Facility Location Problem. Learning objectives. Antti Salonen Farzaneh Ahmadzadeh

Transcription

1 Antt Salonen Farzaneh Ahmadzadeh 1 Faclty Locaton Problem The study of faclty locaton problems, also known as locaton analyss, s a branch of operatons research concerned wth the optmal placement of facltes to mnmze transportaton costs whle consderng factors lke avodng placng hazardous materals, near housng, and compettors' facltes. Learnng objectves Ø Introducton and defnton Ø Explan locaton decsons Ø Descrbe the factors affectng locaton decsons Ø Methods of evaluatng locaton alternatves Ø Methods of evaluatng transportaton 1

2 Defnton Faclty locaton s the process of determnng geographcal stes for a frms operatons. It s the process of dentfyng the best geographc locaton for a servce or producton faclty Objectve: o Maxmze beneft of locaton to frm o Optmum locaton wth greatest advantage to the organzaton Strategc Decson v Long term decsons v Dffcult to reverse v Large nvestment made v Affect fxed and varable cost Should be based on long range polcy and forecasts ncludng expansons polcy, antcpated dversfcaton of products, changng markets, changng sources of raw materals, etc. v Affect processes throughout the organzaton Locaton decsons Locaton decsons affect processes and departments Marketng Human resources Accountng and fnance Operatons 6 2

3 Locaton decsons Domnant factors n manufacturng Favorable labor clmate Proxmty to markets Proxmty to supplers and resources Proxmty to the parent company s facltes Utltes, taxes, and real estate costs Domnant factors n servces on sales and customer satsfacton Proxmty to customers Transportaton costs and proxmty to markets Locaton of compettors Ste specfc factors KPP227 7 Selectng a new faclty Step 1: Identfy the mportant locaton factors and categorze them as domnant or secondary Step 2: Consder alternatve regons; then narrow to alternatve communtes and fnally specfc stes Step 3: Collect data on the alternatves Step 4: Analyze the data collected, begnnng wth the quanttatve factors Step 5: Brng the qualtatve factors pertanng to each ste nto the evaluaton 8 Dfferent methods of establshng a faclty locaton Weghted score Load dstance Centre of gravty Break even analyss 3

4 Weghted scores EXAMPLE 11.1 A new medcal faclty, Health-Watch, s to be located n Ere, Pennsylvana. The followng table shows the locaton factors, weghts, and scores (1 = poor, 5 = excellent) for one potental ste. The weghts n ths case add up to 100 percent. A weghted score (WS) wll be calculated for each ste. What s the WS for ths ste? Locaton Factor Weght Score Total patent mles per month 25 4 Faclty utlzaton 20 3 Average tme per emergency trp 20 3 Expressway accessblty 15 4 Land and constructon costs 10 1 Employee preferences Weghted scores The WS for ths partcular ste s calculated by multplyng each factor s weght by ts score and addng the results: Locaton Factor Weght Score Total patent mles per month 25 4 Faclty utlzaton 20 3 Average tme per emergency trp 20 3 Expressway accessblty 15 4 Land and constructon costs 10 1 Employee preferences 10 5 WS = (25 4) + (20 3) + (20 3) + (15 4) + (10 1) + (10 5) = = 340 The total WS of 340 can be compared wth the total weghted scores for other stes beng evaluated. 11 Example: Weghted scores Management s consderng three potental locatons for a new ball bearng factory. They have assgned scores shown below to the relevant factors on a 0 to 10 bass (10 s best). Usng the preference matrx, whch locaton would be preferred? Locaton Factor Weght Eastland Westland Northland Materal Supply Qualty of Lfe Mld Clmate Labor Sklls

5 Example: Weghted scores Management s consderng three potental locatons for a new ball bearng factory. They have assgned scores shown below to the relevant factors on a 0 to 10 bass (10 s best). Usng the preference matrx, whch locaton would be preferred? Locaton Factor Weght Eastland Westland Northland Materal Supply Qualty of Lfe Mld Clmate Labor Sklls Load-Dstance (ld) method Identfy and compare canddate locatons Lke weghted-dstance method Select a locaton that mnmzes the sum of the loads multpled by the dstance the load travels Tme may be used nstead of dstance 14 Load-Dstance (ld) method Calculatng a load-dstance score Vares by ndustry Use the actual dstance to calculate ld score Use Rectlnear or Eucldean dstances Dfferent measures for dstance Fnd one acceptable faclty locaton that mnmzes the ld score Formula for the ld score: ld = S l d 15 5

