Stepped-variable costs

In practice, costs do not increase smoothly or remain constant. Fixed costs frequently move in a series of steps and variable costs change unevenly. There may be several break-even points at different levels of sales and outputs (Figure 61.11). 

The economic benefits alone are also driving the adoption of biotechnology. BASF has reduced the production process for Vitamin B2 from eight steps to one through biotechnology, while DSM s bioroute for Cephalexin has also substantially reduced the number of process steps. These examples and those of dozens of pharmaceutical intermediates demonstrate that cost savings of 50 percent and more are not unlikely. The savings may come directly from lower variable costs, but also from reduced capital expenditures for simpler production assets, or from reduced scale and therefore lower risk, transportation costs, and/or overcapacity. 

Step 2 Calculate the differential cost (average variable cost). 

Multiple-step variable-speed fan control, type d. is best applied with steam-turbine drives. In aplant with ac auxiliary motor drives, slip-ring motors with damper integration must be used between steps, making the installation expensive. Although dc motor drives would be less costly, few power plants other than marine propulsion plants have direct current available. And since marine units normally operate at full load 90 percent or more of the time, part-load operating economics are unimportant. If steam-turbine drive will be used for the fans, plot the power-input curve LMD, using data from the fan manufacturer. 

The individual steps and cost estimations may be somewhat lengthy, as indicated in Section 4.4, but are well within the power of a digital computer. The major difficulty in a problem of this kind is that a function of (m + 1) variables has to be calculated, stored and interpolated. A device that is sometimes used to overcome this... 

The revenues and variable costs of production are obtained by multiplying the product, feed, or utility flow rates from the flowsheet by the appropriate prices. The difficult step is usually finding good price data. 

Variable costs are ongoing costs proportional to sales volume, and include items like raw materials and delivery charges. Fixed costs are ongoing costs treated as independent of sales volume, although more correctly they are step functions of sales volume. These include items like depreciation and administrative overheads. [15] Some costs, like labor and utilities, fall somewhere in between these two idealizations, and may be treated as either. Note that a fixed capital investment, unlike depreciation, is not an ongoing cost, and hence is not a fixed cost. 

Obviously the enzymatic process is beneficial concerning the ecological balance. Energy input, side products and emissions are reduced or avoided completely. By simplifying the production plant to only a few steps fixed and variable costs drop down. 

Overall process control. Decaffeination plants provide an ideal application area for computerised control. The control system can signal to the operators when each step should be taken and what this step should be. This results in a considerable reduction in operating costs and allows the complete plant to be operated by as few as 3 or 4 operators per shift. Even so, labour costs account for between 25 and 40% of the variable costs. 

Since the step stool was the highest-volume product in the plant, the organization had become quite proficient in producing it. But the overhead rate was full of costs for inefficiencies from making lower-volume products. In effect, the efficient step stool production subsidized the inefficient products. Actual variable costs for the step stool were 5. AAftth fully absorbed costs, the client would seem to lose 2 on every unit. In direct costing, he would put 3 in his pocket. He refused Sears offer. 

The next step is to construct cells for the constraints in Equations 5.1 and 5.2 and the objective function. The constraint cells and objective function are shown in Figure 5-5. Cells B22 B26 contain the capacity constraints in Equation 5.2, and cells B28 F28 contain the demand constraints in Equation 5.1. The objective function is shown in cell B31 and measures the total fixed cost plus the variable cost of operating the network. 

The first step in setting up the Solver model is to enter the cost, demand, and capacity information as shown in Figure 5-9 (see sheet Figure 5-12 in spreadsheet Figures 5-9 to 12). The fixed costs X for the five plants are entered in cells H4 to H8. The capacities Kj of the five plants are entered in cells 14 to 18. The variable costs from each plant to each demand city, Cy, are entered in cells B4 to G8. The demands Dj of the six markets are entered in cells B9 to G9. Next, corresponding to decision variables Xy andy cells B14 to G18 and H14 to H18, respectively, are assigned as shown in Figure 5-9. Initially, all variables are set to be 0. 

The objective function measures the total fixed and variable cost of the supply chain network and is evaluated in cell B32. The next step is to invoke Solver, as shown in Figure 5-11. 

The optimization formulation (presented in Eqs. I.II-I.I6) consists of the objective function (e.g., minimize TAG Eq. l.II) subjected to process constraints, the process models and constraints (Eqs. I.I-I.IO) of the generic model block mentioned earlier (x is a process variable, the mass flow rate), structural constraints (Eqs. 1.12 and 1.13) representing the superstructure which allows selection of only one process alternative in each step, and cost functions (Eqs. 1.14-1.16) to calculate the operating and capital costs using cost parameters (f l", waste treatment cost utility or chemicals cost , reactor... 

Optimization. Optimi2ation of the design variables is an important yet often neglected step in the design of extractive distillation sequences. The cost of the solvent recovery (qv) step affects the optimi2ation and thus must also be included. Optimi2ation not only yields the most efficient extractive distillation design, it is also a prerequisite for vaUd comparisons with other separation sequences and methods. 

Now that the values of Pp and n have been determined, we can model the system as described by Section 11.2. Wfith the proper cost functions, die total annualized cost TAC of the system can be evaluated for this iteration. Next, a new value of Cp is selected and steps 2-10 are repeated. The TAC of the system can be plotted vs. Cp (or any of the 10 other variables) to determine the minimum TAC of the system. 

The manufacturing and quality control departments face higher costs because they have to eliminate process and measurement variability, even if they are already operating at the technological limit. They will have to add people to their staffs to mn all of the investigations and handle the additional paperwork (because malicious intent is suspected, peers and supervisors have to sign off at every step to confirm that each SOP was strictly adhered to whether the SOPs made sense, scientifically speaking, or were installed to satisfy formalistic requirements is of no interest here). 

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