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Spring 2011 - ÇGIE 398 Lecture 71 lecture 7 : costs this lecture is about how to handle costs in hard-OR models types of costs costs that are relevant.

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Presentation on theme: "Spring 2011 - ÇGIE 398 Lecture 71 lecture 7 : costs this lecture is about how to handle costs in hard-OR models types of costs costs that are relevant."— Presentation transcript:

1 Spring 2011 - ÇGIE 398 Lecture 71 lecture 7 : costs this lecture is about how to handle costs in hard-OR models types of costs costs that are relevant to decision making an exam question case example

2 cost is a decrease in wealth that results from committing a resource to a particular use before the benefits are calcuated costs can be classified in many ways: –explicit cost - implicit cost –tangible cost - intangible cost –accounting cost - economic (or opportunity) cost, –direct cost - indirect cost –fixed cost - variable cost –short run cost - long run cost –relevant cost - irrelevant cost –... these partitions necessarily overlap, like for example, –a fixed, explicit accounting cost that is irrelevant –an implicit, intangible opportunity cost that is relevant etc.. Spring 2011 - ÇGIE 398 Lecture 72

3 Spring 2011 - ÇGIE 398 Lecture 73 explicit - implicit costs 1.explicit costs: out-of-pocket costs involving an actual transfer of funds; examples: payrol costs purchasing costs... 2.implicit costs: no funds change hand but cost is incurred; examples: depreciation cost of reduced productivity and disruption caused by rescheduling due to an emergency the social cost of unemployment cost of goodwill loss cost of late delivery...

4 economists’ fixed-variable / short-run-long-run costs 1.variable costs change in the short-run with the output level 2.fixed costs do not change in the short-run with the level of output, but they can change in the long-run accountants’ direct (prime) - indirect (overhead) costs costs are directly associated with one product or service 2.indirect costs are associated with all products and services; hence these are joint costs Spring 2011 - ÇGIE 398 Lecture 74

5 note that: –capital, or capacity costs are fixed in the short-run but variable in the long-run –in the long-run all costs are variable, they change with output level and with output capacity –indirect costs remain fixed over a wide interval of output level but will change when output exceeds that interval –direct costs can be variable or fixed when for example a machine is dedicated to a product so its fixed depreciation is a cost directly related to the product relevant costs are costs that change as a result of making decisions, irrelevant costs are costs that do not change with the decision; this means that the relevant cost of an activity would change when that activity takes place Spring 2011 - ÇGIE 398 Lecture 75

6 implicit costs that are shown in a balance sheet are intangible costs from an accounting point of view; these are often not relevant to OR; examples are: –depreciation –goodwill (when purchase cost exceeds the net value of assets) –reserves for bad debts, a form of asset value reduction it is relatively easy to put an exact figure on the amount of these costs there are also implicit intangible costs relevant to OR decisions; these are potential future costs or loss of benefits: − goodwill cost that might result from late deliveries is a relevant intangible cost for OR; this is not the same goodwill cost that accountants record in books − depreciation is often not relevant for OR decisions it is very difficult to put an exact figure on this type of intangible costs Spring 2011 - ÇGIE 398 Lecture 76

7 Spring 2011 - ÇGIE 398 Lecture 77 accounting costs - economic costs 1.accounting costs are recorded in balance sheets and income statements; they are either explicit or implicit costs 2.economic costs or opportunity costs; the implicit (or explicit) cost of a resource calculated as forgone benefits from the best alternative activity that the resource could have been used for an opportunity cost can be equal to the explicit accounting cost an opportunity cost can be intangible

8 opportunity cost of a resource is the answer to the question: what is the highest net additional income that not committing this resource can generate? opportunity cost is measured in units of an objective function (cost or profit), so it is a shadow price opportunity cost of an identically replaceable resource is equal to the replacement cost, (which is an explicit cost) eg. cost of cement or plain sugar opportunity cost of an identically irreplaceable resource is equal to the cost of replacing the resource with less desirable substitutes ( eg. the opportunity cost of assigning a uniquely talented engineer from project B to project A would equal the income lost in B plus the wages of replacing engineers) Spring 2011 - ÇGIE 398 Lecture 78

9 Spring 2011 - ÇGIE 398 Lecture 79 Max 90 xA + 60 xB subject to 2xA + xB < 8 xA < 3 xB < 4 OBJECTIVE FUNCTION VALUE 1) 420.0000 VARIABLE VALUE REDUCED COST XA 2.000000 0.000000 XB 4.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 45.000000 3) 1.000000 0.000000 4) 0.000000 15.000000

