Forecasting PDF

Forecasting is the process of making predictions of the future based on past and present data. This is most commonly by analysis of trends. A commonplace example might be estimation of some variable of interest at some specified future date. Prediction is a similar, but more general term. Both might...

Forecasting is the process of making predictions of the future based on past and present data. This is most commonly by analysis of trends. A commonplace example might be estimation of some variable of interest at some specified future date. Prediction is a similar, but more general term. Both might refer to formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods. Usage can differ between areas of application: for example, in hydrology, the terms “forecast” and “forecasting” are sometimes reserved for estimates of values at certain specific future times, while the term “prediction” is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction; it is generally considered good practice to indicate the degree of uncertainty attached to specific forecasts. In any case, the data must be up to date in order for the forecast to be as accurate as possible. In some cases, the data used to predict the variable of interest is itself forecasted. As discussed in the previous chapter, functional strategies need to be aligned and supportive to the higher level corporate strategy of the organization. One of these functional areas is marketing. Creating marketing strategy is not a single event, nor is the implementation of marketing strategy something only the marketing department has to worry about. When the strategy is implemented, the rest of the company must be poised to deal with the consequences. An important component in this implementation is the sales forecast, which is the estimate of how much the company will actually sell. The rest of the company must then be geared up (or down) to meet that demand. In this module, we explore forecasting in more detail, as there are many choices that can be made in developing a forecast. Accuracy is important when it comes to forecasts. If executives overestimate the demand for a product, the company could end up spending money on manufacturing, distribution, and servicing activities it won’t need. Data Impact, a software developer, recently overestimated the demand for one of its new products. Because the sales of the product didn’t meet projections, Data Impact lacked the cash available to pay its vendors, utility providers, and others. Employees had to be terminated in many areas of the firm to trim costs. Underestimating demand can be just as devastating. When a company introduces a new product, it launches marketing and sales campaigns to create demand for it. But if the company isn’t ready to deliver the amount of the product the market demands, then other competitors can steal sales the firm might otherwise have captured. Sony’s inability to deliver the e-Reader in sufficient numbers made Amazon’s Kindle more readily accepted in the market; other features then gave the Kindle an advantage that Sony is finding difficult to overcome. The firm has to do more than just forecast the company’s sales. The process can be complex, because how much the company can sell will depend on many factors such as how much the product will cost, how competitors will react, and so forth. Each of these factors has to be taken into account in order to determine how much the company is likely to sell. As factors change, the forecast has to change as well. Thus, a sales forecast is actually a composite of a number of estimates and has to be dynamic as those other estimates change. A common first step is to determine market potential, or total industrywide sales expected in a particular product category for the time period of interest. (The time period of interest might be the coming year, quarter, month, or some other time period.) Some marketing research companies, such as Nielsen, Gartner, and others, estimate the market potential for various products and then sell that research to companies that produce those products. Once the firm has an idea of the market potential, the company’s sales potential can be estimated. A firm’s sales potential is the maximum total revenue it hopes to generate from a product or the number of units of it the company can hope to sell. The sales potential for the product is typically represented as a percentage of its market potential and equivalent to the company’s estimated maximum market share for the time period. In your budget, you’ll want to forecast the revenues earned from the product against the market potential, as well as against the product’s costs. Forecasting Horizons Long term forecasting tends to be completed at high levels in the organization. The time frame is generally considered longer than 2 years into the future. Detailed knowledge about the products and markets are required due to the high degree of uncertainty. This is commonly the case with new products entering the market, emerging new technologies and opening new facilities. Often