to optimality for all scenarios of the input data while a robust model remains almost feasible for all the data of the scenarios. In refinery planning, model robustness or model feasibility is as essential as solution optimality. For example, in mitigating demand uncertainty, model feasibility is represented by an optimal solution that has almost no shortfalls or surpluses in production. A trade-off exists... 

For simplicity of demonstration, it is assumed that there is no alternative source of production hence, in a case of a shortfall in production, the demand is actually lost. Thus, the corresponding model considers the case where the in-house production of the refinery has to be anticipated at the beginning of the planning horizon. 

A 5% standard deviation from the mean value of market demand for the saleable products in the LP model is assumed to be reasonable based on statistical analyses of the available historical data. To be consistent, the three scenarios assumed for price uncertainty with their corresponding probabilities are similarly applied to describe uncertainty in the product demands, as shown in Table 6.2, alongside the corresponding penalty costs incurred due to the unit production shortfalls or surpluses for these products. To ensure that the original information structure associated with the decision process sequence is respected, three new constraints to model the scenarios generated are added to the stochastic model. Altogether, this adds up to 3 x 5 = 15 new constraints in place of the five constraints in the deterministic model. 

Although increasing 02 with fixed value of 0 corresponds to decreasing expected profit, it generally leads to a reduction in expected production shortfalls and surpluses. Therefore, a suitable operating range of 02 values should be selected to achieve a proper trade-off between expected profit and expected production feasibility. Increasing 02 also reduces the expected deviation in the recourse penalty costs under different scenarios. This, in turn, translates to increased solution robustness. In that sense, the selection of 0j and 02 values depends primarily on the policy adopted by the decision maker. 

Operational risk factor 02 Optimal objective value Expected variation in profit V(z0)(E + 8) Expected total unmet demand/ production shortfall Expected total excess production/ production surplus Expected recourse penalty costs Es Expected variation in recourse penalty costs Vs p = E[z ] - Es c a P... 

First- stage variable Stochastic solution Product (i) Production shortfall zjf or surplus Zy (t/d) Scenario 1 Scenario 2 Scenario 3 ... 

One of the reasons why the pair of decreasing values of 0, with a fixed value of 03 leads to increasing profit is due to the decrease in production shortfalls and, at the same time, increase in production surpluses. Typically, the fixed penalty cost for shortfalls is lower than surpluses. A good start would be to select a lower operating value of 0 j to achieve both high model feasibility as well as increased profit. Moreover, lower values of 03 correspond to decreasing variation in the recourse penalty costs, which implies solution robustness. 

The above formulation is an extension of the deterministic model explained in Chapter 5. We will mainly explain the stochastic part of the above formulation. The above formulation is a two-stage stochastic mixed-integer linear programming (MILP) model. Objective function (9.1) minimizes the first stage variables and the penalized second stage variables. The production over the target demand is penalized as an additional inventory cost per ton of refinery and petrochemical products. Similarly, shortfall in a certain product demand is assumed to be satisfied at the product spot market price. The recourse variables V [ +, , V e)+ and V e[ in... 

Equations 9.11 and 9.13 represent the refinery production shortfall and surplus as well as the petrochemical production shortfall and surplus, respectively, for each random realization Ic C N. These variables will compensate for the violations in Equations 9.11 and 9.13 and will be penalized in the objective function using appropriate shortfall and surplus costs C r 1 and for the refinery products, and C et + and C 1 for the petrochemical products, respectively. Uncertain parameters are assumed to follow a normal distribution for each outcome of the random realization Although this might sound restrictive, this assumption imposes no limitation on the generality of the proposed approach as other distributions can be easily incorporated instead. Furthermore, in Equation 9.13 an additional term xi 1 was added to the left-hand-side representing the flow of intermediate petrochemical... 

From March 1941, with the passing of the Lend-Lease Act, British war production could take increasing account of what could be better supplied from the United States. The falling off in British tank production after 1942 reflected the fact that it was no longer necessary for Britain to be self-sufficient on the other hand, continued British production was a necessary insurance against a shortfall in American deliveries. Likewise the fact that British steel production peaked in 1942 and declined by 9.8 per cent by 1944 reflected the shipping shortage, which made it more sensible to import flnished steel from the United States than to import more bulky iron ore. ... 

Sulfur is used in a wide variety of industrial processes, however, its single most important use is as sulfuric acid in the production of phosphatic fertilizers. World demand for sulfur (in all forms) has traditionally grown at a fairly steady pace while world supply has been subjected to various sudden surges and shortfalls. The resulting interplay of supply/demand forces has led to an interesting price history for this commodity both worldwide and in North America. 

The product development PPPs have reported their pledged and required funding up to 2007, as shown in Table 4.2 (Ziemba 2004). This demonstrates a substantial shortfall in committed funds. 

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