10 Spring 2011 - ÇGIE 398 Lecture 710 Max 90xA + 60xB subject to 2xA + xB < 7 xA < 3 xB < 4 OBJECTIVE FUNCTION VALUE 1) 375.0000 VARIABLE VALUE REDUCED COST XA 1.500000 0.000000 XB 4.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 45.000000 3) 1.500000 0.000000 4) 0.000000 15.000000 the shadow price of one hour of labour, £45, is an opportunity cost

11 Spring 2011 - ÇGIE 398 Lecture 711 relevant costs and benefits explicit costs are often relevant unless they are − sunk costs, which are irrelevant (eg. suppose the LOD project has costed $ 8 000 already and requires a further spending of $ 30 000 in order to provide benefits of $ 35 000; the $ 30 000 should be payed since the $ 8 000 is only a sunk cost and irrelevant for decision making) sunk costs can be hidden, (eg. as depreciation entered for accounting purposes rather than as a wear-and-tear cost; identifying a sunk cost may not be always straightforward all relevant costs, explicit or implicit, should be opportunity costs of resources used; in general they are not the same as historical ie. accounting costs (eg. the cost of warehousing space at LOD could be zero if there were no alternative use for the warehouse, or it could be $ 44/m 2 for example, if it could be rented out or used for parking)

12 Spring 2011 - ÇGIE 398 Lecture 712 –replacement costs represent opportunity costs that are often relevant, unlike historical purchase costs which are irrelevant –future costs and benefits are relevant opportunity costs that can be explicit such as a decommissioning cost or a salvage value –intangible costs are relevant opportunity costs in the form of shortage costs, goodwill costs etc.; these are often important but difficult to determine; extensive sensitivity analysis will be needed to estimate intangibles conclusions: accounting records provide important historical cost and benefit data not all of these are relevant to managerial decision making all costs used for decision making, whether implicit or explicit or intangible must be opportunity costs

13 an exam question A customer has offered to buy from LOD, a special type of high- technology lubricant which is not among the lubricants that LOD normally produces. Therefore the present offer represents a one-time project and the customer has offered to pay €200 000 for the required amount. The lubricant requires mixing an oil A and a special agent B. The necessary amount of A is available in the stocks of LOD, but B must be obtained from an outside supplier and an order has already been placed when the project was offered to LOD. The mixing process is quite complicated and requires the use of two kinds of capital equipment C and D; C is already owned by LOD but D must be leased from outside. Mixing also requires that expert scientific help be obtained from a nearby University. LOD accountants calculate the following cost estimates for the project: Spring 2011 - ÇGIE 398 Lecture 713

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17 Spring 2011 - ÇGIE 398 Lecture 717 case example: Champignons Galore, a French mushroom grower a three stage process: –put compost in trays –mycelium growing – 26 to 28 days –mushroom harvesting – in flushes with decreasing yield and size at 6 to 8 day intervals (<5 times per cycle) 66 sheds (400 trays in each shed) 65 of them always in use except for 2 days cleaning between cycles

18 Spring 2011 - ÇGIE 398 Lecture 718 three alternatives considered to increase production: 1.adopting two-layer sheds at the current site 2.acquiring a second site for new sheds 3.optimising the number of flushes without adding new sheds an OR study on costs and yields is initiated: only the third alternative is investigated based on the objective to maximise profits making the following boundary judgements: –the production process remains unchanged, using 66 sheds and 400 trays/shed –additional output can be sold at current prices –additional inputs can be obtained at current prices –the number of flushes per cycle can be 1, 2, 3, 4 or 5

19 Spring 2011 - ÇGIE 398 Lecture 719 the problem elements are: –decision maker : Gerard Mousse –objective : high annual profit –performance measure : profit (= revenue – total cost) –decision criterion : maximize profit –alternative courses of action : number of flushes in each cycle –problem context : defined by the boundary judgements

20 Spring 2011 - ÇGIE 398 Lecture 720

21 Spring 2011 - ÇGIE 398 Lecture 721 ~~-- SectionRelevanceNature of effectInput parameter Compost/tray preparation: raw materialsyesprop.ltrayprep. cost/tray (1) electricityyesvariable/trayprep. cost/tray(2) diesel fuelyesprop.ltrayprep. cost/tray(3) maintenance on vehiclesyesvariable/trayprep. cost/tray(4) vehicle depreciationnoconstantfixed cost yard/build. maintenancenoconstantfixed cost yard workers wagesyesprop.ltrayprep. cost/tray(5) salary J.Brownseynoconstantfixed cost Shed loading and maintenance: supplies & diesel fuel yesprop.ltrayshed cost/tray compost pack materialyesprop.ltrayshed cost/tray