6 Load-Dstance (ld) method Example: What s the dstance between (20, 10) and (80, 60)? Eucldean dstance: d AB = (x A x B ) 2 + (y A y B ) 2 = (20 80) 2 + (10 60) 2 = 78.1 Rectlnear dstance: d AB = x A x B + y A y B = = Load-Dstance (ld) method Example: Management s nvestgatng whch locaton would be best to poston ts new plant relatve to two supplers (located n Cleveland and Toledo) and three market areas (represented by Cncnnat, Dayton, and Lma). Management has lmted the search for ths plant to those fve locatons. The followng nformaton has been collected. Whch s best, assumng rectlnear dstance? Locaton x,y coordnates Trps/year Cncnnat (11,6) 15 Dayton (6,10) 20 Cleveland (14,12) 30 Toledo (9,12) 25 Lma (13,8) Load-Dstance (ld) method Calculatons: Cncnnat = Dayton = Cleveland = Toledo = Lma = Locaton x,y coordnates Trps/year Cncnnat (11,6) 15 Dayton (6,10) 20 Cleveland (14,12) 30 Toledo (9,12) 25 Lma (13,8) 40 15(0) + 20(9) + 30(9) + 25(8) + 40(4) = (9) + 20(0) + 30(10) + 25(5) + 40(9) = (9) + 20(10) + 30(0) + 25(5) + 40(5) = (8) + 20(5) + 30(5) + 25(0) + 40(8) = (4) + 20(9) + 30(5) + 25(8) + 40(0) =

7 Center of Gravty Method A good startng pont Fnd x coordnate, x*, by multplyng each pont s x coordnate by ts load (l t ), summng these products Sl x, and dvdng by Sl The center of gravty s y coordnate y* found the same way Generally not the optmal locaton x* = Sl x Sl y* = Sl y Sl 19 Center of Gravty Method EXAMPLE 11.2 A suppler to the electrc utlty ndustry produces power generators; the transportaton costs are hgh. One market area ncludes the lower part of the Great Lakes regon and the upper porton of the southeastern regon. More than 600,000 tons are to be shpped to eght major customer locatons as shown below: Customer Locaton Tons Shpped x, y Coordnates Three Rvers, MI 5,000 (7, 13) Fort Wayne, IN 92,000 (8, 12) Columbus, OH 70,000 (11, 10) Ashland, KY 35,000 (11, 7) Kngsport, TN 9,000 (12, 4) Akron, OH 227,000 (13, 11) Wheelng, WV 16,000 (14, 10) Roanoke, VA 153,000 (15, 5) 20 Fndng the Center of Gravty What s the center of gravty for the electrc utltes suppler? Usng rectlnear dstance, what s the resultng load dstance score for ths locaton? The center of gravty s calculated as shown below: Customer Locaton Tons Shpped x, y Coordnates Three Rvers, MI 5,000 (7, 13) Fort Wayne, IN 92,000 (8, 12) Columbus, OH 70,000 (11, 10) Ashland, KY 35,000 (11, 7) Kngsport, TN 9,000 (12, 4) Akron, OH 227,000 (13, 11) Wheelng, WV 16,000 (14, 10) Roanoke, VA 153,000 (15, 5) Sl = = 607 Sl x = 5(7) + 92(8) + 70(11) + 35(11) + 9(12) + 227(13) + 16(14) + 153(15) = 7,504 Sl x x* = Sl = 7, =

8 Fndng the Center of Gravty What s the center of gravty for the electrc utltes suppler? Usng rectlnear dstance, what s the resultng load dstance score for ths locaton? Customer Locaton Tons Shpped x, y Coordnates Three Rvers, MI 5,000 (7, 13) Fort Wayne, IN 92,000 (8, 12) Columbus, OH 70,000 (11, 10) Ashland, KY 35,000 (11, 7) Kngsport, TN 9,000 (12, 4) Akron, OH 227,000 (13, 11) Wheelng, WV 16,000 (14, 10) Roanoke, VA 153,000 (15, 5) Sl y = 5(13) + 92(12) + 70(10) + 35(7) + 9(4) + 227(11) + 16(10) + 153(5) = 5,572 Sl y y* = Sl = 5, = Fndng the Center of Gravty What s the center of gravty for the electrc utltes suppler? Usng rectlnear dstance, what s the resultng load dstance score for ths locaton? Customer Locaton Tons Shpped x, y Coordnates Three Rvers, MI 5,000 (7, 13) Fort Wayne, IN 92,000 (8, 12) Columbus, OH 70,000 (11, 10) Ashland, KY 35,000 (11, 7) Kngsport, TN 9,000 (12, 4) Akron, OH 227,000 (13, 11) The resultng load-dstance score s: Wheelng, WV 16,000 (14, 10) Roanoke, VA 153,000 (15, 5) ld = S l d = 5( ) + 92( ) + 70( ) + 35( ) + 9( ) + 227( ) + 16( ) + 153( ) = 2,662.4 where d = x x* + y y* 23 Break-Even analyss Compare locaton alternatves on the bass of quanttatve factors expressed n total costs Determne the varable costs and fxed costs for each ste Plot total cost lnes Identfy the approxmate ranges for whch each locaton has lowest cost Solve algebracally for break-even ponts over the relevant ranges 24 8

