THE INVENTORY ROUTING THE INVENTORY ROUTING PROBLEMPROBLEM

Presented by:Presented by:I.Esra Buyuktahtakin

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OUTLINEOUTLINE

• Vendor Managed Inventory ReplenishmentVendor Managed Inventory Replenishment• Inventory Routing ProblemInventory Routing Problem• Review of Related ResearchReview of Related Research• Solution ApproachesSolution Approaches

• ConclusionConclusion

Savelsbergh,2003

Conventional Inventory Conventional Inventory ManagementManagement

• Customer– monitors inventory levels

– places orders

• Vendor– manufactures/purchases product

– assembles order

– loads vehicles

– makes deliveries

You call - We haulYou call - We haul

Savelsbergh,2003 4

Problems with Conventional Problems with Conventional Inventory ManagementInventory Management

• Large variation in demands on production and transportation facilities– production costs

– transportation costs

– inventory costs

• workload balancing

• utilization of resources

• urgent vs nonurgent orders

• setting priorities– shortage costs

Savelsbergh,2003 5

Vendor Managed InventoryVendor Managed Inventory

• Customer– trusts the vendor to manage inventory

• Vendor– monitors customer’s inventory

– controls inventory replenishment & decides• which customers to replenish

• when to deliver

• how much product

You rely- We supplyYou rely- We supply

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Advantages of VMIAdvantages of VMI• Customer

– less resources for inventory management– assurance that product will be

available when required

• Vendor– more freedom in when & how to manufacture

product and make deliveries– better coordination of inventory levels

at different customers– better coordination of deliveries to

decrease transportation cost

Win - WinWin - Win

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Inventory Routing ProblemInventory Routing Problem

• Inventory routing problem is one of the core problems that has to be solved when implementing VMI

• IRP adresses the coordination of inventory management and transportation

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Inventory Routing ProblemInventory Routing Problem

Customer Satisfaction– product availability– timeliness and consistency of the delivery– ease of placing orders

• IRP (when solved) provides improvements on these factors

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Applications of IRPApplications of IRP

• Industrial GasesIndustrial Gases

– air products distribution

– carbon black distribution

• Petrochemical industry

– gas stations

• Automotive Industry

– parts distribution

• Food Industry

• Blood collection

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Inventory RoutingInventory Routing Problem Problem

– single / multiple facilities

– single / multiple customers

– single / multiple products

– planned time horizon

– set of limited / unlimited homogenous vehicles of capacity Q Cost elements

•Transportation cost•Shortage cost•Inventory Holding cost

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Inventory Routing ProblemInventory Routing Problem

• Objective– Minimize distribution costs without

causing any stock-outs over a planning period

or

– Maximize the total profit (revenue minus costs) over a planning period

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Inventory Routing ProblemInventory Routing Problem

It is a challenging and intriguing problem that requires the integration of inventory

management and transportation decisions

Three decisions have to be made:When to deliver?

How much to deliver?

Which delivery routes to use?

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Inventory Routing ProblemInventory Routing Problem

• In real life IRP is a long term dynamic and stochastic control problem

• So, it is extremely difficult to solve

• Simplifying assumptions are considered in the earlier studies

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Reference Demands Vehichles Horizon Delivery Contribution

Fisher et al. (1983) Deterministic Limited Short Multiple PolicyFedergruen and Zipkin (1984) Stochastic Limited Short Multiple PolicyGolden, Assad and Dahl (1984) Deterministic Limited Short Multiple PolicyBurns et al. (1985) Deterministic Limited Short Direct, Multiple BoundDror, Ball and Golden (1985) Deterministic Limited Reduced Multiple PolicyDror and Levy (1986) Deterministic Limited Reduced Multiple PolicyDror and Ball (1987) Stochastic Limited Reduced Multiple PolicyChien, Balakrishnan and Wong (1989) Deterministic Limited Reduced Multiple PolicyAnily and Federgruen (1990) Deterministic Unlimited Long Multiple Bound and PolicyGallego and Simchi-Levi (1990) Deterministic Unlimited Long Direct Bound Trideau and Dror (1992) Stochastic Unlimited Reduced Multiple PolicyAnily and Federgruen (1993) Stochastic Unlimited Long Multiple Bound and PolicyBramel and Simchi-Levi (1995) Deterministic Unlimited Long Multiple Bound and PolicyJaillet et al.(1997) Stochastic Limited Reduced Multiple PolicyViswanathan and Mathur(1997) Deterministic Unlimited Long Multiple Bound and Policy

Problem Characteristics Considered by Previous Researchers

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Solution ApproachesSolution Approaches

• Deterministic– Based on average product usage

• Stochastic– Based on probability distribution of product

usage• future usage amount is random

• current inventories are modeled as known

Savelsbergh et al.,2000 16

Deterministic Solution Deterministic Solution ApproachesApproaches

Two Phase Approach

– Phase I: Determine which customers should receive a delivery on each day of the planning period and how much

– Phase II: Construct the precise delivery routes for each day

Savelsbergh et al.,2000 17

Deterministic Solution Deterministic Solution ApproachesApproaches

Two Phase Approach

– Phase I: Integer Program

– Phase II: Insertion Heuristic

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Solution ApproachesSolution Approaches

• Short term In the previous studies many solution approaches are proposed to solve short

term planning problem

– single day• an extension of VRP• based on latest inventory reading and predicted usage for that day• much simpler• useful when demand is unpredictable

– a couple of days• much harder• much better solutions• formulated as mathematical programs• solved using decomposition techniques, such as Lagrangean relaxation

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Solution ApproachesSolution Approaches

• Long Term– some researchers model the objective of

maximizing the profit over a long period of time

• Reduced– consider the proper projection of a long term

objective into a short term planning problem

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Some topics to investigateSome topics to investigate

• The effects of the changes in

operating modes

ex: changes in cost factors• The importance of the factors which affect the

customer selection in a given route• Delivery time windows

– restricts when a customer can receive a delivery

THANK YOUTHANK YOU

Q & AQ & A