On Supply Chain Inventory Management Utilizing Extensions of the MultiProduct Newsboy Models

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On Supply Chain Inventory Management Utilizing
Extensions of the Multi-Product Newsboy Models
New Jersey Institute of Technology 2506 GITC,
University Heights Newark, N.J. 07102.
Tel [phone] Email mko3_at_njit.edu,
layek.abdel-malek_at_njit.edu
Mojisola Kike Otegbeye Layek L. Abdel-Malek
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Presentation Outline

• Goal of the Research
• Relevance to SCIM
• Literature Review
• Research Focus
• The Newsboy Dilemma
• The Basic Newsboy Model

3
Presentation Outline

• Research Extensions
• Separable Programming Duality Concepts
• The Model
• Problem Formulation
• Possible Cases
• Supplier Selection

4
Presentation Outline

• Illustrative Example
• Experimental Instances
• Flow Diagram of Methodology
• Conclusion/Future Extensions
• Discussion

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Goal of the Research

• Establish a single period ordering strategy.
• Competing suppliers with random yields.
• Simultaneously select vendor and establish lot
  size.

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Relevance to SCIM

• Global orientation and e-bidding practices.
• Increase competition amongst suppliers.
• Optimum supplier selection lot sizes imperative
  for SCIM success.

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Literature Review

• Hadley Whitin (1963).
• Extensions to Hadley Whitin prior to 1999
  (Mouaz Khouja, 1999).
• Optimal heuristic solutions (Erlebacher, 2000).

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Literature Review

• Investment strategies for manufacturing firm
  (Harrison et al., 1999).
• Revenue sharing between vendor manufacturer
  (Pasternack, 2001).
• Graphical analysis of solution space (Abdel-Malek
  et al., 2005).

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Literature Review

• Early studies on ordered ? received (Silver,
  1976).
• Utilized general EOQ model.
• µ s only additional EOQ factors.

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Literature Review

• Early extension to Silver using Newsboy (Noori et
  al., 1986).
• Two cases considered
• s independent of quantity ordered
• s proportional to quantity ordered
• µ usually s only additional factors.

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Literature Review

• Shift in purchase practices to auctions.
• Most notable is e-bidding.
• Increasing lack of trade commitments.
• Profit maximizing mechanisms for seller.
• Optimal strategies for buyer at infancy.

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Research Focus

• Reduce objective function to separable form.
• Express problem as functions of resource duals.
• Competing supply sources for each item.
• Different supply yield cost structures.

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The Newsboy Dilemma
Holding cost

Excess
Place order ahead of demand
Sell within single demand period
Shortage
Lost Opportunities
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The Basic Newsboy Model

• Common form of multi-product Newsboy.
• Min
• Max

(1)
(2)
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Research Extensions

• Uniformly distributed supply with yield rates
  .
• Each item - more than one supplier.
• Constrained decision environment.

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Research Extensions

• The extended Newsboy problem

(3)
Subject to
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Research Extensions

• And in quadratic form Eqn (3) becomes

(4)
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Research Extensions

• For uniform demand supply

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Separable Programming Duality Concepts

• Objective function of form
• Thus, decentralized
  Lagrangian.

(5)
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Separable Programming Duality

• Evan L. Porteus (2002)
• If each maximizes over xtj , then
  the
• vector will
  maximize the
• Lagrangian over the Cartesian product
• Basis on which model is built.
  

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The Model

• Separable programming duality.
• Separable problems of each item.
• Duals of resources as variables.
• Reveals infeasible orders quickly.
• Reveals unbinding resources quickly.

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Problem Formulation

• For N items each having n supply sources, the
  decentralized Lagrangian functions are given by
• 1,, N and j 1,, n

(6)
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Problem Formulation...

• The optimizer can be obtained from
• 
  1,, N and j 1,, n
• From which

(7)
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Problem Formulation

• Substituting for in the constraints, we
  arrive at the following solution matrix.

(8)
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Possible Cases

• Case 1
• Take zero lower bound.
• Delete items from order list.
• Compute new with remaining items.

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Possible Cases

• Case 2
• Resource not binding.
• Set dual to zero minimum value.
• Obtain new values for remaining

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Supplier Selection

• First phase.
• Supplier cost yield structures determinants.
• Operational constraints relaxed.

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Supplier Selection

• Ordering costs Vs yield reliability (Abdel-Malek
  et al., 2004).
• Supplier gets all or nothing (0, 1).
• Two competing suppliers/item.

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Supplier Selection...

• Assignment constraints given by
• , ,
  ,

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Illustrative Example

• Example 1
• Number of items 3
• Budget 1600
• Available Space 1000m2
• Item 1 6m2, Item 2 10m2, Item 3 4m2

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Illustrative Example...

• Uniformly distributed demand supply.
• 2 competing suppliers/item.
• 1,2 - item 1
• 3,4 item 2
• 5,6 item 3
• Different supply yield cost structures.

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Illustrative Example...

• Table 1 Pertinent data for Example 1

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Illustrative Example

• From assignment constraints
• Supplier 1 - item 1
• Supplier 4 - item 2 and
• Supplier 6 - item 3.

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Illustrative Example

• Note
• Suppliers 1 2 - same yield variance
• Supplier 1, yield rates (0.6, 0.9) at 11.5
• Supplier 2, yield rates (0.4, 0.7) at 11.32
• For 10.9, supplier 2 selected

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Illustrative Example

• Resulting equations from solution matrix
• And from which

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Illustrative Example

• Unbinding budget constraint
• Set its dual to zero
• Compute new dual for space

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Illustrative Example

• Solving for optimal order quantities

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Illustrative Example

• Infeasible orders for items 1 3
• Compute new space dual
• Compute new order for item 2

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Illustrative Example

• Optimal ordering strategy
• 143 units of item 2 from supplier 4
• No order for 1 3
• Total expected cost (TEC) of 10,239
• Other alternatives give higher TEC.

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Experimental Instances

• Table 3 Study on how yield structures costs
  influence supplier selection.

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Experimental Instances...

• Interactions between yield rates, costs.
• For same costs, higher yield wins.
• Competitive pricing could favor lower yield.
• Trade off between cost and yield structures.

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Experimental Instances...

• Fig 1 How suppliers costs influence supplier
  selection for item 5

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Flow Diagram of Methodology

Select Vendor
Compute All ?
Set to zero
NO
YES
Set to zero
Compute All ?
NO
YES
Optimal solution
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Conclusion/Future Extensions

• Cases of random yield
• Supplier selection
• Supplier cost yield structures
• Supplier capacity
• Optimum supplier mix
• Other distribution functions

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Discussion

• Discussants
• Charles Corbett, UCLA, USA
• Patrik Tydesjö, Lund University, Sweden