A WINERY COMPUTER MODEL

A WINERY COMPUTER MODEL David S. Tower Department of Viticulture and Enology, University of California, Davis, California 95616. Present address: Commonwealth Winery, Cordage Park, Plymouth, Massachusetts 02360. Professors V. L. Singleton and D. Carlson are thanked for their crucial help and advice on the Master's degree research project that is the basis of this article. The Department of Viticulture and Enology is thanked for the funding of the computer time necessary for the project. Manuscript submitted September 28, 1976. Revised manuscript received February 22, 1979. Accepted for publication February 22, 1979. A computer program was written which simulates the production of table wines of a small-to-mediumsized winery. Important production and financial constraints, such as capacities in each step of winemaking, availability and prices of different grape varieties and blending formulas, are provided by management as input for the computer. The computer, fitting the data into a linear programming model, chooses the best combination of grape varieties and wines so that the winery's profit is maximized. Additional information ABSTRACT provided by the computer includes which production steps are the bottlenecks and how much profit would increase if a bottleneck is removed. How much labor is required for each production step is also computed. The article first discusses the application of linear programming to a simplified production model. The actual model, which can be solved by the computer program, is then presented. Computer output of a hypothetical small winery is interpreted. Additional aspects of the flexibility of the program are discussed. The mathematics of linear programming have been used successfully in building computer models in many different production industries (2). Winemaking, a batch process, is well suited to computer analysis using linear programming. The technique has been used in an analysis of optimum production practices of cooperative wineries in Germany (1). METHODS To show how such a mathematical model of wine production can be constructed, a simplified example of wine production will be presented first. This model will then be expanded to demonstrate how the time constraints of winemaking are constructed for the computer. Finally, the actual model will be described in general terms. A simple model: The wine production of the simplified model contains only three steps: fermentation, aging and sales. A flow diagram of the simple model is as follows: Fermentation : Bulk aging : Sales The simplified winery produces two wines, a red wine and a white wine. Let R be the number of gallons of red wine produced in d season, and W the number of gallons of white wine. If the winery earns three dollars profit on one gallon of red wine, the profit from the red wine sales of the season's production would be 3 x R, and if the winery makes two dollars profit per gallon of white wine, the white wine profits would be 2 x W. If P is the total profit from the season's production, then the equation for the profit would be 3R + 2W = P. The winery, as a commercial operation, wishes to produce and sell the amounts of red and white wines, R and W, which maximize the profit, P. Every winery is subject to restrictions or constraints in availability of raw materials, production capacities and ability to sell its products. Such constraints can be formulated mathematically. They are in the form of mathematical sentences, generally inequalities. This is so because not all of the capacity of a process must be used, but it is impossible to use more capacity than is available. In our simple model, assume that the maximum amount of white wine that can be sold is seven gallons. Market saturation of white wines is a possible cause. Algebraically this marketing constraint is expressed by the inequality lw <- 7 or OR + lw <~ 7, which is stating the same thing in a different form. Assume that all the red wine produced can be sold. The winery is also subject to production capacity constraints. Its total bulk aging capacity is eight gallons. Each gallon of red or white wine produced requires one gallon of bulk aging capacity. Since the total gallons of red and white wine produced cannot exceed the gallonage of the aging facility, the bulk aging constraint can be formulated as 1R + l W ~ 8. Assume the total fermentation capacity is 10 gallons. Further assume that every gallon of red wine requires two gallons of fermentation capacity in order to provide sufficient space for the rising cap. A gallon of white wine requires only one gallon of fermentation capacity. The fermentation constraint would then be 2R + lw <_ 10. Thus, this simple model has a profit equation and 208

