VIEWS: 2 PAGES: 31 POSTED ON: 9/19/2011
ENGR 3210 Fundamentals of Logistics Engineering Class 33 November 11, 2002 How do you size a warehouse? What are the important variables? Throughput or demand for goods moving through Inventory turnover (defines how much inventory is stored in the warehouse) Storage size requirements for the units to be stored The fraction of the total warehouse that is actually used for storage (vs. aisle and other space) Material handling equipment and storage systems used helps to define this fraction 2 A simple example The warehouse will handle 2,400,000 lbs of widgets per month Monthly turnover of inventory is 3 turns per month (turnover is monthly sales divided by average inventory) The storage system to be used requires that 50% of the floor space would be devoted to aisles Only 70% of the warehouse is really used for storage. The rest will be used for office facilities One pound of widgets is packaged in boxes that are 0.5 cubic feet in size The boxes of widgets can be stacked 16 feet high on pallets 3 How many square feet do we need in the warehouse? How many pounds of widgets are going to be stored in the warehouse? 2,400,000 lbs / 3 turns per month =800,000 lbs How many cubic feet do the widgets take up? 800,000 lbs (0.5 cu. ft. per lb.) = 400,000 cu. ft. How many square feet do the widgets occupy? 400,000 cu. Ft. / 16 ft. = 25,000 sq ft. How much aisle space do we need? An equal amount to the widget space = 25,000 sq. ft. What about office space ? 50,000 sq. ft. / 70% = 71,428 sq, ft in the entire warehouse 4 The real question here is not size but cost (If we are to minimize Total Logistics Costs) Construction of the warehouse is assumed to cost $30 / sq. ft. The construction cost is amortized over 20 years with an interest rate that breaks the construction cost down to $1.50 per sq. ft. each year. The annual fixed cost to operate a warehouse of this type is $3.00 per sq. ft. The materials handling charge for this material is $0.05 per lb. of throughput. 5 What is the annual cost of operating the warehouse? What is needed to pay off the construction loan? 71,428 sq. ft. ($1.50 per sq. ft.) = $107,142 What is needed to operate the warehouse for a year? 71,428 sq. ft. ($3.00 per sq. ft.) = $214,284 What is needed to handle the material for a year? 2,400,000 lbs. (12months) ($0.05) = $1,440,000 Total cost = $1,761,426 per year 6 A simplified computation for the example Space (sq. ft.)=Monthly demand(lbs.) x (1/3)(0.5/16)(1/0.5)(1/.7) = Monthly demand x .03 Annual Cost = Space (sq. ft.) ($4.50) + Monthly demand ($0.60) 7 Exploring some design tradeoffs What is the cost of the warehouse if the aisle requirements are: 35% of the total space? 40% of the total space? 45% of the total space? What is the cost of the warehouse if the stacking height is: 17 feet? 18 feet? 19 feet? What could you afford to spend on equipment to achieve each of these improvements? 8 A spreadsheet solution Throughput 2,400,000 lbs/mo Construction Cost/sf/yr $1.50 Turns 3 turns/mo Operation Cost/sf/yr $3.00 Handling Cost/lb $0.05 Cubic feet/lb 0.50 SQUARE FEET REQUIRED Stack height Aisle % 14 15 16 17 18 19 20 35.00% 62,794 58,608 54,945 51,713 48,840 46,270 43,956 40.00% 68,027 63,492 59,524 56,022 52,910 50,125 47,619 45.00% 74,212 69,264 64,935 61,115 57,720 54,682 51,948 50.00% 81,633 76,190 71,429 67,227 63,492 60,150 57,143 55.00% 90,703 84,656 79,365 74,697 70,547 66,834 63,492 60.00% 102,041 95,238 89,286 84,034 79,365 75,188 71,429 ANNUAL COST Stack height Aisle % 14 15 16 17 18 19 20 AVG $/ft 35.00% $1,722,575 $1,703,736 $1,687,253 $1,672,708 $1,659,780 $1,648,213 $1,637,802 $14,129 40.00% $1,746,122 $1,725,714 $1,707,857 $1,692,101 $1,678,095 $1,665,564 $1,654,286 $15,306 45.00% $1,773,952 $1,751,688 $1,732,208 $1,715,019 $1,699,740 $1,686,070 $1,673,766 $16,698 50.00% $1,807,347 $1,782,857 $1,761,429 $1,742,521 $1,725,714 $1,710,677 $1,697,143 $18,367 55.00% $1,848,163 $1,820,952 $1,797,143 $1,776,134 $1,757,460 $1,740,752 $1,725,714 $20,408 60.00% $1,899,184 $1,868,571 $1,841,786 $1,818,151 $1,797,143 $1,778,346 $1,761,429 $22,959 Avg $/5% $35,322 $32,967 $30,907 $29,089 $27,473 $26,027 $24,725 9 The results graphed $1,900,000 $1,850,000 $1,800,000 $1,750,000 35% 40% $1,700,000 45% 50% $1,650,000 55% $1,600,000 60% 60% $1,550,000 55% 50% $1,500,000 45% 14 40% 15 16 17 35% 18 19 20 10 Which variable promises the biggest bang for your dollar? Throughput 2,400,000 lbs/mo Construction Cost/sf/yr $1.50 Turns 3 turns/mo Operation Cost/sf/yr $3.00 Handling Cost/lb $0.05 Cubic feet/lb 0.50 SQUARE FEET REQUIRED Stack height Aisle % 14 15 16 17 18 19 20 35.00% 62,794 58,608 54,945 51,713 48,840 46,270 43,956 40.00% 68,027 63,492 59,524 56,022 52,910 50,125 47,619 45.00% 74,212 69,264 64,935 61,115 57,720 54,682 51,948 50.00% 81,633 76,190 71,429 67,227 63,492 60,150 57,143 55.00% 90,703 84,656 79,365 74,697 70,547 66,834 63,492 60.00% 102,041 95,238 89,286 84,034 79,365 75,188 71,429 ANNUAL COST Stack height Aisle % 14 15 16 17 18 19 20 AVG $/ft 35.00% $1,722,575 $1,703,736 $1,687,253 $1,672,708 $1,659,780 $1,648,213 $1,637,802 $14,129 40.00% $1,746,122 $1,725,714 $1,707,857 $1,692,101 $1,678,095 $1,665,564 $1,654,286 $15,306 45.00% $1,773,952 $1,751,688 $1,732,208 $1,715,019 $1,699,740 $1,686,070 $1,673,766 $16,698 50.00% $1,807,347 $1,782,857 $1,761,429 $1,742,521 $1,725,714 $1,710,677 $1,697,143 $18,367 55.00% $1,848,163 $1,820,952 $1,797,143 $1,776,134 $1,757,460 $1,740,752 $1,725,714 $20,408 60.00% $1,899,184 $1,868,571 $1,841,786 $1,818,151 $1,797,143 $1,778,346 $1,761,429 $22,959 Avg $/5% $35,322 $32,967 $30,907 $29,089 $27,473 $26,027 $24,725 11 Which has a steeper slope? $1,900,000 $1,850,000 $1,800,000 $1,750,000 35% 40% $1,700,000 45% 50% $1,650,000 55% $1,600,000 60% 60% $1,550,000 55% 50% $1,500,000 45% 14 40% 15 16 17 35% 18 19 20 12 Implications for design For these economic assumptions the total costs are more sensitive to reducing aisle width than increasing stacking height Therefore we would favor materials handling and storage systems which minimized aisle width (over increasing stacking height) Reducing aisle width by 5% will save about $30,000 annually How much could I spend on equipment to achieve this? 13 Engineering Economics greatly simplified A dollar in your pocket today is worth more than the promise of a dollar one year from now If you had a dollar today you could put it into a savings account earning interest and at the end of one year you could extract the dollar plus the interest There is a “time value of money” Comparing equipment investment strategies that have different initial costs and varying annual costs and benefits require comparing the costs at a single point in time 14 Engineering Economics generally refers to the process of making economic comparisons of Engineering investments like the Equipment in the warehouse Forecast or estimate the “streams” of costs (or cost savings over time) Convert those streams to a common point in time using interest rate concepts Compare the alternative designs at a common point in time in order to make the most economical choice 15 A very simple example of the time value of money Would you prefer $3000 now or $3100 a year from now? If I