no historical data is available. Medium term forecasting tends to be several months up to 2 years into the future and is referred to as intermediate term. Both quantitative and qualitative forecasting may be used in this time frame. Short term forecasting is daily up to months in the future. These forecasts are used for operational decision making such as inventory planning, ordering and scheduling of the workforce. Usually quantitative methods such as time series analysis are used in this time frame. Categories of Forecasting Methods Qualitative Forecasting Qualitative forecasting techniques are subjective, based on the opinion and judgment of consumers and experts; they are appropriate when past data are not available. They are usually applied to intermediate- or longrange decisions. In the following, we discuss some examples of qualitative forecasting techniques: Executive Judgement (Top Down) Groups of high-level executives will often assume responsibility for the forecast. They will collaborate to examine market data and look at future trends for the business. Often, they will use statistical models as well as market experts to arrive at a forecast. Sales Force Opinions (Bottom up) The sales force in a business are those persons most close to the customers. Their opinions are of high value. Often the sales force personnel are asked to give their future projections for their area or territory. Once all of those are reviewed, they may be combined to form an overall forecast for district or region. Delphi Method This method was created by the Rand Corporation in the 1950s. A group of experts are recruited to participate in a forecast. The administrator of the forecast will send out a series of questionnaires and ask for inputs and justifications. These responses will be collated and sent out again to allow respondents to evaluate and adjust their answers. A key aspect of the Delphi method is that the responses are anonymous, respondents do not have any knowledge about what information has come from which sources. That permits all of the opinions to be given equal consideration. The set of questionnaires will go back and forth multiple times until a forecast is agreed upon. Market Surveys Some organizations will employ market research firms to solicit information from consumers regarding opinions on products and future purchasing plans. Quantitative Forecasting Quantitative forecasting models are used to forecast future data as a function of past data. They are appropriate to use when past numerical data is available and when it is reasonable to assume that some of the patterns in the data are expected to continue into the future. These methods are usually applied to short- or intermediate-range decisions. Some examples of quantitative forecasting methods are causal (econometric) forecasting methods, last period demand (naïve), simple and weighted N-Period moving averages and simple exponential smoothing, which are categorizes as time-series methods. Quantitative forecasting models are often judged against each other by comparing their accuracy performance measures. Some of these measures include Mean Absolute Deviation (MAD), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE). We will elaborate on some of these forecasting methods and the accuracy measure in the following sections. Causal (Econometric) Forecasting Methods (Degree) Some forecasting methods try to identify the underlying factors that might influence the variable that is being forecast. For example, including information about climate patterns might improve the ability of a model to predict umbrella sales. Forecasting models often take account of regular seasonal variations. In addition to climate, such variations can also be due to holidays and customs: for example, one might predict that sales of college football apparel will be higher during the football season than during the off-season. Several informal methods used in causal forecasting do not rely solely on the output of mathematical algorithms, but instead use the judgment of the forecaster. Some forecasts take account of past relationships between variables: if one variable has, for example, been approximately linearly related to another for a long period of time, it may be appropriate to extrapolate such a relationship into the future, without necessarily understanding the reasons for the relationship. One of the most famous causal models is regression analysis. In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or ‘predictors’). More specifically, regression analysis helps one understand how the typical value of the dependent variable (or ‘criterion variable’) changes when any one of the independent variables is varied, while the other independent variables are held fixed. Figure 3.1: Example of regression analysis. Common Forecasting Assumptions: 1. Forecasts are rarely, if ever, perfect. It is nearly impossible to 100% accurately estimate what the future will hold. Firms need to understand and expect some error in their forecasts. 