9 Break-Even analyss for locaton EXAMPLE 11.3 An operatons manager narrowed the search for a new faclty locaton to four communtes. The annual fxed costs (land, property taxes, nsurance, equpment, and buldngs) and the varable costs (labor, materals, transportaton, and varable overhead) are as follows: Communty Fxed Costs per Year Varable Costs per Unt A $150,000 $62 B $300,000 $38 C $500,000 $24 D $600,000 $30 25 Break-Even analyss for locaton Step 1: Plot the total cost curves for all the communtes on a sngle graph. Identfy on the graph the approxmate range over whch each communty provdes the lowest cost. Step 2: Usng break-even analyss, calculate the break-even quanttes over the relevant ranges. If the expected demand s 15,000 unts per year, what s the best locaton? 26 Break-Even analyss for locaton To plot a communty s total cost lne, let us frst compute the total cost for two output levels: Q = 0 and Q = 20,000 unts per year. For the Q = 0 level, the total cost s smply the fxed costs. For the Q = 20,000 level, the total cost (fxed plus varable costs) s as follows: Communty Fxed Costs Varable Costs (Cost per Unt)(No. of Unts) Total Cost (Fxed + Varable) A $150,000 B $300,000 C $500,000 D $600,

10 Break-Even analyss for locaton To plot a communty s total cost lne, let us frst compute the total cost for two output levels: Q = 0 and Q = 20,000 unts per year. For the Q = 0 level, the total cost s smply the fxed costs. For the Q = 20,000 level, the total cost (fxed plus varable costs) s as follows: Communty Fxed Costs A $150,000 B $300,000 C $500,000 D $600,000 Varable Costs (Cost per Unt)(No. of Unts) Total Cost (Fxed + Varable) $62(20,000) = $1,240,000 $1,390,000 $38(20,000) = $760,000 $1,060,000 $24(20,000) = $480,000 $980,000 $30(20,000) = $600,000 $1,200, Break-Even analyss for locaton The fgure shows the graph of the total cost lnes. The lne for communty A goes from (0, 150) to (20, 1,390). The graph ndcates that communty A s best for low volumes, B for ntermedate volumes, and C for hgh volumes. We should no longer consder communty D, because both ts fxed and ts varable costs are hgher than communty C s. Annual cost (thousands of dollars) 1,600 A (20, 1,390) 1,400 (20, 1,200) D 1,200 B (20, 1,060) C 1,000 (20, 980) 800 Break-even 600 pont 400 Break-even pont 200 A best B best C best Q (thousands of unts) 29 Break-Even analyss for locaton Step 2: The break-even quantty between A and B les at the end of the frst range, where A s best, and the begnnng of the second range, where B s best. We fnd t by settng both communtes total cost equatons equal to each other and solvng: (A) (B) $150,000 + $62Q = $300,000 + $38Q Q = 6,250 unts The break-even quantty between B and C les at the end of the range over whch B s best and the begnnng of the fnal range where C s best. It s (B) (C) $300,000 + $38Q = $500,000 + $24Q Q = 14,286 unts 30 10

11 No other break-even quanttes are needed. The break-even pont between A and C les above the shaded area, whch does not mark ether the start or the end of one of the three relevant ranges. KPP227 HT 2010 Le 1: Introducton to logstcs Karn Romvall 31 Relevant book chapters Chapter: Locatng facltes 32 Questons? Farzaneh.ahmadzadeh@mdh.se Antt.salonen@mdh.se Next part of the lecture: Transportaton method 33 11