COMPUTER MODEL- 209 inequality constraints for fermentation, bulk aging and sales. Algebraically it consists of the following: Profit 3r + 2W = P Fermentation 2R + lw <-- 10 Aging 1R + l W <- 8 Sales 0R+ lw<-7 Each constraint restricts what values R and W could have. One would like to find among the possible values the value for R and the value for W which would maximize the profit, P. Even for this most simple model, finding the best values by trial and error would take some time. However, the computer can be programmed to find quickly such optimum values. The model is fed into the computer as a block of numbers, called a linear programming input matrix. In our model the matrix would look like this: 3 2 P 2 1 10 1 1 8 0 1 7 These numbers are taken directly from the algebraic formulation of the model. The first column are the coefficients for the R variable, the second for the W variable and the third is the right-hand side of each equation or inequality. A more complex model: The model can be expanded in numerous ways to fit the real situation of the crushing season better. For example, available fermentation capacity on a daily basis is important in determining how much of each type of wine to make. For our model, assume that it takes two days to ferment either type of wine and that the crushing season is three days long. Based on past seasons' experience and on projections for the current season, management can make reasonable estimates of the arrival patterns for each grape variety during the crushing season. Let us assume that none of the grapes for the red wine variety will arrive on the first day of crushing, 40% will arrive on the second day and 60% on the third. For the white wine variety, 40% arrives on the first day, 30% on the second and 30% on the third. Every day the same fermentation capacity, 10 gallons, is available. The first day's fermentation constraint is: [2 x 0] R + [1 x 0.4] W -< 10. The coefficients for R and W are the decimal equivalents of the percent of the variety arriving on a particular day times the fermenting space that one gallon of the variety occupies. This coefficient times the total amount of the variety, R or W in our model, gives the amount of fermentation space that the variety occupies on that particular day. In our example, no red wine arrives on the first day, so it occupies no fermentation space then. On day one, 40% or 0.4 of the white wine variety arrives, so it occupies 0.4W gallons fermentation space. The total of fermenting wines cannot exceed the day's capacity, which is what the constraint states. The fermentation constraint for the second day is more complex. On that day, 0.4 of the red wine variety arrives, so the amount of fermentation space occupied by the red variety is [2 x 0.4] R. Forty percent or 0.4 of the white wine variety arrived the first day and would still be fermenting on the second. On the second day 0.3 of it arrives, so 0.4 + 0.3 or 0.7 of it requires fermentation space. The gallon requirement for the white wine variety would be [1 x (0.4 + 0.3)] W or [1 x 0.7] W. The fermentation space used by both varieties must be less than or equal to the space available. Algebraically this would be written as [2 x 0.4] R + [1 x 0.7] W ~ 10. On the third day, 0.6 of the red wine variety arrives. Still fermenting is the 0.4, which arrived on the second day. Hence, all of the red variety requires fermentation space and this would be represented by the expression [2 x (0.4 + 0.6)] R or [2 x 1.0] R. For the white variety, the 0.4, which arrived on the first day, is finished fermenting and no longer occupies fermentation space. The 0.3 that arrived on day two is still fermenting and 0.3 arrives on day three. The space occupied by the white variety would be [1 x (0.3 + 0.3)] W or [1 x 0.6] W. The constraint would be [2 x 1.0] R + [1 x 0.6] W <-_ 10. Substituting the three fermentation constraints for the one in the original model, the revised model would be: Profit 3.0R + 1.0W = P Fermentation Day 1 0.0R + 0.4W <- 10 Day 2 0.8R + 0.7W <- 10 Day 3 2.0R + 0.6W <- 10 Aging 1.0R + 1.0W <- 8 Sales 0.0R + 1.0W <- 7 This model can be further expanded in several ways to make it more closely fit reality. More wine varieties could be added. More production steps in the form of more constraints could be added. Production steps during the crush would have daily constraints as does fermentation capacity in the above model. Labor is also a limited resource in wine production, especially during the crushing season. Constraints for labor could be added. The limitation to the size of the model is the capacity of the computer to handle a matrix of many numbers. The computer program: A computer program, called WINERY, written for this project, creates a linear programming input matrix. Data for WINERY is supplied by management. Another computer program, TEMPO, which is stored in the computer at the University of California, Davis, Computer Center, finds the variable values which yield the highest profit and still satisfies the constraints. The program is intended to be run by people with minimal computer experience (3). The actual model: The winery model which forms the basis of the computer program, WINERY, is shown as a flow diagram, Fig. 1. The program considers all the major cost and production factors that influence the choice and amount of grapes to be purchased and the wines to be made. Determining the optimum amount of each variety to process and the best sales channels for the product is the major purpose of the program.