2. Forecasts tend to be more accurate for groups of items than for individual items in the group. The popular Fitbit may be producing six different models. Each model may be offered in several different colours. Each of those colours may come in small, large and extra large. The forecast for each model will be far more accurate than the forecast for each specific end item. 3. Forecast accuracy will tend to decrease as the time horizon increases. The farther away the forecast is from the current date, the more uncertainty it will contain. Demand Patterns When we plot our historical product demand, the following patterns can often be found: Trend – A trend is consistent upward or downward movement of the demand. This may be related to the product’s life cycle. Cycle – A cycle is a pattern in the data that tends to last more than one year in duration. Often, they are related to events such as interest rates, the political climate, consumer confidence or other market factors. Seasonal – Many products have a seasonal pattern, generally predictable changes in demand that are recurring every year. Fashion products and sporting goods are heavily influenced by seasonality. Irregular variations – Often demand can be influenced by an event or series of events that are not expected to be repeated in the future. Examples might include an extreme weather event, a strike at a college campus, or a power outage. Random variations – Random variations are the unexplained variations in demand that remain after all other factors are considered. Often this is referred to as noise. Figure 3.2: Diagram of trend, cyclical, and seasonal demand patterns. Time Series Methods Time series methods use historical data as the basis of estimating future outcomes. A time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus, it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. Time series are very frequently plotted via line charts. Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. In the following, we will elaborate more on some of the simpler timeseries methods and go over some numerical examples. Naïve Method The simplest forecasting method is the naïve method. In this case, the forecast for the next period is set at the actual demand for the previous period. This method of forecasting may often be used as a benchmark in order to evaluate and compare other forecast methods. Simple Moving Average In this method, we take the average of the last “n” periods and use that as the forecast for the next period. The value of “n” can be defined by the management in order to achieve a more accurate forecast. For example, a manager may decide to use the demand values from the last four periods (i.e., n = 4) to calculate the 4-period moving average forecast for the next period. Example Some relevant notation: Dt = Actual demand observed in period t Ft = Forecast for period t Using the following table, calculate the forecast for period 5 based on a 3period moving average. Period Actual Demand 1 42 2 37 3 34 4 40 Solution Forecast for period 5 = F5 = (D4 + D3 + D2) / 3 = (40 + 34 + 37) / 3 = 111 / 3 = 37 Weighted Moving Average This method is the same as the simple moving average with the addition of a weight for each one of the last “n” periods. In practice, these weights need to be determined in a way to produce the most accurate forecast. Let’s have a look at the same example, but this time, with weights: Example Period Actual Demand Weight 1 42 2 37 0.2 3 34 0.3 4 40 0.5 Solution Forecast for period 5 = F5 = (0.5 x D4 + 0.3 x D3 + 0.2 x D2) = (0.5 x 40+ 0.3 x 34 + 0.2 x 37) = 37.6 Note that if the sum of all the weights were not equal to 1, this number above had to be divided by the sum of all the weights to get the correct weighted moving average. Exponential Smoothing This method uses a combination of the last actual demand and the last forecast to produce the forecast for the next period. There are a number of advantages to using this method. It can often result in a more accurate forecast. It is an easy method that enables forecasts to quickly react to new trends or changes. A benefit to exponential smoothing is that it does not require a large amount of historical data. Exponential smoothing requires the use of a smoothing coefficient called Alpha (α). The Alpha that is chosen will determines how quickly the forecast responds to changes in demand. It is also referred to as the Smoothing Factor. There are two versions of the same formula for calculating the exponential smoothing. Here is version #1: Ft = (1 – α) Ft-1 + α Dt-1 Note that α is a coefficient between 0 and 1 For this method to work, we need to have the forecast for the previous period. This forecast is assumed to be obtained using the same exponential smoothing method. If there were no previous period forecast for any of the past periods, we will need to initiate this method of forecasting by making some assumptions. This is explained in the next example. Example Period Actual Demand 1 42 2 37 3 34 4 40 Forecast 5 In this example, period 5 is our next period for which we are looking for a forecast. In order to have