22 Spring 2011 - ÇGIE 398 Lecture 722 tray repair & maint 'nceyesprop.ltrayshed cost/tray vehicle maintenanceyesvariable/trayshed cost/tray vehicle depreciationnoconstantfixed cost shed workers' wagesyesprop.ltrayshed cost/tray salary ofM. MeTraenoconstantfixed cost Climate control: electricitynoapprox. constantfixed cost materialsnoapprox. constantfixed cost lab. maintenancenoconstantfixed cost equipment depreciationnoconstantfixed cost new equipmentnosunk costexcluded Picking, sorting, packaging: packing materialsyesprop.lkgsort/pack. cost/kg supplies & electricityyesvariable/kgsort/pack. cost/kg new equipmentnosunk costexcluded maintenance equip.yesvariable/kgsort/pack. cost/kg equip. depreciationnoconstantfixed cost diesel fuel trucksyesprop.lkgsort/pack. cost/kg maintenance trucksyesvariable/kgsort/pack. cost/kg depreciation trucksnoconstantfixed cost wages sort/packyesprop.lkgsort/pack. cost/kg wages for driversyesvariable/kgsort/pack. cost/kg salary J. Fleurettenoconstantfixed cost wages pickingyesvariable/hourpick pay/hr vacation/sick payyesvariable/hourpick pay/hr

23 Spring 2011 - ÇGIE 398 Lecture 723 Local marketing: salary J. Marchandnoconstantfixed cost travel J. Marchandnoapprox. constantfixed cost Other costs: office suppliesnoapprox. constantfixed cost new equipmentnosunk costexcluded company cars running costnoapprox. constantfixed cost depreciation company carsnoconstantfixed cost office salariesnoapprox. constantfixed cost gardenernoconstantfixed cost maintenance officenoconstantfixed cost depreciation office bldgnoconstantfixed cost insurance, mortgage interestnoconstantfixed cost salaried employees accidentnoconstantfixed cost insurance, pension fund worker accidentyesprop.l€ paidprep. cost/tray & insurance &shed cost/tray & pension fundsort/pack. cost/kg & pick cost/hour salary C. Moussenoconstantfixed cost travel C. Moussenoapprox. constantfixed cost

24 Mathematical model for annual profit All expressions are defined for a decision choice of n consecutive flushes in each cycle. where n can be 5, 4, 3, 2, or 1. The expressions are labelled by the numbers shown in each circle or output of the influence diagram. 1. Length of each cycle: [cycle length] = [growing phase duration]+[average flush length] x n = 28 + 7n 2.Number of cycles per year: [cycles/year] = [days in year]/([cycle length] + [change-over time]) = 365/([ cycle length] + 2) 3. Number of trays prepared per year: [trays/year] = [number of sheds] x [trays/shed] x [cycles/year] = 65 x 400 x [cycles/year] Spring 2011 - ÇGIE 398 Lecture 724

25 5. Annual output of mushrooms: [annual output] = [trays/year] x [cumulative yield/tray for n flushes] 6. Annual tray preparation cost: [annual tray preparation cost] = [preparation cost/tray] x [trays/year] 7. Annual shed loading and unloading cost: [annual shed cost] = [shed cost/tray] x [trays/year] 8. Mushroom picking time per tray: The picking time per kg increases with each consecutive flush. As for the yield, Jennifer's figures allow us to compute an average picking rate for each consecutive flush 9. Annual number of hours required for picking mushroom output: [annual picking labour] = [trays/year] x [cumulative hours/tray] 10. Annual cost of picking labour: [annual picking cost] = [annual picking labour] x [picking pay/hour] 11. Annual sorting and packing cost: [annual sorting & packing cost] = [annual output] x [sort. & pack. cost-kg] Spring 2011 - ÇGIE 398 Lecture 725

26 12. Annual compost revenue: [annual compost revenue] = [spent compost/tray] x [trays/year] x [net compost selling price/kg] 13. Annual mushroom revenue: [annual mushroom revenue] = [annual output] x [mushroom revenue/kg] 14. Annual net profit, total revenue less total costs: [annual net profit] = [annual mushroom revenue] + [annual compost revenue] - [annual tray preparation cost] - [annual shed cost] - [annual picking cost] - [annual sorting & packing cost] -[annualfixedcost] Spring 2011 - ÇGIE 398 Lecture 726

27 Spring 2011 - ÇGIE 398 Lecture 727

28 Spring 2011 - ÇGIE 398 Lecture 728 Yield data : yield and picking data are collected by observations over a 5-flush cycle in two sheds: Flushes per cycle: 1 2345 Cycle length in days3744515865 Number of cycles/year9.8658.2957.1576.2935.615 Yield/tray in kg22.97316.0807.1034.2782.610 Cumul. yield/tray in kg22.97339.05346.15550.43353.043 Picking hours/tray2.1261.6701.0240.8410.625 Cumul. picking hr/tray2.1263.7964.8205.6616.286 Number of trays/year256,486215,682186,078163,621146,000 Total output/year in kg5,892,1368,422,9148,588,4508,251,8007,744,205

