Supply Chain Scheduling Just In Time Environment

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Supply Chain Scheduling Just In Time Environment

• Chelliah Sriskandarajah
• School of Management
• University of Texas at Dallas
• Joint
  work with Manoj, U.V, Gupta, J.N.D, Gupta. S

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Problem
Manufacturer
Distributor
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Conflict in supply chain Scheduling

• Conflict arises when the dominant member in the
  supply chain imposes its preferred schedule on
  the non dominant member.
• Consequences of conflict are
• Increase in cost for non-dominant members
• Decrease in overall performance of the supply
  chain
• Increased cost measures of the supply chain
• Conflict can be resolved by co-ordination between
  members
• Sharing of surplus is a method to resolve
  conflict

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Issues addressed

• Two Stage supply chain (manufacturer and
  distributor)
• Conflicting Objectives
• Manufacturer Minimize his production cost
• Distributor Reduce the inventory holding cost.
• Each members objective to minimize his
  individual cost leads to supply chain conflict
• Can cooperation reduce overall cost?
• Discuss a cooperation mechanism that would
  minimize the total system cost.

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Single Assembly line- Multiple Products

• Toyota Global Body Line, Georgetown Kentucky
  Camry and Sienna (mini van) (Source Wards Auto
  World)
• Chrysler Windsor, Ontario Minivans and Pacificas
  (Source Industrial Engineer)
• NIMS, Nissan Motors Canton, Mississippi Quest,
  Altima, Armada. (Source www.nissannews.com)

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Toyota

• Global Body Line, Kentucky U.S.A
• Introduced Sienna in 1998 on this line
• Produces Sienna and Camry
• Camry and Sienna are based on the same platform
• Van uses 3L-V6 engine that powers
  the-top-of-the-line Camry
• Sienna 8 in. longer, 12 in. taller, 3.3 in. wider
  weighs 745 lbs. heavier
• Overall rate for example 14
• Net increase of only seven workers/ shift
• Motomachi Plant, Japan
• Produces RAV4 and Ipsum (minivan)

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Just In Time Production Plan- an example

• Demand 9,600 cars/month
• 20 working days/month
• 8 hours/day 480 min/day
• Monthly Demand for car type
• A 4800 Car Model A
• B 2400 Car Model B
• C 1200 Car Model C
• D 600 Car Model D
• E 600 Car Model E
• Minimum Product Set 8A, 4B, 2C, 1D, 1E

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An illustration Example 1
Total P1 250, P2 250 C100 P1 P2 11
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50 P1 50 P2
50 P1 50 P2
50 P1 50 P2
50 P1 50 P2
50 P1 50 P2
Manufg Dominates
(50,50,50,50,50)
30 P1 70 P2
40 P1 60 P2
80 P1 20 P2
70 P1 30 P2
30 P1 70 P2
Disb Dominates
100 units
100 units
100 units
100 units
100 units
(30,40,80,70,30)
Prdn. Period
1
2
3
4
5
30 P1 70 P2
40 P1 60 P2
80 P1 20 P2
70 P1 30 P2
30 P1 70 P2
R1
R2
R3
R4
R5
Distribution Cycle
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Costs

• Manufacturer ( )
• Rate change involves cost in organizing the
  required parts, coordinating the change with the
  suppliers, mobilizing extra resources etc.
• Installing roof molding for Sienna requires the
  worker to stand on a platform dolly but if Camry
  comes next then he will have to get down from it.
  Sienna requires specialized work force to do the
  rear strut job and these work force is idle if
  Camry comes next.
• (source Wards Auto World)
• Since rate change cost is the only cost
  associated with scheduling all other production
  costs are assumed constant.

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Costs

• Distributor Inventory holding cost. (h1 , h2
  and h1 h2 )
• System Manufacture cost Distributor cost

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Assumptions

• Demand for a problem horizon is known in advance.
• Each retailer gets one truck load in a period.
• This assumption is not restrictive. If a retailer
  requires multiple truck loads, then the retailer
  can be treated as multiple retailers, each with a
  demand of one truck load
• Demand is in multiple of truck loads
• Capacity matches demand.