that, we will need the forecast for the last period (i.e., period 4). But there is no forecast given for period 4. Thus, we will need to calculate the forecast for period 4 first. However, a similar issue exists for period 4, since we do not have the forecast for period 3. So, we need to go back for one more period and calculate the forecast for period 3. As you see, this will take us all the way back to period 1. Because there is no period before period 1, we will need to make some assumption for the forecast of period 1. One common assumption is to use the same demand of period 1 for its forecast. This will give us a forecast to start, and then, we can calculate the forecast for period 2 from there. Let’s see how the calculations work out: If α = 0.3 (assume it is given here, but in practice, this value needs to be selected properly to produce the most accurate forecast) Assume F1 = D1, which is equal to 42. Then, calculate F2 = (1 – α) F1+ α D1 = (1 – 0.3) x 42 + 0.3 x 42 = 42 Next, calculate F3 = (1 – α) F2+ α D2 = (1 – 0.3) x 42 + 0.3 x 37 = 40.5 And similarly, F4 = (1 – α) F3+ α D3 = (1 – 0.3) x 40.5 + 0.3 x 34 = 38.55 And finally, F5 = (1 – α) F4+ α D4 = (1 – 0.3) x 38.55 + 0.3 x 40 = 38.985 Figure 3.3: Solution for Exponential Smoothing Version 1 Accessible format for Figure 3.3 Here is version #2: Ft = Ft-1 + α(Dt-1 – Ft-1) Assume you are given an alpha of 0.3 Figure 3.4: Solution for Exponential Smoothing Version 2 Strategic Capacity Planning This module examines how important strategic capacity planning is for products and services. The overall objective of strategic capacity planning is to reach an optimal level where production capabilities meet demand. Capacity needs include equipment, space, and employee skills. If production capabilities are not meeting demand, it will result in higher costs, strains on resources, and possible customer loss. It is important to note that capacity planning has many long-term concerns given the longterm commitment of resources. Managers should recognize the broader effects capacity decisions have on the entire organization. Common strategies include leading capacity, where capacity is increased to meet expected demand, and following capacity, where companies wait for demand increases before expanding capabilities. A third approach is tracking capacity, which adds incremental capacity over time to meet demand. Finally, the two most useful functions of capacity planning are design capacity and effective capacity. Design capacity refers to the maximum designed capacity or output rate and the effective capacity is the design capacity minus personal and other allowances. These two functions of capacity can be used to find the efficiency and utilization. These are calculated by the formulas below: Efficiency = (Actual Output / Effective Capacity) x 100% Utilization = (Actual Output / Design Capacity) x 100% Example Actual production last week = 25,000 units Effective capacity = 28,000 units Design capacity = 230 units per hour Factory operates 7 days / week, three 8-hour shifts 1. What is the design capacity for one week? 2. Calculate the efficiency and utilization rates. Solution (Using the formulas above) 1. Design capacity = (7 x 3 x 8) x (230) = 38,640 units per week 2. Utilization = 25,000 / 38,640 = 64.7% Efficiency = 25,000 / 28,000 = 89.3% Capacity Planning for Products and Services Capacity refers to a system’s potential for producing goods or delivering services over a specified time interval. Capacity planning involves longterm and short- term considerations. Long-term considerations relate to the overall level of capacity; short-term considerations relate to variations in capacity requirements due to seasonal, random, and irregular fluctuations in demand. Excess capacity arises when actual production is less than what is achievable or optimal for a firm. This often means that the demand in the market for the product is below what the firm could potentially supply to the market. Excess capacity is inefficient and will cause manufacturers to incur extra costs. Capacity can be broken down in two categories: Design Capacity and Effective Capacity. Three key inputs to capacity planning are: 1. The kind of capacity that will be needed 2. How much capacity will be needed? 3. When will it be needed? Defining and Measuring Capacity When selecting a measure of capacity, it is best to choose one that doesn’t need updating. For example, dollar amounts are often a poor measure of capacity (e.g., a restaurant may have capacity of $1 million of sales a year) because price changes over time necessitate updating of that measure. When dealing with more than one product, it is best to measure capacity in terms of each product. For example, the capacity of a firm is to either produce 100 microwaves or 75 refrigerators. This is less confusing than just saying the capacity is 100 or 75. Another method of measuring capacity is by referring to the availability of inputs. This is usually more helpful if we are dealing with several type of output. Note that one specific measure of capacity