29 Spring 2011 - ÇGIE 398 Lecture 729 relevant and irrelevant costs 1.C. Brun’s section (composting and preparation): –€ 5,493,557 for raw materials (straw, manure, peat, casing sand, sterilization agent etc.). Most raw materials were purchased regularly, some like straw almost daily, with raw material stocks being small and remaining fairly constant over the entire year. –€ 267,844 for electricity for peak heating, operation of tray filling equipment, etc. –€ 27,911 diesel fuel for yard vehicles. –€ 25,787 maintenance and repair costs on yard vehicles. –€ 123,000 depreciation on yard vehicles and equipment. –€ 86,520 yard ground and building maintenance and repair costs. –€ 428,211 for yard workers’ wages, including vacation pay. –€ 36,400 salary of C. Brun.

30 Spring 2011 - ÇGIE 398 Lecture 730 2.Michel Boite’s section (shed loading/unloading): –€ 51,333 for supplies (sterilization and cleaning chemicals for sheds). –€ 219, 102 packing material for spent compost. –€ 24,451 for diesel fuel. –€ 12,211 for vehicle maintenance and repairs; € 35,600 depreciation on vehicles. –€ 44,898 repairs and maintenance of sheds. –€ 281,346 for replacement, repairs, and maintenance oftrays. –€ 188,231 wages, including vacation pay. –€ 31,200 salary of M. Boite. 3.Karl Scharf’s section (climate control): –€ 37,866 electricity for climate control (approx. const.) –€ 34,613 for materials (approx. const.) –€ 12,452 laboratory maintenance, cleaning, etc. –€ 33,200 depreciation on climate control and lab equipment. –€ 55,800 new climate control and lab equipment (sunk) –€ 68,400 salary of K. Scharf and Tina Paille.

31 Spring 2011 - ÇGIE 398 Lecture 731 4.Jennifer Fleurette’s section (picking, sorting, and packaging): –€ 4,071,758 for packing materials. –€ 14,881 for supplies; €6,554 for electricity. –€ 24,600 for new sorting machine (sunk) –€ 4,212 for sorting and packing equipment maintenance. –€ 14,600 depreciation on sorting and packing equipment. –€ 5,602 maintenance and repair of sorting and packing shed. –€ 18,006 for diesel fuel for trucks. –€ 5,787 for truck maintenance and repairs; € 37,800 depreciation on trucks –€ 2,044,324 wages for sorting and packing staff, including vacation pay. –€ 52,120 wages for drivers. –€ 36,000 salary of J. Fleurette. –Pickers hourly wage: € 9.20; vacation and sick pay allowance: 8% on wages. 5. local marketing: –€ 34,800 salary of J. Marchand. –€ 26,922 travel and daily allowances (approx. cons.)

32 Spring 2011 - ÇGIE 398 Lecture 732 6. other costs: € 48,766 for office supplies (approx. cons.) € 32,688 for new office equipment and computers (sunk) € 3,435 for office building electricity. € 12,111 fuel and maintenance costs for two cars (approx. cons.) € 6,600 depreciation on company cars. € 288,420 salaries of office staff (approx. cons.) €22,600 gardener. € 8,688 office building maintenance € I90,000 depreciation € I,360,000 mortgage interest; €124,005 fire and property insurance. € 301,887 accident insurance on waged workers (2.5%). € 8,517 accident insurance on salaried employees (1.5%). € 483,019 pension fund contribution on waged workers (4%). € 34,069 pension fund contribution on salaried employees (6%). € 72,000 salary of G. Mousse. € 35,210 travel cost for G. Mousse (approx. cons.)

33 Spring 2011 - ÇGIE 398 Lecture 733 Revenue and cost computations flushes / cycle12345 Mushroom revenue 21,211,68930,322,49130,918,420 29,706,48 2 27 879 138 Compost revenue 2,154,4861,811,7271,563,0591,374,4141,226,400 Tray preparation cost 11,017,6299,264,8247,993,1827,028,4876,271,573 Shed cost 1,385,8401,165,3661,005,414884,071788,863 Picking cost 5,744,7638,625,0519,447,9249,757,6199,668,026 Sorting & packing cost 4,834,3386,910,7737,046,5916,770,3796,353,911 Fixed cost 2,914,294 Net profit (2,530,689)3,253,9104,074,0753,726,0453,108,871 Difference -578,182145,040965,204617,1740

34 Spring 2011 - ÇGIE 398 Lecture 734 growing three flushes per cycle instead of five, provides higher profits as well as a 10% increase in output this is effectively equivalent to acquiring seven additional sheds, so it seems that the other options can be ignored for the time being

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