Collaborative LogisticsRicha AgarwalSchool of Industrial & Systems EngineeringGeorgia Institute of TechnologyWhy collaborate? Increasing pressure on companies to operate more efficiently Increasing pressure from customers for better service Realization that suppliers, consumers, and even competitors, can be potential collaborative partners Connectivity provided by the InternetHorizontal Collaboration Buyers’ collaboration Group Purchasing Organizations (GPO) Joint procurement of goods Economies of scale Example – automotive industry, healthcare industry Logistics exchanges: shippers’ collaboration Joint procurement of services  Operational synergies Example - truckingHorizontal Collaboration Sellers’ collaboration Alliances among carriers Coordinate/regulate prices Operational synergies Example – airlines’, ocean-carriers, and trucking companiesVertical Collaboration Sellers collaborating with buyers Vendor managed inventory Information sharing Operational synergies Example – one supplier and one buyer, one supplier and multiple buyers Logistics networks Operational synergiesTools Model and solve the underlying problems Optimization Allocate cost/benefit among members in a fairway for sustainable collaborations Concepts from cooperative game theoryOutline Cooperative game theory Shippers’ collaboration Trucking Finding the system optimal solution  Allocating cost/benefits Carriers’ collaboration Containerized sea-cargo Network design from an alliance perspective Shippers’ and carriers’ collaboration Trucking An exampleCooperative game theory A cooperative game is a game where groups of players ("coalitions") may enforce cooperative behavior. The game is a competition between coalitionsof players, rather than between individual players.Notation N – set of players (grand alliance) S – subset of N (sub-coalition) opt(S) – optimal value achieved by players in S {x1, x2, … xn} – payoff to playersSolution Concept: CorePk∈Sxk≥ opt (S)Pk∈Nxk=opt(N)StabilityBudget balanceCollaboration among ShippersTrucking industryTrucking IndustryEach shipper plans each shipment with only a handful of carriersEach carrier works with only a handful of shippersU.S. Truckload capacity moves empty nearly 20% of the time$165 billion + inefficiency yearlyHighly fragmented: 100,000+ shipper & 250,000+ CarriersAsset Repositioning Asset repositioning is a “hidden” cost that everybody pays for, but no one controls individually Neither shipper understands how its actions affect the costs of asset repositioning Carrier must optimize asset utilization to respond to both shipper requirementsTuesdayShipper AWednesdayThursdayShipper BShipper Collaboration Asset repositioning The cost of asset repositioning is included in the price charged by carriers Shipper collaboration By providing continuous moves shippers can negotiate better rates from carriers Increase the opportunities for continuous moves by collaborating Since no single player controls asset repositioning costs, they are a “hidden”cost paid for by all … this problem may be relieved through use of collaborationCollaborative LogisticsCollaborative Logistics Business Model Shippers collaborate with shippers and selected carriers Create and execute regularly scheduled and dynamic collaborative routes Major Benefits Reduced asset repositioning Cost reductions ~10%Continuous Move Example from Nistevo NetworkKentChicagoNew JerseyChicago: Land O’ Lakes packaging vendor Kent: Land O’ Lakes plantNew Jersey: Land O’ Lakes distribution centerThrough Nistevo a third company with New Jersey – Chicago traffic was identified• 2.5 % savings of Land O’ Lakes $40 - $50 million finished goods freight bill• Carrier avoids any empty movements and uses 1 truck instead of 2Goal: Collaborative RoutesCedar RapidsBangorWellsMechanicsburgChicagoBuffaloGreen BayCompany 1Company 2Stand AloneStand Alone$3,821K$3,821KTogetherTogether$3,090K$3,090KSavingsSavings$ 731K$ 731K19% Savings19% SavingsState-of-the-art Shippers meet quarterly Identify load matching opportunities Build regularly scheduled continuous moves Jointly negotiate with a carrier Allocate the costs among themselves Industry standard: proportional allocationsCollaborative Tours Optimization Problem Given a set of lanes, find a minimum cost set of routes covering all lanesTraversing a laneRepositioningLane Covering Problem (LCP) Given  A complete bidirected graph D=(N,A) A nonnegative cost cijfor each arc (i,j) A subset of arcs L (lane set) Find  A set of simple directed cycles (not necessarily disjoint) of minimum total cost covering all arcs in LLane Covering Problem  LCP can be solved in polynomial time: Solve min-cost network flow problem  Decompose the solution into simple cyclesDesigning a Sustainable Collaboration MechanismDesign a mechanism to allocate gains from collaboration such that All costs are allocated No one (no subset of the members) should have an incentive to break away from the collaboration.The Core Does there exist a cost allocation α in the core: The total payment collected from the shippers is equal to the total cost of covering all the lanes No group of shippers would be better off if they decided to opt out and collaborate only among themselvescost recovery budget balancecompetitiveness stabilityStable Cost AllocationCost of each lane = 1Total cost without collaboration = 6Total cost with collaboration = 4If blue + green collaborate, their total cost = 2If red + green collaborate, their total cost = 2Payment(blue + green) = 8/3 > 2Payment(red + green) = 8/3 > 2NOABIs an allocation of 4/3 per lane stable?Stable Cost Allocation?Primal problemDual problemCost Allocation From Dual Payment that is allocated for covering lane (i,j) ∈ L  Then Budget: Stable:Cost Allocation From Dual Given any S ⊆ L, let (lS,yS) be the optimal dual solution for the associated linear program LP(S) Note that the optimal solution (l,y) to the original dual when restricted to S is feasible for LP(S)Fair Cost Allocation Is this solution fair? By complementary slackness:If a lane is traversed more than once the cost allocated to that lane is 0Stable Cost AllocationABCost of each lane =