Supply chain and logistic optimization

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Supply chain and logistic optimization
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Road Map

• Definition and concept of supply chain.
• Primary tool box at strategic level (software).
• Models at strategic level.
• Models at tactical level.

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Potential of SCM

• A box of cereal spends, on average, more than 100
  days from factory to sale.
• - A car spend around 2 weeks from factory to
  dealer.
• National Semiconductor (USA) used air
  transportation and closed 6 warehouses, 34
  increase in sales and 47 decrease in delivery
  lead time.

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• Compaq estimates it lost 0.5 billion to 1
  billion in sales in 1995 because laptops were not
  available when and where needed.
• When the 1 gig processor was introduced by AMD
  (Advanced Micro Devices), the price of the 800
  meg processor dropped by 30.
• PG estimates it saved retail customers 65
  million (in 18 months) by collaboration resulting
  in a better match of supply and demand.

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• IBM claims that it lost a major market share for
  desktops in 93, for not been able to purchase
  enough of a display chip.
• US companies spent 898 B for SC activities in
  98. Out of the above 58 of SC costs were
  incurred for transportation and 38 for inventory.

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Advantage of low inventories

• Less time in storage less deteriorate-High
  quality.
• Effective distribution process (Fast delivery to
  customers)
• Switching from old technology to new technology
  without scraping lot of products.
• Of course less storage cost.

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• Gartner Group
• By 2004 90 of enterprises that fail to apply
  supply-chain management technology and processes
  to increase their agility will lose their status
  as preferred suppliers.
• AMR Research The biggest issue enterprises face
  today is intelligent visibility of their supply
  chains both upstream and down

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Why supply chain A tutorial
Supplier
Retailer
Demand
Retailer
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Traditional scenario
Demand (Q) A - BZ
Assume A 120
B 2
Supplier buys a goods at price
X Sells to retailer at a price
Y Retailer sells to customer at a price
Z
Retailers profit (R) (Z-Y) (A-BZ)
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Retailers profit (R) (Z-Y) (A-BZ) Y40
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Suppliers profit Q (Y-X)
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Retailers profit w.r.t. Y
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Combined profit
CP0.25 (A2 / B -2 . A .X 2 . B. X. Y B. Y2)
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Retailers profit w.r.t. Y
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Summery
Traditional scenario
Demand 20 units Retail price
50.0 Retailers profit 200.0 Suppliers
profit 200.0
Collaborative scenario
Demand 30 units Retail price
45.0 Retailers profit 225.0 Suppliers
profit 225.0
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Example

• A Retailer and a manufacturer.
• Retailer faces customer demand.
• Retailer orders from manufacturer.

Demand Curve
Variable Production Cost200
Selling Price?
Manufacturer
Retailer
Wholesale Price900
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Example

• Retailer profit(PR-PM)(1/0.22)(2,000 - PR)
• Manufacturer profit(PM-CM) (1/0.22)(2,000 - PR)
• Retailer takes PM900
• Sets PR1450 to maximize (PR -900)
  (1/0.22)(2,000 - PR)
• Q (1/0.22)(2,000 1,450) 2,500 units
• Retailer Profit (1,450-900)2,500 1,375,000
• Manufacturer takes CMvariable cost
• Manufacturer profit(900-200)2,500 1,750,000

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Example Discount

• Case with 100 discount
• New demand
• Q (1/0.22) 2,000 (PR-Discount) (1/0.22)
  2,000 (1450-100) 2954
• Retailer Profit (1,450-900)2,955 1,625,250
• Manufacturer profit(900-200-100)2,955
  1,773,000

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Wholesale discount

• 100 wholesale discount to retailer
• Retailer takes PM800
• Sets PR1400 to maximize (PR -800)
  (1/0.22)(2,000 - PR)
• Q (1/0.22)(2,000 1,400) 2,727 units
• Retailer Profit (1,400-800)2,727 1,499,850
• Manufacturer takes PR800 and CMvariable cost
• Manufacturer profit(800-200)2,727 1,499,850

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Global Optimization

• What happens if both collaborate (SCM)?
• Manufacturer sets PR1,100 to maximize (PM -200)
  (1/0.22)(2,000 - PM)
• Q (1/0.22)(2,000 1,100) 4,091 units
• Net profit (1100-200) 4,091 3,681,900

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Strategy Comparison
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Market Requirement

• Low price.
• High quality.
• Product customization.
• Fast delivery.
• Fast technology induction.