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Example 2D1(7,4,5,4) D2(3,6,5,6) C 10 P1P220

• ss1(5,5,5,5) (1,3,2,4)

h11 ,h23 Number of rate change 1
H111/2(27) 1/2(05) 1/2(05)
1/2(16)13 H231/2(05) 1/2(27) 1/2(27)
1/2(16)45 Total Avg. inv.H1H2 58 Total rate
change cost110 10 Total system cost 68
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D1(7,4,5,4) D2(3,6,5,6) C 10 P1P220

• s(v)(7,5,4,4) ? (1,3,2,4)

h11 ,h23 Number of rate change 3
H111/2(70) 1/2(50) 1/2(40)
1/2(40)10 H231/2(03) 1/2(05) 1/2(06)
1/2(06)30 Total Avg. inv.H1H2 40 Total rate
change cost 10330 Total system cost 70
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• D1(7,4,5,4) D2(3,6,5,6) C 10
• P1P220

• (6,6,4,4) ?( ) (1,3,2,4)

h11 ,h23 Number of rate change 2
H111/2(71) 1/2(60) 1/2(51)
1/2(51)13 H231/2(04) 1/2(15) 1/2(06)
1/2(06)33 Total Avg. inv.H1H2 46 Total rate
change cost 10220 Total system cost 66
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Overview

• Motivation
• Problem definition
• Literature Review
• Distributors Problem
• Manufacturers Problem
• Coordination
• Computational study
• Conclusion

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Problem Scenario

• Two closely related products P1 and P2
• Manufactured sequentially on the same production
  line.
• pij rate of production of product j on period i.
• Production during a period equals, C, the truck
  capacity
• pi2 C pi1
• Demand for product Dj (d1j, d2j, dnj), j1,2

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Problem Scenario

• Transportation is done by a 3rd party
  distributor.
• Once each periods production is over its shipped
  to retailers (n)
• Inventory is the responsibility of the
  distributor (bundling operation).

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Literature Review

• Munson et al., 1999 Discuss the use and abuse of
  power in supply chains
• Banker Khosla, 1995 motivate coordination
• Chandra Fisher, 1994 production-distribution
  systems
• Hall C.N.Potts, 2003 benefits of coordination
• Chen Vairaktarakis, 2004 integrated scheduling
  model with production and distribution
  operations.
• Dawande et al, 2004 studied conflict between
  manufacturer and distributor
• Chen, 2004 Integrated Production and
  Distribution Operations Taxonomy, Models and
  Review
• Chen Hall, 2004 Supplier- Manufacturer
  Co-ordination
• Thomas Griffin, 1996 Review Paper. They
  address the need for research in the area of
  operational supply chain

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Distributors problem

• Manufacturer dominates and decides its production
  schedule.
• Given a manufactures schedule find a distribution
  sequence that will minimize its inventory
  carrying cost.

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Manufacturer Dominates- Distributors Problem
C3, n3

• One rate change at the beginning
• Manufacturers schedule -
• Distributor determines his optimal schedule -
• Objective minimize the total inventory cost -

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Inventory Diagram Example 1
C100
?(s) (1,4,5,3,2) D1 (30,40,80,70,30) D2
(70,60,20,30,70) s s1 (50,50,50,50,50) s2
(50,50,50,50,50)
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Solving Distributors problem
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Problem NP Hard

• Theorem For the production rate sequence
• finding the
  distributors sequence is strongly NP-hard
• Proof It can be shown that Numerical Matching
  with target sums (NMTS) reduces to the problem.

