BMM4733_Quality Engineering Industrial Engineering Chapter 1 Introduction to IE (Part 3) Mohamad Zairi bin Baharom Faculty of Mechanical Engineering Universiti Malaysia Pahang BMM4733_Quality Engineering

Contents: Learning Objective: Determine process selection with break- even analysis Contents: Production section with break-even analysis Break-even analysis

Production Selection with Break-even Analysis A quantitative technique Useful for comparing capacity alternatives At what volume of sales and production we can expect to earn a profit The components are; Volume Cost Revenue Profit

Break-even Analysis Technique for evaluating process and equipment alternatives Objective is to find the point in dollars and units at which cost equals revenue Requires estimation of fixed costs, variable costs, and revenue This chart introduces breakeven analysis and the breakeven or crossover chart. As you discuss the assumptions upon which this techniques is based, it might be a good time to introduce the more general topic of the limitations of and use of models. Certainly one does not know all information with certainty, money does have a time value, and the hypothesized linear relationships hold only within a range of production volumes. What impact does this have on our use of the models?

Break-even Analysis (cont..) Volume: level of production Cost: fixed cost and variable cost Fixed cost: remains constant regardless of the number of units produced (cost of the machine used, cost of installing the machine, cost of designing and fabricating the work holding devices, cost of the space for machine) Variable cost: vary with the volume of the units produced (cost of machine operator’s time, cost of running the machine, cost of cutting tools, cost of material used). Revenue: the price at which the item is sold Total revenue: price times volume sold Profit: difference between total revenue and total cost

Break-even Analysis (cont..) – 900 – 800 – 700 – 600 – 500 – 400 – 300 – 200 – 100 – | | | | | | | | | | | | 0 100 200 300 400 500 600 700 800 900 1000 1100 Cost in dollars Volume (units per period) Total revenue line Profit corridor Loss corridor Total cost line Break-even point Total cost = Total revenue Variable cost This chart introduces breakeven analysis and the breakeven or crossover chart. As you discuss the assumptions upon which this techniques is based, it might be a good time to introduce the more general topic of the limitations of and use of models. Certainly one does not know all information with certainty, money does have a time value, and the hypothesized linear relationships hold only within a range of production volumes. What impact does this have on our use of the models? Fixed cost

Break-even Analysis (cont..) Variables: cf = fixed cost v = volume (i.e., number of units produced and sold) cv = variable cost per unit p = price per unit

Break-even Analysis (cont..) Total cost = fixed cost + total variable cost TC = cf + vcv Total revenue = volume x price TR = vp Profit = total revenue - total cost Z = TR - TC = vp - (cf + vcv)

Break-even Analysis (cont..) Break even volume: TR = TC vp = cf + vcv vp - vcv = cf v(p - cv) = cf v = cf p - cv

Example 1 Travis and Jeff own an adventure company called Whitewater Rafting. Due to quality and availability problems, the two entrepreneurs have decided to produce their own rubber rafts. The initial investment in plant and equipment is estimated to be $2,000. labor and material cost is approximately $5 per raft. If the rafts can be sold at a price of $10 each, what volume of demand would be necessary to break even?

Example 1 (cont..) $ Units Total revenue PROFIT Total cost 4,000 2,000 LOSS 400 Units Break-Even Point

Example 1 (cont..) The intersection of these two lines is the break even point If demand is less than the break even point, the company will operate at a loss If demand exceeds the break even point, the company will be profitable The company need to sell more than 400 rafts to make a profit

Example 1 (cont..) Break even analysis – useful when evaluating different degrees of automation More automated processes have higher fixed costs but lower variable costs The best process depends on the anticipated volume of demand for the product and the trade offs between fixed and variable costs

Example 2 The owner of Whitewater Rafting believe demand for their product will far exceed the break even point in example 1. they are now contemplating a larger initial investment of $10,000 for more automated equipment that would reduce the variable cost of manufacture to $2 per raft. Compare the old manufacturing process in example 1 with the new process proposed here. For what volume of demand should each process be chosen?

Example 2 (cont..) Point of Indifference Volume where cost of A = cost of B Rule for choosing process: Demand above point of indifference choose process with lowest variable cost Demand below point of indifference choose process with lowest fixed cost nnnnooo

Example 2 (cont..) Point of indifference Process Fixed cost Variable A $2,000 $5 B $10,000 $2 Cost TC process A TC process B 15,000 Point of indifference 10,000 5000 1000 2000 3000 4000 units Point of indifference = 2667

Example 2 (cont..) If demand is less than or equal to 2667 rafts, the alternative with the lowest fixed cost (process A) should be chosen If demand is greater than or equal to 2667 rafts, the alternative with the lowest variable cost (process B) is preferred

Example 2 (cont..) Above Below Total cost for Each alternative Point of indifference Above Choose alternative with The lowest variable cost Below Choose alternative with The lowest fixed cost

Example 3 Texloy Mfg Company must select a process for its new product, TX2, from among three different alternatives. The following cost data have been gathered; For what volume of demand would each process be desirable? Process A Process B Process C Fixed cost $10,000 $20,000 $50,000 Variable cost $5/unit $4/unit $2/unit

Example 3 (cont..) Cost 10,000 15,000 units TC process B TC process A Total cost for process A = $10,000 + $5v Total cost for process B = $20,000 + $4v Total cost for process C = $50,000 + $2v Point of indifference Always begin with the process that has the lowest fixed cost and compare it to the process with the next lowest fixed cost. Cost TC process B TC process A TC process C 10,000 15,000 units

Example 3 (cont..) Process A versus Process B; $10,000 + $5v = $20,000 + $4v v = 10,000 units If demand is less than or equal to 10,000, we should choose the alternative with the lowest fixed cost (Process A). If demand is greater than 10,000, we should choose the alternative with the lowest variable cost (Process B) At 10,000 units we can actually choose either A or B Process B versus Process C; $20,000 + $4v = $50,000 + $2v v = 15,000 units If demand is greater than or equal to 15,000, we should choose process C If demand is less than 15,000 but greater than 10,000, we should choose process B At 15,000 units we can actually choose either B or C

Example 3 (cont..) Summary Below 10,000 units, choose process A Between 10,000 units and 15,000 units, choose process B Above 15,000 units, choose process C Cost TC process B TC process A TC process C 10,000 15,000 units

Exercise A firm plans to begin production of a new product. The manager must decide whether to purchase one part from a vendor at $7 each or to produce them in house. Either of two processes could be use for in house production; one would have an annual fixed cost of $160,000 and a variable cost of $5 per unit, and the other would have an annual fixed cost of $190,000 and a variable cost of $4 per unit. Determine the range of annual volume for which each of the alternatives would be best.