can’t be used in all situations; it needs to be tailored to the specific situation at hand. The following table shows examples of both output and input used for capacity measures. Figure 4.1: Various businesses and their respective input and output measures of capacity. Determinants of Effective Capacity Facilities: The size and provision for expansion are key in the design of facilities. Other facility factors include locational factors, such as transportation costs, distance to market, labor supply, and energy sources. The layout of the work area can determine how smoothly work can be performed. Product and Service Factors: The more uniform the output, the more opportunities there are for standardization of methods and materials. This leads to greater capacity. Process Factors: Quantity capability is an important determinant of capacity, but so is output quality. If the quality does not meet standards, then output rate decreases because of need of inspection and rework activities. Process improvements that increase quality and productivity can result in increased capacity. Another process factor to consider is the time it takes to change over equipment settings for different products or services. Human Factors: the tasks that are needed in certain jobs, the array of activities involved, and the training, skill, and experience required to perform a job all affect the potential and actual output. Employee motivation, absenteeism, and labour turnover all affect the output rate as well. Policy Factors: Management policy can affect capacity by allowing or disallowing capacity options such as overtime or second or third shifts Operational Factors: Scheduling problems may occur when an organization has differences in equipment capabilities among different pieces of equipment or differences in job requirements. Other areas of impact on effective capacity include inventory stocking decisions, late deliveries, purchasing requirements, acceptability of purchased materials and parts, and quality inspection and control procedures. Supply Chain Factors: Questions include: What impact will the changes have on suppliers, warehousing, transportation, and distributors? If capacity will be increased, will these elements of the supply chain be able to handle the increase? If capacity is to be decreased, what impact will the loss of business have on these elements of the supply chain? External Factors: Minimum quality and performance standards can restrict management’s options for increasing and using capacity. Figure 4.2: Summary of examples of capacity factors. Inadequate planning can be a major limitation in determining the effective capacity. The most important parts of effective capacity are process and human factors. Process factors must be efficient and must operate smoothly. If not, the rate of output will dramatically decrease. They must be motivated and have a low absenteeism and labour turnover. In resolving constraint issues, all possible alternative solutions must be evaluated. Steps in the Capacity Planning Process: 1. Estimate future capacity requirements 2. Evaluate existing capacity and facilities and identify gaps 3. Identify alternatives for meeting requirements 4. Conduct financial analyses of each alternative 5. Assess key qualitative issues for each alternative 6. Select the alternative to pursue that will be best in the long term 7. Implement the selected alternative 8. Monitor results The above content is an adaptation of Saylor Academy’s BUS300 course. The Sequential Processes and the Bottleneck Any process that has several steps, one after another, is considered a sequential process. A good example of these processes is the manufacturing assembly line in which each workstation gets inputs from a previous workstation and give its outputs to the next workstation. It is safe to assume that each step has its own staff member, since this is exactly what happens in assembly lines. For this kind of process, it is crucial to have a balanced time across all steps. That is, there should not be any big difference between the amounts of time that different steps take to process one unit of product. For example, if step 1, 2 and 3 take 3, 10 and 5 minutes consecutively to process one unit of product, two main issues will happen during the production: 1) There will be a big pile of inventory sitting right before step 2, since step 1 is much faster than step 2, and the products that are already processed in step 1 will need to wait for step 2 to be done with its current unit at hand. As a result, this becomes an inventory holding issue, which is costly. 