Exercise 1 Network Planning Design Teresa Grilo Dep. of Engineering and Manageent Instituto Superior Técnico Lisbon, Portugal SCM/IST 1 SCM/IST IST Lisbon Ana Ana Carvalho 2015 2015
Introduction Find the right balance between inventory, transportation and anufacturing costs. Match supply and deand under uncertainty by positioning and anaging inventory effectively. Utilize resources effectively by sourcing products fro the ost appropriate anufacturing facility. 2 SCM/IST IST Lisbon Ana Carvalho 2015
Obectives 1) Develop a atheatical odel, which translates the supply chain network, and which can be used to optiize the network design while iniizing the costs; 2) Optiize the network design finding the nuber and location of the distribution centers and the flows that should be established between all entities of the supply chain, in order to iniize the total costs. 3 SCM/IST IST Lisbon Ana Carvalho 2015
Proble 1. Plants Lisbon = 500 ton Porto = 300 ton? 2. Distribution Centers Paris = 500 ton Berlin =300 ton London =350 ton 3. Markets Spain France Gerany UK 4 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Matheatical odels are coposed by: Variables: decisions to be taken on the syste and quantities to calculate. Operators: act on these variables, which can be algebraic operators (paraeters), functions, differential operators, etc. Indices: identify entities in the syste. If the obective functions and constraints are represented entirely by linear equations, then the odel is regarded as a linear odel. If one or ore of the obective functions or constraints are represented with a nonlinear equation, then the odel is known as a nonlinear odel. 5 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) 1.What is the syste in study? 2. What are the different entities involved in the syste? How any indices do we need? 3. What is the available data? How any paraeters do we need? 4. What is the unknown data? How any variables do we need? 5. What are the costs involved in this supply chain? How any ters do we need for the obective function? 6. Do we have constraints? How any? 6 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Indices Paraeters Variables 7 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Indices i i 8 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Indices i plants distribution centers arkets s scenarios i i 9 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Paraeters i i 10 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Paraeters prob s - probability of each scenario; i i CPD - distribution centers capacity; CPP i - plants capacity; distp i - distance fro plants i to distribution centers, in k; distdc - distance fro distribution centers to arkets, in k; Deand s - deand of arket in scenario s, in ton; CF - distribution centers fixed costs; CT - transportation cost 11 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Variables i i 12 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Variables 1. Continuous variables XD is flow fro plant i to distribution center in scenario s, in ton; XF s flow fro distribution center to arket in scenario s, in ton. 2. Binary variable i i Y variable that assues value 1 if distribution center is open and 0 otherwise. 13 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) i i Obective function The obective function iniizes the total costs, which includes: i. In the first part, the fixed costs of opening a distribution center; ii. In the second part, the weighted su of the expected transportation costs in each scenario. Min CF Y Fix Cost + prob s CT distpi XDis + 14 SCM/IST IST Lisbon Ana Carvalho 2015 s i Variable Cost Plant->DC distdc XF Variable Cost DC->Market s
Matheatical Model Forulation a) Constraints 15 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Forulation a) Constraints 1. It is guaranteed that all deand is et. 2. The flow sent fro each plantito all distribution centers has to be lower or equal than its production capacity. 3. Guarantees that each distribution center doesn t keep inventory, so the flow that arrives has to leave it. 4. XFs = Deand s XD i XD is CPP i = is XF s XF CPD Y s, s i, s, s, s Ensures that the distribution centers capacity is not exceeded, in case that distribution center exists. 16 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) 1. Open Excel:Ex1-Teplate 2. Fill out paraeters data. 3. Ipleent Constraints. How?? 17 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) Ipleent Constraints. How?? To start, insert the nae of the variables into the cells. 18 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) XFs = Deand s, s Constraint 1- The flow sent fro all distribution centers to each arket has to be equal to its deand. XF + 1 1 1 1,1+ XF2,1 XF3,1 XF + 1 1 1 1,4 + XF2,4 XF3,4 XF + 2 2 2 1,1+ XF2,1 XF3,1 XF + 2 2 2 1,4 + XF2,4 XF3,4 19 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) XFs = Deand s, s Constraint 1- The flow sent fro all distribution centers to each arket has to be equal to its deand. Add solver tool: 1. File 2. Options 3. Add-Ins 4. Select solver add-in 5. ClickGo 6. ClickOK 20 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) XFs = Deand s, s Constraint 1- The flow sent fro all distribution centers to each arket has to be equal to its deand. Click Data and then Solver 21 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) Cell defining the obective function Define the obective Cells representing the variables Constraints Linear odel 22 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) XFs = Deand s, s Constraint 1- The flow sent fro all distribution centers to each arket has to be equal to its deand. Repeat to other arkets and scenarios 23 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) XD is CPP i i, s Constraint 2- The flow sent fro each plantito all distribution centers has to be lower or equal to its production capacity. XD + 1 1 1 1,1+ XD1,2 XD1,3 XD + 2 2 2 1,1+ XD1,2 XD1,3 XD + 1 1 1 2,1+ XD2,2 XD2,3 XD + 2 2 2 2,1+ XD2,2 XD2,3 24 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) XD is CPP i i, s Constraint 2- The flow sent fro each plantito all distribution centers has to be lower or equal to its production capacity. Repeat to other scenarios and plants 25 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) i XD = is XF s Constraint 3- The flow that arrives to a distribution centerhas to be equal to the flow that leaves it. 1 XD 1,1+ XD 1 2,1, s XD + 2 2 1,1 XD2,1 1 XD 1,3+ XD 1 2,3 XF + 2 2 2 2 1,1+ XF1,2 + XF1,3 XF1,4 XF + 1 1 1 1 3,1+ XF3,2 + XF3,3 XF3,4 26 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) i XD = is XF s Constraint 3- The flow that arrives to a distribution centerhas to be equal to the flow that leaves it., s Repeat to other distribution centers and scenarios 27 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) XF s CPD Y, s Constraint 4- The flow that leaves each distribution center has to be lower or equal to its capacity, if that distribution center is built. Repeat to other distribution centers and scenarios 28 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) Constraint 5- Variables definition. Define binary variables 29 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) Define the obective 1 1 CT ( distp 1,1 XD 1, +... + distp 2,3 XD 1 2, 3 ) CF + 1Y1 + CF2Y2 CF3Y3 30 SCM/IST IST Lisbon Ana Carvalho 2015
Matheatical Model Ipleentation b) Run solver 31 SCM/IST IST Lisbon Ana Carvalho 2015
Results Scenario 1 Total Cost: 567,192.5 Plants operating: Porto DC: Paris & London 32 SCM/IST IST Lisbon Ana Carvalho 2015
Results Scenario 2 Total Cost: 567,192.5 Plants operating: Porto & Lisbon DC: Paris & London 33 SCM/IST IST Lisbon Ana Carvalho 2015
What else could have been included in the odel? Possible locations for new distribution centers Better estiation for distances Transportation odes Expanding capacities Direct shipents And so on But reeber coplexity increases 34 SCM/IST IST Lisbon Ana Carvalho 2015
Conclusions Through network planning, firs can globally optiize supply chain perforance. Matheatical odels can describe the supply chains network and help in the optiization of the supply chain. The atheatical odels can be ipleented in coputational software in order to optiize. Attention to non-linear probles: the solution achieved ight not be the global optiu. 35 SCM/IST IST Lisbon Ana Carvalho 2015