I
JAMES E. BORNER' Technical Service Division, Erso Standard Oil Co., Linden, N. J.
Computer Analysis of Wax Manufacture and Storage Use of the model #or scheduling plant operations should provide more efficient use of process equipment, lower inventory carrying costs, and improve service to customers
~
H o w much more equipment is needed? This is a question commonly asked any industry supplying an expanding market. I n a wax manufacturing plant, this was answered by mathematical analysis of the operations. Information was also required on how to divide this additional equipment investment between expanding process units and increasing tankage. Plant expansion based on a simple ratio of the expected demand to the current demand or even more complicated design practices is not adequate for processes as complex as wax making and products of wide daily and seasonal fluctuations. A mathematical model has been developed which simulates wax operations from the producing, storing, and blending of wax components to the treating and selling of the products. Its basis is a series of equations describing a logical operations scheduling procedure. The model was programmed for an IBM Type 705 electronic data+processing machine. The combination of mathematical analyses of operations and the calculating speed of 705 computer is a tool not generally available to operators of processing plants. Yet, a plant whose design has been specified by these methods will perform satisfactorily only if its operations scheduling is consistent with the equations used. Consequently, these new techniques must be considered for guiding field operations as well as design. The program simulates day-to-day wax operations. It analyzes the behavior of the plant for any levels of demand assumed and for any combinations of process equipment sizes and levels and distributions of tankage. Included are many operational details specific to the wax plant being studied, such as scheduled and nonscheduled downtimes. However, the areas emphasized here are those of general applicability to processes and products similar to wax. Generation of Demand Data If results are to be realistic, the customer order pattern for the 16 major Present address, Supply Department, Esso Standard Oil Co., 15 West 51st St., New York 19, N. Y.
grades of wax products must reflect accurately the wide daily and seasonal fluctuations. A statistical examination of actual demand data demonstrated that the number of orders received on any day for the wax product was adequately approximated by a Poisson distribution. As a Poisson distribution can be completely defined by the mean value, once the future level or mean value of sales for any product has been predicted, a Poisson can be described for that product. The distribution provides the basis for generating a day-by-day order pattern for the product grade. The order pattern, however, is only part of the total demand picture. Also to be considered is the size of each order. I n the case of wax, these sizes generally correspond to the mode of shipment-tanker, tank car, of truck. As each grade will probably continue to be shipped via the carriers currently used, by summarizing sufficient past data, a table can be prepared for each product, entered randomly to extract sizes for each order received; the sizes now being experienced will be statistically duplicated. A separate IBM 705 program generates the number of orders and the size of each order, Using present estimates of future sales for each wax grade, adjusted on a monthly basis for seasonal sales, provides a mean value for the Poisson distribution of orders for each grade for each month of any future year. Each distribution is then sampled randomly to determine the number of orders for any day or each grade. This sampling may be done for as many days of data as needed. After the number of orders has been selected for any day for any grade, the program then samples randomly the table of order sizes representing the summary of plant experience on mode of shipment for each product. The table is sampled for each order received. Thus, as the number of orders and the size of each order are known, the demand picture is complete. For each year generated in this fashion, the mean value of sales for each grade will be about the same as the expected level of sales Dredicted. However, as the distribuGons are sampled on a random basis, each generated year will be a different but
equally valid reflection of the demand for each product grade. When a number of years of demand data have been generated, this information is fed to the wax processing program. The equipment size and tankage limitations which were selected for various sections of the plant determine the success with which the orders are met. Selection of Products for Processing The feed stock for the wax manufacturing process is a wax-oil mixture. The wax is separated by crystallization in the dewaxing step and Then purified. More than a dozen components can be produced by separating the wax feed stream into streams with different melting points, The operating conditions of the separation process may be varied. As a result there are about ten different basic operating schemes, each producing several different components simultaneously. The components are stored prior to being blended into the 20 or more product mixes, each with different physical properties making it ,suitable for its particular end use. Each product may be blended from components in as many as three different ways. The blends are then filtered through adsorbent material for color and odor purification and the filtered products are stored for shipment (Figure 2 ) . I n scheduling any day's operation, it is necessary to know which components must be produced, to provide adequate quantities for use as blending stocks. This decision is based largely upon which products are desired. The various products are therefore ranked in order of need. For each product the program calls for a daily calculation of the value of the urgency, U,, for blending any product
j where
I, = inventory of product j ready f o r shipment Di = A j m
4- A*iim-1
+
A*jm-2
+ . , .(2)
where
Aim
= a function of the quantity
ordered and the number VOL.