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Numerical Matching with Target Sums (NMTS)

• X x1, x2, x3, xj,, xk,, xs-1, xs

Assume


Y y1, y2, y3, , yj,, yk,, ys-1, ys


Z z1, z2, z3, , zj,, zk,, zs-1, zs
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Reduction

• Creating an instance of distributors problem from
  NMTS
• L 3(XYZ)
• Z X Y
• K Max(z1, z2....zs), MC Capacity of
  Truck
• h12, h21

C2xi M L xi i1,2..,s C2yi M 2L yi
i1,2..,s C2zi M - 3L - zi i1,2..,s
C1xi M - L xi C1yi M - 2L yi C1zi M
3L zi.
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NMTS

• Decision Problem Given a set of retailers with a
  given set of demand for products P1 and P2, does
  there exist a sequence ?, such that the total
  inventory for the sequence, I(?), is less than
  or equal to D?
• D 4.5 Ms 13sL 3sK XZ
• M 3LZ

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NMTS

• It can be shown there exists a sequence ? such
  that I(?) D if and only if there exists a
  solution to the NMTS problem.

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Manufacturers problem

• Distributor dominates and dictates the production
  schedule for the manufacturer
• Given a distribution sequence find a
  manufacturing schedule that minimizes his rate
  change cost.
• Lemma 2 For any distribution sequence , there
  exists a rate sequence
  j 1, 2, where
• i 1, 2,.. , n j 1, 2 that minimizes
  the total inventory cost for the distributor.
• Lemma 3 There exists a distribution sequence
  with
  
  
• 
  such that retailers demands are served in the
  nonincreasing order
  (or nondecreasing order ) which minimizes the
  number of rate changes for the manufacturer.

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Distributor Dominates-Manufacturers Problem
C3, n3

• Frequent rate changes
• Distributors inventory is minimum
• Manufacturer has to find his optimal schedule
  s(?) given the distribution sequence ?.

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Inventory Diagram- Example1C100
4 rate changes
? (3,4,2,1,5) D1 (30,40,80,70,30) D2
(70,60,20,30,70) s s1 (80,70,40,30,30) s2
(20,30,60,70,70)
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Solving Manufacturers problem

• Theorem Manufacturers problem is solved if the
  distributor serves retailers in the nonincreasing
  (nondecreasing) order of their order size
• Consider two sequences which gives the same
  inventory holding cost
• s1 (30, 80, 30, 70, 30) number of rate
  changes 5
• s1 (80, 70, 30, 30, 30) number of rate
  changes 3

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Cooperation

• Manufacturer and distributor cooperates and take
  combined decisions
• The non-dominating member pays dominating member
  an incentive to deviate from his preferred
  schedule. This will bring down the system cost.
• Theorem The system problem of finding the
  sequence combination ( v( )) to minimize
  the total system cost, S( ) T( v( ))
  is strongly NP-hard.

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Inventory Diagram Example1C100
Number of rate changes 3
?( ) (1,3,4,2,5) D1 (30,40,80,70,30) D2
(70,60,20,30,70) s1 (30,75,75,35,35) s2
(70,25,25,65,65)
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Conflict
Example 1
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Computational Study

• Integer programs for the Manufacturers and
  system problem are solved to optimality using
  CPLEX 8.01
• Data sets ,Dj j 1, 2 (integer) are generated
  randomly from a U10 95 distribution with C100
  and 25
• Five different problem instances are generated
  for each chosen value of n (9,8,7,6)
• Three different sets of holding costs tested
  (h11, h21), (h11.5, h21), (h12, h21) for
  all problem instances generated.
• Found conflict and the system surplus

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Conflict

• Conflict measures the increase in cost for the
  non-dominant member for following the rules set
  by the dominant member.

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Surplus

• Surplus when manufacturer dominates
• Surplus when Distributor dominates

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Surplus
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Co-ordination mechanisms

• It may not be possible for the non-dominating
  member to persuade the dominating member to
  accept the co-ordination schedule just by paying
  for its increased cost. It may require sharing of
  the surplus.
• Depending on the relative bargaining power of the
  non-dominant member he will share his surplus
  with the dominant member.
• Co-ordination requires sufficient information
  flow within the supply chain

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Conclusion

• Studied Manufacturers and Distributors problem in
  a Just In Time environment with deterministic
  data.
• Proved Distributors problem is NP-Hard
• Provided a polynomial time algorithm for
  Manufacturers problem
• Proved System problem is also NP-Hard
• Showed a positive surplus in the system
• Showed there always exists a chance for
  co-ordination due to the positive surplus.