had $3000 now and could invest it in a bank earning 3% interest, the bank would give me $3090 at the end of the year. Take the $3100 next year. If I could invest it in another bank which offered 5% interest, that bank would give me $3150 at the end of the year. Take the $3000 now. 16 Translating present worth to future sums using interest i = annual rate of interest n = number of interest periods (usually years) P = the principal or present value of money F= the future amount of money 17 Relating F to P is what it is all about F=P(1+i) at the end of the first year F= (P(1+i))(1+i)=P(1+i)2 at the end of the second year F=P(1+i)n at the end of the nth year Or P=F/(1+i)n to bring a future value back to a present value 18 This enables comparison of alternatives with different cash flows Alternative A: Costs $10,000 now but returns $4,000 each of the next 3 years Alternative B: Costs $8,000 now but returns $3,000 each of the next 3 years 19 Graphic Cash Flow Diagrams Interest periods on horizontal axis Upward arrows represent receipts (positive cash flow) Downward arrows represent costs (negative cash flows) Flows assumed to be at end of period 20 The two alternatives depicted graphically: $4,000 $4,000 $4,000 Alternative A 0 1 2 3 $10,000 $3,000 $3,000 $3,000 Alternative B 0 1 2 3 $8,000 21 How do you compare them using Net Present Worth? Assume some time value of money or interest rate Convert the cash flows to a common point in time Select the alternative with the largest net present worth 22 To convert to the present use the formula: P=F/(1+i)n $4,000 $4,000 $4,000 Alternative A 0 1 2 3 $10,000 $3,000 $3,000 $3,000 Alternative B 0 1 2 3 $8,000 23 Choosing an appropriate interest rate One way is to think about what it will cost to borrow the money from a bank Another way to acquire capital is to sell shares of stock A third method is to think about what could be earned if the money were invested in some other “project” Often a blending of the three Seek guidance from your accounting or finance department 24 To convert to the present use the formula: P=F/(1+i)n (Choose 8% for i) $4,000 $4,000 $4,000 Each future value must Alternative A 0 1 be converted 2 3 back to the $10,000 present time, 0 $3,000 $3,000 $3,000 Alternative B 0 1 2 3 PA,2=4000/(1+.08)2 $8,000 PA,2= 3429 25 To convert to the present use the formula: P=F/(1+i)n $3429 $4,000 $4,000 Each future value must Alternative A 0 1 be converted 2 3 back to the $10,000 present time, 0 $3,000 $3,000 $3,000 Alternative B 0 1 2 3 PA,2=4000/(1+.08)2 $8,000 PA,2= 3429 26 Convert all the future values to present values using P=F/(1+i)n $3704 Net Present Worth = $10,308 - $10,000 $3429 Alternative A $3175 = $308 0 1 2 3 $10,000 $2778 Net Present Worth $2572 = $7,731 - $8,000 $2381 = - $269 Alternative B 0 1 2 3 $8,000 27 Lets go back to the equipment expense question How much can I afford to spend on equipment to reduce the aisle percentage by 5%? Reducing the aisle percentage by 5% saves us $30,000 annually $30k $30k $30k ?? 28 Some key questions needed to find the appropriate investment in the equipment What is the useful life of the equipment? Are there operating charges that should be estimated for each year? Is there a salvage value at the end of the useful life? What is an appropriate interest rate? 29 Including $5k operating costs and a salvage value of $5k at the end of 8 years $30k $30k $30k $5k ?? $5k $5k 30 We could invest 146,000 dollars Interest= 0.08 Future Present Value Value 1 25 23.14815 2 25 21.43347 3 25 19.84581 4 25 18.37575 5 25 17.01458 6 25 15.75424 7 25 14.58726 8 30 16.20807 Total 146.3673 31