so,
NO. 5
MAY 1958
721.
A*,?+
1
of customers ordering the j t h product on the mth day = a function of the quantity of unmet orders, the number of customers, and the time delay of orders for the j t h product received during the m - l t h day.
A plot of the urgency of any product, U,, against its inventory, I,, at various demand levels, D,,is shown in Figure 1. For any product, U , decreases with increase in inventory of the product, but increases with increase in demand, number of customers, and delay in meeting orders. Although the urgency function has no meaning as an absolute value, it relates the need for each wax grade to its inventory and its backlog of orders. The use of this function is consistent with the objective of the study-to determine the equipment required by an efficient plant to satisfy customers on all products. From the list of ranked products the top four are selected as candidates for blending and filtration. Four is the maximum number of products that can be handled simultaneously by the filtration plant. I t remains to decide whether the filtration should be performed on a full batch of a single product, on two half-batches of two products, or on quarter-batches of four products. The choice rests on which technique most reduces the over-all level of urgency. In considering this urgency reduction, a concept of the time sequence of the process is important. At the beginning of the nth day, the products have been ranked in order of urgency based on current inventory and demand accumulated through the end of the previous day (Figure 3). The components required for blending the product or products selected must be either drawn from component inventory or produced during the nth day. The preparation of these components is indicated by the dotted arrow near the end of the nth day. The components are then blended and fed to the filter plant during the n 1th day; the four 1th day show the one, arrows in the n two, or four products being fed to filters l , 2. 3, and 4. These emerge as finished products during the n 2th day. Because of these process delays, the scheduling decisions made now are concerned with products to be sold at the 2th day. Consequently, end of the n the decision as to the number of products to be treated must reflect the expected or average demand for products anticipated during the nth day and the two days to follow. What the program tries to achieve is the greatest reduction possible in the over-all urgency by the 2th day. This is done by end of the n assuming first on a trial basis that the four most urgent products will be produced and sold to meet the demand that
+
is expected to accumulate through the end of the n 2th day. From this it calculates the urgencies of these top four products at the end of the n 2th day. The sum of these urgencies can be compared with the sum for the same four products now, at the beginning of the nth period. The difference is the reduction in urgency if the top four products are blended and filtered. A similar trial calculation is performed for the production of the top two products and finally for a full batch of the top product alone. These trial calculations permit a decision as to which alternative to select. The change in urgency of the top four products has been calculated for three cases: one product, two products, or four products. The procedure showing the greatest reduction in urgencies is naturally c I iosen.
+
+
v.
Scheduling Corn ponent Production In this way the schedule can determine which product blends will be re2th quired for treating during the n day and the quantities of each needed. Still undecided is which of several possible blending methods to use for each product and how to operate the separation process to produce the required amounts of components. The number of possible blending methods can be large. A maximum of four products can be scheduled to be blended, and there can be as many as three methods of blending each product. In many cases, therefore, the choice of blending scheme is made from a field of ( 3 ) 4or 81 possibilities. To illustrate the selection process that has been programmed, assume that a decision has been reached in the manner described to produce only the two most urgent products. Each of these two products can be blended by two methods. These methods and the quantities of each component are :
+
+
XLLI
+ X&I,l+
X9.1,l
= PI
(3)
+
A. 3 and 5 B. 3 and 6 C. 4 and 5 D. 4 a n d 6
The best will have the following characteristics:
1. As much as possible of the total component requirement should be drawn from inventory, thus permitting the separation plant to produce components needed on future days. Satisfying this requirement tends to prevent excessive build-up of any component and reduce the amount of tankage required. 2. There are about ten basic operating plans for the separation plant. In general, each operation produces three specific components. If the plant is operating to produce a required component, the other two components produced concurrently (secondary components) may not be required for the products we wish to blend. The best blending scheme will produce secondary components of most use in future days. For any scheme, the length of time that the separation plant must operate to produce the required amount of any component can be calculated by Equation 7. When the total required operating time is low, the amount of components being drawn from inventory is high compared to the amount being produced.