2) Step 3 will always need to wait for step 2 for an extra 5 minutes. This is due to the fact that step 3 finished its current product at hand in 5 minutes, but step 2 needs a total of 10 minutes to finish its work and feed it to step 3. This causes step 3 to be idle for a long time, which is also costly for the company. This is costly, because the company is already paying the staff who works in step 3 for the whole time, but they are not able to produce as many units as they should due to the very slow entry of the inputs coming from step 2. Figure 4.3: A diagram displaying the effects of a bottleneck. The bottleneck is the slowest step in each process or the slowest process in a system. The capacity of the bottleneck defines the capacity of the whole process. In our example above, step 2 was the slowest, and as a result, the bottleneck. This means that the whole process (including all steps 1 to 3) will not be able to have an output any faster than one every 10 minutes. In the following, let’s see why this is happening: In an 8-hour shift per day, we have 8 x 60 = 480 minutes Assuming that step 1 has enough input to process during the day, the total output from step 1 will be 480 / 3 = 160 units per day. This is the capacity for step 1. In a similar way, the capacity for step 2 is 480 / 10 = 48, and the capacity for step 3 is 480 / 5 = 96 units. This means that the input to step 2 will be 160 units to be processed. But as we see, step 2 will only be able to process a maximum of 48 units per day. That means that only 48 units get to step 3 for processing. Since step 3 has a capacity of 96 units per day, it will easily process those 48 units of inputs, and the output from step 3 will be 48 units. Because the step 3 is the last step of our process, this output of 48 units will automatically be the total output of the whole process per day. The key observation here is that the capacity of step 2, which is the bottleneck, determined the capacity of the whole process. This concept is very important in practice. Often times, the companies that do not pay attention to the concept of bottleneck and its implications invest in parts of the process that are not bottleneck. This will keep the bottleneck unchanged and as a result, they will not see any improvement in the capacity of the whole process. Example Caroline has a thriving business selling her tote bags through several popular websites. Her business volume has caused her to hire full-time employees. Her business has four main manufacturing operations: 1) cutting fabric (4 min), 2) stitching fabric (7 min), 3) adding zippers, toggles, and liner (10 min), and 4) inspecting, packing, and labeling (5 min). 4.3: Flow diagram depicting the time taken for each step of Caroline’s manufacturing process. Employees work 7 hours per day. Help Caroline to determine the following: 1. Based on her very high demand, is there a bottleneck and what stage is it? What is the capacity of the process per day? 2. Caroline’s employee at step #2 has found a new machine that will enable him to do the stitching faster, at a rate of 5 min per bag instead of 7 min. The machine costs $3500. Would you suggest this is a good investment to help Caroline increase her output? Why or why not? 3. If there were another person to be added to the process, where should Caroline add him or her and what would be the new capacity? Solution Figure 4.4: Solution for Caroline’s Totes example (Based on 7×60 = 420 min per day) Accessible format for Figure 4.4 1. The maximum output is 42 units, because that is what the bottleneck can do. The bottleneck is at stage #3, which is the slowest part of the process. 2. Caroline should NOT invest any funds into step #2. This may speed up the stitching, but the maximum output of the process will still be 42 units because step #3 has not changed. 3. If Caroline added another person, she should add it to step #3. (Install zippers/ toggles/ liner). Because that is where the bottleneck is. The capacity at stage three would now double to 84 units per day. The new capacity for the whole process would now be 60 units per day, as determined by Step 2 (Basic stitching) which is the new bottleneck of the process. Evaluating Capacity Alternatives There are two major ways to evaluate the capacity alternatives to select the best one: economic and non-economic. Economic considerations take into account the cost, useful life, compatibility and revenue for each alternative. Techniques used for evaluation are: Break Even Analysis (this is the only one discussed in this chapter) Payback Period Net Present Value Non-economic considerations include public opinion, reactions from employees and community pressure. Break Even Analysis Basically, since there is usually a fixed cost (FC) associated with the usage of a capacity, we look for the right quantity of output that gives us enough total revenue (TR) to cover for the total cost (TC) that we have to incur. This quantity is called Break-Even Point (BEP), Break-Even Quantity (Q BEP). Total cost is the summation of the fixed cost and the total variable cost (VC, which depends on the quantity of output). In other words, at Q BEP, we have: TC = FC + VC A list of relevant notation can be found below: TC = total cost FC = total fixed cost VC = total variable cost TR = total revenue v = variable cost per unit R = revenue per unit Q = volume of output QBEP = break even volume P = profit Fixed cost is regardless of the quantity of output. Some examples of fixed costs are rental costs, property taxes, equipment costs, heating and cooling expenses, and certain administrative costs With the above notation and some simplification in the calculation, we have: TC = FC + VC VC = Q x v TR = Q x r P = TR – TC = Q x r – (FC + Q x v) QBEP = FC / (r – v) Example The management of a pizza place would like to add a new line of small pizza, which will require leasing a new equipment for a monthly payment of $4,000. Variable costs would be $4 per pizza, and pizzas would retail for $9 each. 1. How many pizzas must be sold per month in order to break even? 2. What would the profit (loss) be if 1200 pizzas are made and sold in a month? 