Optimizing Heavy Equipment Transshipment and Job Assignments

School

Sebelas Maret University**We aren't endorsed by this school

Course

SOLO 3

Subject

Industrial Engineering

Date

Dec 12, 2024

Pages

Uploaded by UltraFlower635

Nabila Nur Amalina LuthfiF0222129Assignment 51.A heavy equipment company “Mbah Bejo” is a company that rents out heavyequipment such as excavators (backhoe), fork-lifts, palette-jacks, mini-cranes, etc.This company has 14 heavy equipment located in Jakarta totalling 6 units and inSurabaya 8 units. Heavy equipment will be rented by a road construction company forthe construction of Trans-Java toll roads which will be used in 6 cities, namelyTasikmalaya 2, Cirebon 1, Jogja 4, Solo 3, Madiun 2, and Jember 2. Due to roadconditions, transportation cannot go directly from the origin city to the destinationcity and must go through transit cities, namely Bandung, Semarang and Malang. Theflow of goods delivery and the cost of transporting a heavy equipment is shown in thefollowing table.Table of transportation cost/unit from origin city to transit city.BandungSemarangMalangJakarta101725Surabaya221512Table of transportation cost/unit from transit city to destination city.TasikmalayaCirebonJogjakartaSoloMadiunJemberBandung812Semarang151210Malang2318712a.Draw the supply/availability of equipment, the demand/need of equipment and thetransshipment cost/unit from origin city to transit city, then from transit city todestination city.b.Formulate the problem into a linear programming to determine the minimum costof transshipment faced by the company.c.Solve the problem using POM-QM for Windows.d.Interpret and explain the route of transshipment from origin city, transit city todestination city.e.How much minimum transshipment cost should be incurred by the company toship the heavy equipment from origin city to destination city.f.Draw the route and allocation of heavy equipment rented by the constructioncompany from origin city to destination city which have the minimum shipmentcost.2.Four automobiles have entered Bubba’s Repair Shop for various types of work,ranging from a transmission overhaul to a brake job. The experience level of themechanics is quite varied, and Bubba would like to minimizethe time required tocomplete all of the jobs. He has estimated the time in minutes for each mechanic tocomplete each job. Billy can complete job 1 in 400 minutes, job 2 in 90 minutes, job 3in 60 minutes, and job 4 in 120 minutes. Taylor will finish job 1 in 650 minutes, job 2in 120 minutes, job 3 in 90 minutes, and job 4 in 180 minutes. Mark will finish job 1in 480 minutes, job 2 in 120 minutes, job 3 in 80 minutes, and job 4 in 180 minutes.John will complete job 1 in 500 minutes, job 2 in 110 minutes, job 3 in 90 minutes,and job 4 in 150 minutes. Each mechanic should be assigned to just one of these jobs.

What is the minimum total time required to finish the four jobs? Who should beassigned to each job?***1.a.ToFromTasikmalayaCirebonYogyakartaSoloMadiunJemberBandung (T)Semarang(T)Malang(T)SupplyJakartaXXXXXX1017256SurabayaXXXXXX2215128Bandung(T)812XXXXXXX14Semarang(T)X151210XXXXX14Malang(T)XX2318712XXX14Demmand214322141414ToFromTasikmalayaCirebonYogyakartaSoloMadiunJemberBandung(T)Semarang(T)Malang(T)SupplyJakarta1822292730371017256Surabaya3030272519242215128Bandung(T)812XXXXXXX14Semarang(T)X151210XXXXX14Malang (T)XX2318712XXX14Demmand214322141414b.Minimum Transportation Cost = 10XAC + 17XAD + 25XAE + 22XBC + 15XBD + 12 XBE+ 8XCF + 12XCG + 15XDG + 12XDH + 10XDI + 18XEI + 7XEJ + 12 XEK.Constraint Function =XAC + XAD + XAE = 6 ( Transporation function from Jakarta to the transit point (Bandung,Semarang, Malang))XBC + XBD + XBE = 8 (Transportation function from Surabaya to the transit point(Bandung, Semarang, Malang))

XAC + XBC – XCF – XCG = 0 (To make sure all the goods are out of the Bandung transitarea.)XAD + XBD – XDG – XDH – XDH – XDI = 0 (To make sure all the goods are out of theSemarang transit area.)XAE + XBE – XEI – XEJ – XEK = 0 (To make sure all the goods are out of the Malangtransit area)XCF = 2 (Bandung (T) ke Tasikmalaya)XCG + XDG = 1 (From Bandung (T) and Semarang (T) to Cirebon)XDH + XEH = 4 (From Semarang (T) and Malang (T) to Yogyakarta)XDI + XEI = 3 (From Semarang (T) and Malang (T) to Solo)XEJ = 2 ( From Malang (T) to Madiun)XEK = 2 (From Malang (T) to Jember)c. d. From that QM solve, knowing:-There are 6 Excavator from Jakarta transit to Bandung -There are 8 Excavator fom Surabaya transit to Malang -From Bandung (Transit) the goods will be sent to Jogjakarta (4 unit), Solo (3 unit),Madiun (2 unit), and Jember (2 unit)-From Semarang (Transit) the goods will be sent to Tasikmalaya (2 unit), andSemarang (5 Unit)-From Malang (Transit) the goods will be sent to Cirebon (1 unit) and Semarang (7Unit)e.The minimum transhipment cost that will be borne by the company is as follows := (6 x 10 + 8 x 12) = 60 + 96 = $156f. Delivery routes and machine allocation from Jakarta and Surabaya to destination locations:

2.JobWorker’s NameJob 1Job 2Job 3Job 4Billy4009060120Taylor65012090180Mark48012080180John50011090150Objective Function: minimize employee assignment costZ= 400XA1 + 90XA2 + 60XA3 + 120 XA4 + 650 XB1 + 120XB2 + 90XB3 + 180XB4 +480XC1 + 120XC2 + 80XC3 + 180XC4 + 500XD1 + 110XD2 + 90XD3 + 150XD4Constraint Function = XA1 + XA2 + XA3 + XA4 ≤1 (constraint for Billy)XB1 + XB2 + XB3 + XB4 ≤1 constraint for Taylor)XC1 + XC2 +XC3 + XC4 ≤1 (constraint for Mark)XD1 + XD2 + XD3 + XD4 ≤1 (constraint for John)XA1 + XB1 + XC1 + XD1 ≤1 constraint for Job 1)XA2 + XB2 + XC2 + XD2 ≤1(constraint for Job 2)XA3 + XB3 + XC3 + XD3 ≤1(constraint for Job 3)XA4 + XB4 + XC4 + XD4 ≤1 (constraint for Job 4)JobWorker’s NameJob 1Job 2Job 3Job 4Billy34030060Taylor56030090Mark400400100

John41020060JobWorker’s NameJob 1Job 2Job 3Job 4Billy01000Taylor22010030Mark6020070John70000JobWorker’s NameJob 1Job 2Job 3Job 4Billy010100Taylor2100020Mark5010060John700100WorkersAssigned WorkMinimum costincurredMark380Taylor2120John4150Billy1400Total750