210 -- COMPUTER MODEL i CRUSHING SEPARATI ON OF FREE RUN FROM SKINS PRESSING CENTRIFUGING FERMENTATION k~ l'.i FERMENTATI ON Unpressed PRESSING AGING IN BULK small barrels I BOTTLING STERILE FILTER I POL I SH FILTER F ROUGH FILTER H small barrels casks casks wood tanks CENTRI- F FUGING Oak tanks Non-wooden tanks H WAREHOUSE I.E. BOTTLE AGING ii SALES Wholesale Retail Bulk Fig. 1. The computer model of a winery. Crushing through centrifugation of young wine are activities performed during the crushing in the fall. During this time, daily capacities for each process are important constraints to production. For example, in choosing the amount of each grape variety to process, a winery must be reasonably sure that the daily arrival of grapes does not exceed the winery's ability to press them at the desired time. Therefore, the model sets up constraints for the crushing season processes on a daily basis in a similar manner as was done for fermentation in the simple model. Unlike the winemaking steps during the crushing season, the other activities shown in Fig. 1 can be delayed for days, weeks or sometimes months. Constraints for such activities are constructed on a yearly basis, as were aging and sales in the simple model. Processes, such as settling of pressed white must and cooling during fermentation and for tartrate stability, are assumed not to place constraints on production, since the equipment for such processes is generally part of other systems. Therefore, they were not included in the WINERY program. The program, WINERY, is designed to handle a large number of grape varieties. Each variety can be processed into table wine in a different way. For example, management can stipulate what fraction of each variety will be centrifuged or whether none of a variety is to be centrifuged. Blending is assumed to be done after pressing. The program has the capacity to handle a large number of blends. WINERY provides not only for crushing grapes but also permits the stipulation of a fraction of a variety to arrive at the winery already crushed, as is the case with some mechanical harvesting systems. For white wine varieties, the free run can be separated from the unpressed skins after crushing. Constraints for separation tanks are assumed to be specially constructed tanks which permit easier separation of juice from pomace and easy pomace removal from the tank. Any dejuicing equipment which separates free run continuously from press material is considered to be an

COMPUTER MODEL m 211 integral part of the press system and does not require a separate constraint. Because many wineries have special fermentation tanks for red wines, the model has an option to establish separate constraints for such fermentation. Centrifuging can be done on any fraction of a variety before and/or after fermentation. Fractions of a variety destined for different wines can be aged for different lengths of time in different containers. The container types are labeled small barrels for red wines, small barrels for white wines, casks for red varieties, casks for white varieties, redwood tanks, oak tanks and non-wooden tanks. Blending restrictions can be put on any wine for any number of varieties in the wine. These restrictions force each blend to contain a given fraction of each variety. WINERY has three types of filtration: rough, polish, and sterilizing. Any fraction of each grape variety can be filtered in any combination of the three types. The program allows for bottling a wine or holding it for bulk sale. Since the available filters or bottling line can almost always complete the task, even if they must be run 24 hours a day, there are no capacity constraints for such processes in the model. How much labor needed in the operation is the real consideration in whether the capacity of such equipment is sufficient or not. WINERY generates labor usage figures for all of the non-crush season activities. The values of these variables, in man-hours, will be an indication to management where bigger and faster equipment is needed. It is unnecessary to construct constraints on the total amount of labor available during the non-crush season in the model because the length of the period is such that a winery could always supplement its existing labor force to meet its needs. Labor supply during the crushing season is a different matter. It may be impossible to supplement the supply of labor on hand during the few weeks of the crush. It is assumed that the labor supply during the crush is fixed. Labor constraints for each activity during the crushing season and for each day have been built into the model. Warehouse constraints for bottled wine are set up on a monthly basis. An arrival and withdrawal schedule is given to the computer as part of the input data supplied by management. The model has three ways of selling each wine: wholesale to a distributor, retail through the winery's own outlets, and unbottled in bulk. Management can place restrictions on each sales channel for each wine. The restrictions are upper and/or lower bounds on each wine-sales channel combination. Within these restrictions the computer generates optimum sales figures by wine and channel as part of its solution. The profit figure for the model is calculated by subtracting from the gross return only those costs which vary with the varieties of wines made and how they are sold. Hence, it is not net profit according to normal accounting standards. The variable costs used are the prices of the different grape varieties, labor costs during the non-crush season and the costs directly associated with selling through each of the three different sales channels. Other costs, variable and fixed, do not affect the product mix decision. For example, the labor cost differences