A COLUMN GENERATION FOR LOCOMOTIVE SCHEDULING PROBLEM IN MOLTAN IRON TRANSPORTATION

A COLUMN GENERATION FOR LOCOMOTIVE SCHEDULING PROBLEM IN MOLTAN IRON TRANSPORTATION

PICK UP DELIVERY

Problem Statement Finding one feasible schedule for each locomotive in order to satisfy all moving requests and in such a way that the concerned costs are minimized and algorithm is capable of solving problems in reasonable computation time.Three stepsPots of molten iron from blast furnace are allocated to steel making furnace Torpedo cars are scheduled to load pots of molten metallocomotive are allocated to torpedo car moving request and routes are establishedEmpty and loaded cars can not tow together Empty and loaded cars towed through different tracksEnergy loss is considered Waiting and transportation time is limitedThe moving requests, including moving loaded torpedo cars with molten iron form blast furnaces to steelmaking plants, and moving the empty torpedo cars from steelmaking plants to blast furnacesLet R{L} denote the set of moving loaded torpedo cars with hot molten iron, R {E} denote the set of moving empty torpedo cars.PROBLEM DESCRIPTIONLSP locomotive scheduling problemsSet of moving request {R}to be transported by set of locomotive {L} each moving request r is composed of two task pick up at origin track r+ and delivered to destination track r- RL Loaded torpedo carsRE empty torpedo cars

Direct delivery r+ , r-First in first outFirst in last outCapacity and operation constraintsCost structure

heat energy loss of each loaded torpedo during transportation Molten iron degradation cost due to the delay for drainingafter loadingmolten iron, each loaded torpedo car should be movedfrom the bottom of the blast furnace within a given timeinterval which is termed pickup time window

Assign schedule s is shortest path problem and NP-hard in strongmultidimensional label (i, R,T, C) represent the status of a partial schedule s for a locomotiveLabel L1 = (i1, R1, T1, C1) dominates label L2 = (i2, R2, T2,C2) if i1=i2, R1=R2, and T1