3. How many pizzas must be sold to realize a profit of $10,000 per month? 4. If demand is expected to be 700 pizzas per month, will this be a profitable investment? Solution 1. QBEP = FC / (r – v) = 4000 / (9 – 4) = 800 pizzas per month 2. total revenue – total cost = 1200 x 9 – 1200 x 4 – 4000 = $2000 (i.e. a profit) 3. P = $10000 = Q(r – v) – FC; Solving for Q will give us: Q = (10000 + 4000) / (9 – 4) = 2800 4. Producing less than 800 (i.e. QBEP) pizzas will bring in a loss. Since 700 < 800 (QBEP), it is not a profitable investment. Finding a break-even point between “make” or “buy” decisions: Question: For what quantities would buying the product be preferred to making it in-house? For quantities larger than the break-even quantity or for smaller ones? vm = per unit variable cost of “make” vb = per unit variable cost of “buy” total cost of “make” = total cost of “buy” Q x vm + FC = Q x vb FC = Q x vb – Q x vm Q = FC / (vb – vm) Example The ABX Company has developed a new product and is wondering if they should make this product in-house or have a capable supplier make the product for them. The costs associated with each option are provided in the following table: Make in-house Buy Fixed Cost (annual) Variable Cost $160,000 $100 $150 1. What is the break-even quantity at which the company will be indifferent between the two options? 2. If the annual demand for the new product is estimated at 1000 units, should the company make or buy the product? 3. For what range of demand volume it will be better to make the product in-house? Solution 1. QBEP = FC / (vb – vm) = 160,000 / (150 – 100) = 3200 2. Total cost of “make” = 1000 x 100 + 160,000 = $260,000; Total cost of “buy” = 1000 x 150 = $150,000 Thus, it will be better to buy since it will be less costly in total. 3. It will always be better to use the option with the lower variable cost for quantities greater than the break-even quantity. This can also be proven as follows: We want “make” to be better than “buy” in this part of the question. Thus, for any quantity Q, we need to have: Total cost of “make” < Total cost of “buy” 160,000 + 100Q < 150Q 160,000 < 50Q 3200 < Q Finding a break-even point between two make decisions Question: For what quantities would machine A be preferred to machine B? For quantities larger that the break-even quantity or for smaller ones? If we assume the two options for making a product are machine A, with a fixed cost of FCA and a variable cost of vA, and machine B, with a fixed cost of FCB and a variable cost of vB, we have: total cost of A = total cost of B Q x vA + FCA= Q x VB + FCB FCA – FCB = Q x VB – Q x VA Q = (FCA – FCB) / (VB – VA) In any problem, it is suggested that you write down the total cost of each option and simplify from there to make sure that you do not miss any possible additional cost factors (if any). Example The ABX Company has developed a new product and is going to make this product in-house. To be able to do this, they need to get a new equipment to be able to do the special type of processing required by the new product design. They have found two suppliers that sell such equipment. They are wondering which supplier they go ahead with. The costs associated with each option are provide in the following table: Fixed Cost (annual) Variable Cost Supplier A $160,000 $150 Supplier B $200,000 $100 1. What is the break-even quantity at which the company will be indifferent between the two options? 2. If the annual demand for the new product is estimated at 1000 units, which supplier should the company use? 3. For what range of demand volume each supplier will be better? Solution 1. QBEP = (FCB – FCA) / (vA – vB) = (200,000 – 160,000) / (150 – 100) = 40,000/50 = 800 2. Total cost of Supplier A = 1000 x 150 + 160,000 = $310,000; Total cost of Supplier B = 1000 x 100 + 200,000 = $300,000 Thus, it will be better to go with Supplier B, since it will be less costly in total. 3. It will always be better to use the option with the lower variable cost for quantities greater than the break-even quantity. This can also be proven as follows: Let’s see for what quantities Supplier B will be better than Supplier A. In that case, for the quantity Q, we need to have: Total cost of Supplier B < Total cost of Supplier A 200,000 + 100Q < 160,000 + 150Q 40,000 < 50Q 800 < Q This means that for quantities above 800 units, Supplier B will be cheaper in total. Thus, for quantities less than 800, Supplier A will be cheaper in total.