A heuristic for maritime inventory routing Oddvar Kloster

A heuristic for maritime inventory routing Oddvar Kloster, Truls Flatberg Molde, 2009 -09 -22 ICT 1

Overview n n Background Model Algorithms Test example ICT 2

Invent n Software library to solve generic Inventory Routing Problems n Primary focus on routing and inventories n Upstream/downstream activity disregarded n Contractual and economic aspects n Tramp shipping, industrial shipping and combinations n Prototype with initial construction algorithm, genetic algorithm and nascent optimization n Three applications used as pilot studies n Cement - multiple products, short horizon, no spot n Chemical tankers - tramp and inventory, multiple products, cleaning, tank handling n LNG - single product, long term, contracts, full loads ICT 3

Model features (1) n Heterogeneous vessels n One or more tanks with volume capacities n Or, simple stowage (max products) n Ports, with storages n Variable production/ consumption rates n Partly interruptible n Storage capacities n Per-vessel time/distance/cost table ICT 4

Model features (2) n Multiple products n Keep track of quantity, weight and volume n Fixed or variable densities n Cleaning of tanks between products n Load and discharge rates n Boil-off n Product evaporates during sailing n Full vessel loads n Leave from production ports with full loads n Discharge completely in consumption port except for boil-off needs ICT 5

Model features (3) n Bookings n Transportation demands not related to storages n Contracts n Limit amount delivered to certain ports in certain periods n Define prices ICT 6

Model features (4) n n n n Priority on storages and contracts Arrival and departure load limits (draft restrictions) Port closure periods Vessel maintenance periods Vessel-port compatibility Restrict # visits to storage in period Inter-arrival gaps ICT 7

Plan structure Port Booking Port Storage Port stay Vessel Action ICT 8

Objectives n Basic objectives n Income (contract, stream, booking) n Cost (sailing, port stay, cleaning) n Performance (quantity transported) n Penalized constraints n Combined objectives n Weighted sum n Lexical (prioritized) ICT 9

Solution strategy n Work with concrete plans n Violate constraints by doing too little → penalize n Stockout/overflow n Unserviced booking n Contract limit not met n Too few visits in time period n Add activities, as efficiently as possibly n When doing too much, try delaying ICT 10

Construction: overview n Start with empty plan n Identify earliest (highest priority) penalty event n Stockout/overflow n Unserviced booking n Contract limit n Too few visits in time period n n n Generate journeys Rank journeys Add best journey and repeat If no fix found, forget event … until there are no more penalty events ICT 11

Construction: journey generation n One storage/booking/contract given n Choose n (Contract) n Counterpart storage n (Counterpart contract) n Vessel n Insertion points P 1 P 2 ICT 12

Construction: journey insertion n Large parts of the plan may be affected n Schedule for selected vessel changes after new load action n Schedules for other vessel are unchanged n Schedules may change for storages visited by selected vessel n Many constraints to satisfy n Roughly: n n n Assume small quantity and propagate time Find maximum possible quantity (including tank allocation) Set quantity, propagate time and quantities Insert tank cleaning actions Check feasibility If necessary, delay and repeat ICT 13

Construction: journey ranking n Evaluate criteria for each journey n Transport large quantity n Short sailing time n Large quantity/vessel capacity n Large quantity/sailing time n Low cost/quantity n. . . n Random n Sort journeys for each criterion n Final score is weighted sum of ranks ICT 14

Genetic algorithm n Population of individuals n Each individual’s genome is a set of weights n Fitness of each individual is evaluated by applying the construction algorithm n Weights for new individuals drawn around parents’ weights (+ mutation) ICT 15

Optimization n Remove a bit of the solution n Any journey starting or ending in random (~10%) interval n Compact solution n Regenerate the missing part n Use criteria weights from the best GA individuals n Accept if better or promising n Avoid known solutions n by objective value ICT 16

Test case n LNG. 1 product, boil-off, full loads n 2 production ports n Fixed purchase price n Fixed production rate n 2 consumption ports n Some interruption allowed n Fixed sales price on send-out n 3 identical vessels n 360 day horizon ICT 17

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Example run (GA) 2. 80 E+08 2. 60 E+08 2. 40 E+08 Objective 2. 20 E+08 2. 00 E+08 1. 80 E+08 1. 60 E+08 1. 40 E+08 0 5 10 15 20 Time (sec) 25 30 35 ICT 40 45 20

Example run (optimization) 2. 80 E+08 2. 60 E+08 2. 40 E+08 Objective 2. 20 E+08 2. 00 E+08 1. 80 E+08 1. 60 E+08 1. 40 E+08 0 5 10 15 Time (sec) 20 25 ICT 30 21

A heuristic for maritime inventory routing Oddvar Kloster, Truls Flatberg Molde, 2009 -09 -22 ICT 22