X , - Zi = R, T ,
(7)
where
+
Xi
I
+
722
I n these equations Xi,j,k, represents the amounts of component i required to make product j by blending method k. X l , l , ~is the amount of component 1 required to blend product 1 by method 1, and X,,,,, is the amount of component 9 used to make product 1 by blending method 2. PI and PZ are the amounts of the two most urgent products which can be treated during a filter run. As Equations 3 to 6 show, the four possible ways to prepare PI and PI involve combining blending methods:
Ij
-
Figure 1. Urgency is affected by inventory and demand
INDUSTRIAL AND ENGINEERING CHEMISTRY
total amount of component i needed in preparing PI and PZ by any of the four blending schemes It = inventory of component i Ri = rate of production of component i during separation plant operation e T , = time separation plant must run on operation e to produce amount of i required to blend the products desired =
COMPUTERS IN PETROLEUM RESEARCH
DEWAXING
SEPA- COMPONENT RATION TANKS
Figure 2.
Table 1.
Comparison of Blending Methods A
or
BLEND TANKS
FILTRATION
Wax processing operations
T o be considered next is the production of secondary components when running the separation plant as dictated by A, B, C, or D. For instance, if method A were selected, the plant would operate on methods I, 11, and V for the corresponding calculated times TI, TII, and Tv. During these times, components other thap XI, Xq, and X , would be produced. The potential value of these secondary components is now of concern. For each secondary component there is a desired inventory which is a function of the demand for products blended from the component. The desired inventory, CY,, is expressed by Equation 8.
This equation calculates the operating time, the hours required to produce the amount of components needed above that available in inventory. If the inventory exceeds the amount required, Ii> ZX$,the component is not scheduled for production and T, is set equal to 0. Equation 7 has been applied to blending methods A, B, C, and D to permit study of the operating plan to be used for each method. For each of the above combinations, the total operating time, ZT,,may be C
calculated from the equations shown. The method, A, B, C, or D, which results in the lowest B T, exhibits characteris#
or
tic 1 of the best blending method.
1 2 3 4
A
nth day
or
D
PRODUCT TANKS
1
1 2 3 4
NOW Figure 3. Sequence of operations used in dgtermining urgency based on current inventory and demand VOL. 50, NO. 5
MAY 1958
723
sistent with producing valuable secondary components. where
D,*
=
x,,,=
total unmet demand for product
j
average amount of component i used to blend product j
From the desired inventorv of anv secondary component a desired time, 0,) can be calculated, representing the length of time that the separation plant must produce component i to bring its inventory from the actual level, I,, to the desired level, as. nYi-
(9)
I, = R, 9,
The calculated desired time for any secondary component is an indication of the anticipated amount of time in the near future that the plant would be required to run to produce the component for blending. If method A were selected, the separation plant would perform operations I, 11, and V shown in Table I and the secondary component produced by each of these operations would be governed by times TI, TII. and TT,which were calculated. In considering the secondary components, we are primarily interested in that part of the scheduled time T,, in this case TI, T I I ,and T17, which is useful in bringing the component level u p to the desired level. This useful time is called t, and its value determined as shown. If 0%< 0, t, = 0 Ife, > T,, t, = T , If e, < T,. tz = e, T o evaluate each of the four possible blending schemes an expression has been derived which weighs the various operating times required. I t recognizes the total time the separation plant must operate to produce the primary products as well as the fraction of that time used to produce secondary components most likely to be used as primary blending components in the near future. This expression is called the time factor and is calculated for each blending plan. Time factor = Z T, - 2 e
i
R. Rstp
(10)
ti
where
Ri/Rsip = fraction of component i in total separation product
plant
The first part of the time factor expression represents the total separation plant operating time for any blending scheme ZT,. The second part, Z(R,/ e
i
RBIP)tr, is that fraction of the total operating time devoted to producing valuable secondary components. That blending plan which results in the lowest time factor is the one to select, as it keeps separation plant operating time low con-
724