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My Research in Supply Chain area

• Rajamani, D., Geismar, H. N. and Sriskandarajah,
  C., A Framework to Analyze Cash Supply Chains,
  Production and Operations Management, Feature
  issue on closed-loop supply chain, 2006, to
  appear.
• Dawande, M., Geismar, H. N., Hall, N.G. and
  Sriskandarajah, C.,Supply Chain Scheduling
  Distribution Systems, Production and Operations
  Management, (under review).
• Manoj, U.V., Gupta, J.N.D., Gupta, S. and
  Sriskandarajah, C.,Supply Chain
  SchedulingJust-in-Time Environment, Annals of
  Operations Research, (under review).
• Geismar, H. N., Laporte, G., Lei, L., and
  Sriskandarajah, C., The Integrated Production and
  Scheduling Problem for a Product with Short Life
  Span and Non-InstantaneousTransportation Time,
  INFORMS Journal on Computing, (under review).
• Gale, T., Rajamani, D. and Sriskandarajah, C.,
  The Impact of RFID on Supply ChainPerformance,
  Production and Operations Management, (under
  review).
• Geismar, H.N., Dawande, M, Rajamani, D. and
  Sriskandarajah, C. Efficient Cash Supply Chain
  Models in Response to New Federal Reserve
  Policies Basic Model", Working Paper, October
  2005.
• Geismar, H.N., Dawande, M, and Sriskandarajah,
  C., Efficient Cash Supply Chain Models in
  Response to New Federal Reserve Policies
  Custodial Inventory, Working Paper,October 2005.

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My Research in Production Scheduling area

• Geismar, H. N., Dawande, M. and Sriskandarajah,
  C., Throughput Optimization in Con-stant
  Travel-Time Dual gripper Robotic Cells with
  Parallel Machines, Production andOperations
  Management, 2006, to appear.
• Dawande, M., Geismar, H. N., Sethi, S.P. and
  Sriskandarajah, C., Sequencing and Scheduling in
  Robotic Cells Recent Developments, Journal of
  Scheduling, (2005), 8, pp. 387-426.
• Kumar, S., Ramanan, N., and Sriskandarajah, C.,
  Minimizing Cycle Time in Large Robotic Cells, IIE
  Transactions, 2005, 37, 2, pp. 123-136.
• Sriskandarajah, C., Drobouchevitch, I., Sethi,
  S.P. and Chandrasekaran, R., Scheduling Multiple
  parts in a Robotic Cell Served by a Dual Gripper
  Robot, Operations Research, (2004), 52, 1, pp.
  65-82.
• Geismar, H. N., Sriskandarajah, C. and N.
  Ramanan, N.,Increasing Throughput for Robotic
  Cells with Parallel Machines and Multiple Robots,
  IEEE Transactions on Automation Science
  Engineering, (2004), 1, 1, pp. 84-89.
• Dawande, M., Sriskandarajah, C. and Sethi, S.P.,
  On Throughput Maximization in Constant
  Travel-Time Robotic Cells, Manufacturing and
  Service Operations Management, (2002), 4, 4, pp.
  296-312.
• Kamoun, H., Hall, N.G. and Sriskandarajah, C.,
  Scheduling in Robotic Cells Heuristics and Cell
  Design, Operations Research, (1999), 47, pp.
  821-835.
• Hall, N.G., Kamoun, H. and Sriskandarajah, C.,
  Scheduling in Robotic Cells Classification, Two
  and Three Machine Cells, Operations Research,
  (1997), 45, pp. 421-439.

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• Any questions?????