at the winery during the crushing season of handling Cabernet Sauvignon or Carignane are small, but after fermentation the labor costs of processing each variety can vary greatly depending upon the type of container used for aging and the length of time in that container. RESULTS AND DISCUSSION Interpretation of computer output: The following example is for a fictitious winery. This winery processes four different grape varieties, two white and two red varieties. They arrive at the winery over a four-day period. The winery makes four varietal wines, two reds and two whites and two generic blends, a red and a white. The numbers here are small in order to facilitate interpretation of the results for this article. In making the wines the winery makes use of all of the available production steps provided by the model (Fig. 1), but each wine uses a different combination of these steps, as might be the case in a real winery, producing many different types of wines. The most important results of the program are the recommended amounts of grapes to purchase (Table 1). The grape prices and the upper and lower tonnage limits for each variety are supplied by management. Table 2 lists the computer generated sales recommendations for each wine by sales channel. In this example six wines are produced. With wholesale, retail and bulk sales channels, 18 different wine-sales channel combinations are possible, but the management of our hypothetical winery has limited the possibilities to selling two wines through wholesalers, four wines retail and two wines in bulk. A red varietal, wine 3, and the white generic, wine 5, may be sold to wholesalers. All four varietal wines may be sold through the winery's own retail outlet and both generic blends, wines 5 and 6, may be sold in bulk. The computer neither recommends selling the red varietal, wine 3, through wholesalers nor the white blend, wine 5, in bulk. Table 1. Grape purchasing recommendations in tons. Variety Cost (S/ton) Amount recommended 1 200 61.7 2 400 7.1 3 200 4.0 4 495 50.0 Table 3 lists the gross return per gallon by wine type and sales channels combination. For those combinations not recommended by the computer, the minimum necessary increase in gross return order to make that particular combination profitable is given. As an example, for it to become profitable to sell wine 5

212 ~ COMPUTER MODEL Wine type Table 2. Sales recommendations in gallons. Sales channels Wholesale Retail Bulk #1 varietal m 10,338 ~ Crushing #2 varietal ~ 1,000 #3 varietal None 671 -- grape #4 separation varietal m 5,992 #5 blend 286 m None Press use #6 blend ~ ~ 395 Table 3. Gross return and minimum price increase for profitability (per gallon). Unpressed red Wine type Sales channel fermentation Wholesale Retail Bulk #1 ~ 10 #2 -- 15 #3 5 (5) a 10 #4 ~ 25 #5 10 ~ 4 (6) a #6 ~ ~ 2 a Minimum necessary increase in the gross return in order for it to become profitable to sell a wine through a particular channel. in bulk, the bulk price for it must increase by six dollars. In this simple case the results from the above analysis seem obvious, but in a more complicated situation an analysis of the recommended sales figures would prove valuable. The computer also provides the amount of man hours required to accomplish each of the winemaking activities performed outside of the crushing season (Table 4). Management can use this list to see where labor is being utilized inefficiently. Table 4. Labor requirement for non-crushing season activities. Barrel topping and cleaning Cask topping and cleaning Wooden tank filling and cleaning Non-wooden tank filling and cleaning Rough filtration Polish filtration Sterilizing filtration Bottling Warehouse Man hours 128 76 04 33 38 8 36 0 39 7 60 1 90 The numbers in Table 5, generated as part of the computer results, are the usage and idle capacity for each production step. Also provided with this information is the potential increase in profit as a result of increasing the capacity by one unit of each production facility already operating at full capacity. In our example, at most only 25% of the pressing capacity is used and on the fifth day of the crush the presses are not used at all. Labor, crushing and fermentation capacities are also not fully utilized. Table 5. Usage and idle capacity of each wine processing step. Process Day Usage Idle capacity Profit potential of one unit's additional capacity and pressed red fermentation Centrifuge wine barrel aging wine barrel aging wine cask aging wine cask aging wood tank use Oak tank use Non-wood tank use Crush season labor Non-crush season labor 1 20.4 a 99.5 a 2 29.4 90.5 3 24.9 95.0 4 9.9 110.0 1 18.4 a 26.5 a 2 27.5 17.4 3 22.7 22.2 4 m 45.0 1 18.4 a 101.5 a 2 27.5 92.4 3 24.7 95.2 4 1.9 118.0 5 ~ 120.0 6 19.9 100.0 7 29.9 90.0 1 1.9 a 398.0 a 2 3.9 396.0 3 21.9 378.0 4 49.9 350.0 1 3144.3 b 26855.6 b 2 7793.9 22206.0 3 11979.2 18020.7 4 12334.4 17665.5 5 11979.2 18020.7 6 14420.5 15579.4 7 15071.4 14928.5 8 7825.5 22174.4 9 600.0 29400.0 10 ~ 30000.0 11 ~ 30000.0 1 739.8 b 5260.1 b 2 986.4 5013.5 3 739.8 5260.1 4 ~ 6000.0 5 -- 6000.0 6 2396.9 3603.0 7 6000.0 ~ $25.53 8 3206.0 2793.9 9 2404.5 3595.4 10 ~ 6000.0 b 11 -- 6000.0 1 2 3 4 5 6 7 8 9 10 11 500.0 b 3500.0 b 3329.1 6670.8 a Tons. b Gallons. c Man hours. 500.0 m $25.6 2000.0 -- $20.0 854.5 b 3145.4 b 5143.1 856.8 6000.0 -- $ 6.3 9.2 c 50.7 c 16.8 43.1 23.2 36.7 23.5 36.4 13.8 46.1 23.9 36.0 32.3 27.6 14.4 45.5 6.2 53.7 2.8 57.1 5.5 54.4 207.7 c 5072.2 c