Summary of Calculation Procedure The marhematical decision rules described form the heart of the 705 program. The input data for the program to operate on consist of the following: 1. Tankage Volumes. Each component and each product is assigned a volume of tankage. There are no restrictions on the volumes which may be selected. 2. Process Equipment Capacities. Each process unit is assigned a maximum rate. 3. Demand Data. A separate and independently operated program for supplying product demand has been written. This prograni supplies a tape containing a daily record of the individual product orders. As it is operated independently of the main program, there is no restriction on the predicted level of sales that can be used in generating the demand data tape. 193th this input information available, the main program can begin operalion. I t simulates the day-by-day performance of the plant, using the decision rules to govern product and component selection and production. The customer delavs being experienced are examined each day and an urgency for each product is calculated. From these urgencies and the expected demand for each product, the particular wax grades to be produced are selected. O n the basis of this selection, a blending scheme is chosen which in terms of the criterion established results in the most efficient use of the separation plant. The output data from the program are :
1. Daily Sales 2. Inventory Records. The inventory status of each product and component is recorded daily. 3. Processing Operations. A daily summary lists the throughputs of all units and the operations selected by the decision rules. 4. Customer Service Performance. A record is made of the daily statu? of customer delay on each product. This information is also summarized for each year simulated. The record of delay on each product is the real criterion of the success with which the particular plant described by the input data on capacities is satisfying customer orders. Poor results suggest that a better selection of tank sizes or process equipment capacities is required. An analysis of the output data of the model generally localizes the area of needed improvement. Present Use of Program The first problem to which the program is being applied is the selection of
INDUSTRIAL AND ENGINEERING CHEMISTRY
the best method for possible expansion of a wax plant. A reasonable set of process unit capacities are selected by judgment as adequate to meet the future demand. The customer service and plane operation are then simulated repeatedly for several different tankage patterns. A new set of unit capacities can then be chosen and the reaction of the model again observed with several different tankage layouts. Appropriate investments and operating costs are applied to determine the worth of each combination. This information permits a choice, on the basis of return on investment. of the optimum combination of tankage and equipment necessary to produce a desirable record of customer service. Development of this program and its initial runs have shown that simulating the time behavior of a complex feedback system is difficult and time-consuming. The computer obviously requires a precise definition of procedures to follow. The systam under study does nct always have this precision. Whether the procedures defined for the computer program are realistic cannot be known until the job is complete. Because of this uncertainty. complex simulations should be considered onlv when no satisfactory alternatives are available and \+hen the high cost of the project is decisively counterbalanced by the economic importance of the solution. Future Application of Model I n view of the complexity of the wax process and the large amount of data to be considered, computer scheduling of operations would provide more efficient use of plant equipment, lower inventory carrying charges, and superior service to wax customers. The present model provides a good basis for computer scheduling. Actual component and product inventories and the unmet customer orders to date would provide the input to the scheduling program. The output would be a running plan for the process, showing which products to blend, the components to use, and the operations needed to produce the most valuable components. Acknowledgment The advice of R . W. Schrage, Technical Service Division, and the assistance of D. R. Maynard, Bayonne Refinery, who is largely responsible for the generation of the demand data, are gratefully acknowledged. RECEIVED for review November 7, 1957 ACCEPTED February 17, 1958 Division of Petroleum Chemistry, Symposium on Application of Machine Computation in Petroleum Research, 132nd Meeting, ACS, New York, N. Y., September 1957.
