# Facilities and Aggregate Planning. A digression I am not an advocate of gambling, but use an example here that you might draw on later. Say I have a coin.

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Facilities and Aggregate Planning

A digression I am not an advocate of gambling, but use an example here that you might draw on later. Say I have a coin that comes up heads 50% of the time and comes up tails 50% of the time (is there any other kind of coin? – you bet there is!). Say I offer you the following bet. If you flip the coin and it lands on the floor heads up you give me a dollar and if it ends up tails up I give you a dollar. Of course on any one flip you may win or lose a dollar, but if you play over and over again you would expect to not win or lose any money because the expected value to you is.5(-1) +.5(1) = 0 The expected value, or average, is the sum of the probability of each outcome times the cash flow of each outcome. Note the -1 is your cash flow when it comes up heads.

Overview As you know there are 24 hours a day, 7 days a week. What can you get done in a period of 1 week? Firms need to come to grips with what can be accomplished in any time frame. Capacity is the maximum output that can be produced over a given time period. Nominal, or effective, capacity builds in the downtime for machine repairs, shift breaks and the like that make nominal capacity lower. Facilities and decisions regarding facilities have a major impact on what the firm can accomplish.

Facilities Strategy Of course the author suggests that the firm have an overall strategy about facilities as opposed to “incremental capital budgeting” decisions. This means the firm must look beyond just whether a facility will have more revenue than cost. Factors to consider when formulating strategy are 1) Level of predicted demand, 2) Cost of facilities, 3) Response of competitors to firm decisions, 4) The fit with overall business strategy, and 5) International considerations.

Capacity Cushion Capacity cushion is defined as capacity minus average demand. This is a measure of the firms ability to meet the average demand in the market. Let’s study the solved problem on pages 278 and 279 to put some associated ideas into context. Say demand from period to period is uncertain but has the following probability distribution for a chemical company: 1000’s of gallons demanded100110120130 140 Probability.1.2.3.3.1 The average, or expected, demand is the sum of the product of each demand amount and its associated probability: 100(.1) + 110(.2) + 120(.3) + 130(.3) + 140(.1) = 10 + 22 + 36 + 39 + 14 = 121

Capacity Cushion If capacity is set at 130 there will be a cushion = 130 – 121 = 9. Anytime demand is less than 130 there will be idle capacity and this will occur.1 +.2 +.3 =.6 or 60% of the time. Average utilization of the plant is what % of the 130 is being used and it equals the sum of the product of each utilization rate times its probability of occurrence. When demand is 100 the utilization is 100/130, so in total we have (100/130).1 + (110/130).2 + (120/130).3 + (130/130).3 + (130/130).1 = 10/130 + 22/130 + 36/130 + 39/130 + 13/130 = (10 + 22 + 36 + 39 + 13)/ 130 =.9231 or 92.31% Note when demand is 140 the plant can only make 130 for full utilization.

Capacity Cushion Say that the business will lose \$100,000 in revenue for each 1000 gallons it can not deliver, and it costs \$5000 to build each 1000 gallons of capacity. There is a trade-off then between capacity and not being able to meet demand. I reproduce the probability distribution for a chemical company: 1000’s of gallons demanded100110120130 140 Probability.1.2.3.3.1 So if 100 capacity is built, unmet demand is (add across)0(.1)10(.2)20(.3)30(.3)40(.1) = 21 Similarly for 110 capacity 0(.1) 0(.2)10(.3)20(.3)30(.1) = 12 Similarly for 120 capacity 0(.1) 0(.2)0(.3)10(.3)20(.1) = 5 Similarly for 130 capacity 0(.1) 0(.2)0(.3) 0(.3)10(.1) = 1 Similarly for 140 capacity 0(.1) 0(.2)0(.3) 0(.3) 0(.1) = 0

Capacity Cushion On the previous slide we see if 100 capacity is built the firm will not be able to meet 21 units of demand (in a probabilistic sense). The total cost is thus 500,000 + 2,100,000 = 2,600,000 When it adds 10 more in capacity, an additional 50,000 in cost in building is put on but it reduces lost sale cost on 9 units. SO the extra 50,000 in building cost saves 900,000 in lost sales. This change is a bargain. It makes sense to build 140 capacity because even that extra 10 over 130 adds 50,000 in cost but saves 100,000 on the reduction in lost sales. In this case the building cost is low enough relative to lost revenue to build lots of capacity.

Aggregate Planning Aggregate planning is concerned with matching supply and demand of output over a medium time range, up to approximately 12 months into the future. The planning considers the amount of a product to make and the amount of the resources needed to get the job done. On page 265 you see the characteristics of aggregate planning. Planning options may attempt to modify demand or supply or both.

Workforce Planning The author mentions that firms may use a level strategy or a chase strategy in its use of a workforce. Table 12.1 page 269 has characteristics under which each strategy may be better.

Supply In a basic microeconomics class you may recall the discussion of cost as a major idea behind the supply curve. Much of this chapter is about the costs of production, including the ideas of economies and diseconomies of scale. One thing you may remember from econ is the idea of trade-offs. The last few sections of our chapter here bring these ideas to light and an example is presented.

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