COMPUTER MODEL n 213 The bottlenecks are centrifuging on the seventh day of the crush, white and red cask capacity and non-wooden tank storage. By increasing the capacity of white wine casks by one gallon, the profit would increase by $25.62 (Table 5). Rather than purchasing this additional capacity it would be more economical to use the idle white barrel capacity, i.e. to shift the aging requirements for white wines from casks to barrels. Rerunning the program with the changed requirements would test the validity of such a potential solution. A similar approach for the red cask shortage is also possible. Table 5 shows that the profit would increase by $25.53 if another gallon could be centrifuged on the seventh day. The under utilization of the centrifuge on all other days indicates that the purchase of a new machine would not be worth the expense. A rescheduling of its use could bring the desired result. This could be achieved by rescheduling the arrival of the different grape varieties or reducing the amount of centrifuging for specific varieties. In order to determine the feasibility of either of these strategies, input data must be examined to see which varieties are being centrifuged and when in the winemaking process they are being centrifuged. Running the program several times with different input data would yield further useful information. Different wine prices reflecting projected price changes as input data would indicate possible production changes required to take advantage of the changing market. Plant expansions or new equipment acquisitions could be simulated by running the program with the appropriate changes in the input data to reflect planned changes in plant and equipment. Comparing the output of the current data with output based on proposed changes would show how the changes could affect the product mix and the utilization of existing resources. Long-term planning could be done with the computer results obtained by using future projections as input data. Model limitations: The computer program was written to encompass a wide range of different winemaking possibilities. The program, WINERY, is very complex as a result. It is impossible to test completely such a program. The reliability of the model can only be determined through repeated use and comparison with management's own analysis of their production situation. With a linear programming model of this size and complexity, the constraints are formulated in such a way that unknown and undesirable relationships between production steps could exist. For example, in the simple model at the beginning of the article, the construction of separate fermenting and aging constraints implies that the aging and fermenting facilities are completely separate from each other. If this were not the case, then additional inequalities would have to be added to that model in order to make it conform more closely with reality. Such hidden implications can have gone unnoticed in creating the complex model. Another class of potential difficulties is the result of the discrepancy between a given winery's plant and production methods and the production model which is the basis for the computer program. With the recognition of such a problem, the input data can, in some cases, be modified so that the computer simulates the actual situation satisfactorily. For example, at least one winery in California ferments its Chardonnay in 50-gallon barrels, which in the computer program are only available for aging. The program can handle this special situation, if the fermentation time for Chardonnay is entered as zero, so that none of the normal fermentation tanks would be used for it, and if all of the Chardonnay would be required for the model to age in oak barrels, so that the appropriate barrel space for the must would be reserved. Since the computer sees no use for the barrels during fermentation, it makes no difference for optimum barrel use whether the barrels are filled after pressing or after fermentation. The size of input matrix that the computer can solve is limited. As WINERY and TEMPO are presently constructed, winery data with a crushing season of less than 40 days, crushing less than 30 varieties and making less than 30 different wines can fit into the computer. With a little rewriting of the program, one of these boundaries can be increased but only at the cost of reducing the other. For example, the maximum crush season could be extended to 60 days if the maximums for varieties and wines were dropped to 15. Such a change does not increase the size of the matrix but just shifts space within the matrix. Increasing the maximum size of the matrix would require major rewriting of the program. Another limitation with the model is in the fermentation of constraints for tank usage. In a real situation, important is not only the total tank capacity in gallons but also the number of tanks available. In the model, all tank processes are constrained by gallonage, but tank usage is not adequately constrained by numbers. CONCLUSION The computer model considers the major factors in wine production and product mix decision. The model can be used to determine the amount of each grape variety to purchase and each wine type to be produced in order to maximize profit. Idle capacity and production bottlenecks can also be determined. Using projections of future wine demand and grape supply, the model can be used as a valuable tool in long range planning. LITERATURE CITED 1. Rink, Rudolf. Zur Frage der optimalen Betriebsgestaltung in Winzergenossenschaften. Agrarwissenschaftliche Fakult&t der Landwirtschaftlichen Hochschule Hohenheim in Stuttgart-Hohenheim. (1966). 2. Scott, John G., and Elmer E. Broadbent. A computerized feeding program for replacement and ration formulation. In: Illinois Agricultural Economics, July, 1972: Iron and Steel Production by Tibor Fabian in Management Science, Vol. 4, June, 1955. 3. Tower, David S. A linear programming model of a winery. M.S. Thesis submitted to Univ. Calif., Davis, in partial fulfillment of degree, 1975.