Strategy Right product Right quantity Right
customer Right time
Cost reduction and value addition at each stage
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• Sharing information will lead to reducing
  uncertainty for all the partners and hence
• - reducing safety stocks,
• - reducing lead times,
• - improving brand name.
• Result
• - Value added product/services
• - large market segment (Leading brand),
• - long lasting supply chain,
• - consistent and growing profits,
• - Satisfied customer.
• It is better to collaborate and co-ordinate to
  achieve a win-win situation.

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Definition
Supply Chain refers to the distribution channel
of a product, from its sourcing, to its delivery
to the end consumer. (some time referred as the
value chain)
A supply chain is a global network of
organization that cooperate to improve the flows
of material and information between suppliers and
customers at the lowest cost and the highest
speed.
Objective is customer satisfaction and to get
competency over others
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Supply chain
Information flow
Material Flow
Cooperation
Value addition
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Customer satisfaction
Cost
Value added product
Operational performance
Coordination
Information sharing
Assets Management (Inventory)
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Difficulties

• Increasing product variety.
• Shrinking product life cycle.
• Fragmentation of supply chain.
• Soaring randomness because of new comers.

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Responsiveness (High cost)
Zone of strategic fit
Low cost
Deterministic Uncertainty
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FMCG (Tooth paste, soaps etc )
Price sensitive, Low uncertainty
Fashionable products (Garments), customize
products etc
High responsiveness, high uncertainty
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Ineffective marketing
Wrong material
High Inventories
Low order fill rates
Supply shortages
Inefficient logistics
High stock outs
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• Local objectives vs Global objective

• Production
• - Low production cost.
• High utilization.
• High quality raw material.
• Big order size.
• Stable production.
• Short delivery lead times (Raw materials)

• Marketing
• - High inventories levels.
• Low prices.
• Ability to accept every customer order.
• Short product delivery lead times.
• Various order sizes and product mixes.

SCM is a tool which integrate necessary
activities and decomposing irrelevant activities.
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Management by departments
Management by projects
Finished products
Orders
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Primary decisions
Secondary decisions
Buy
Sell
Make
Move
Store
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Recruitment of employees
Salary, TA, DA
Training, relocation, etc
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Strategic models
Selection of providers

• Provider provides the quantity between two
  limits.
• Cost is a concave function of the shipped
  quantity.
• Objective is to select one or more provider to
  satisfy the demand.

• Case of single manufacturing unit.
• Case of several manufacturing unit.

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Cost function
Problem to be solved
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• Algorithm
• Select the cheapest provider if the quantity to
  be supplied is maximum.
• Adjust the remaining quantity among rest of the
  providers so that the solution remain feasible.

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Exact algorithm for the integer demand

• Compute the cost for the first provider for
  q1,2,A.
• For provider2,N
• - Compute the Q1,2,,A
• F(Pro,Q)Min0ltxltQ (F(Pro-1, Q-x), fpro(x)

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• Case of several manufacturing units

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Approches

• Heuristic approach.
• Piece wise linearization for integer programming.
• Bender decomposition.

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Capacity Planning
Providers
Retailers
Manufacturers
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• Idle processing capacity with providers in
  different periods.
• Idle transportation capacity with providers in
  different periods.
• Idle manufacturing capacity with manufacturers.
• Idle transportation capacity with manufacturers.
• Demand at various retailers and the demand of one
  period may differ from another period.

Objective is to decide how much and where to
invest.
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Supply lt Available Capacity Added
Capacity Added capacity lt BigNumber Binary
Variable 0,1 Investment Cost
BinaryVariableFixedCost SlopeAdded capacity
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Formulation
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• Results
• There exist at least one optimal solution in
  which all the binary constraints are saturated.
• Replacing big number by corresponding capacity,
  if greater than zero, and denote new problem by
  P2m, then m is definite.

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Approach

• Construct the several instances of the
  problem from the relaxed solution of
  the problem . These instance converge
  towards the solution of the problem P.
  Unfortunately, we do not know the conversion
  time.
• For this reason, we derive sub-optimal solution
  from the instances and select the best solution.

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Other approaches

• Langrangean heuristic approach to find good lower
  bound.
• Branch and price approach.
• Presented approach was similar to the
  langrangean approach.

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Short term supply chain formation

• Multi-echelon system.
• Selection of a partner from each echelon.
• Expected demand is known for a given horizon.
• Objective is not to invest at any location.
• - Utilization of idle capacity (Production,
  transportation, storage etc).
• Solution should be feasible for entire horizon.
• Decision Whether the new chain exists and
  profitable?

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Demand
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Costs

• Storage cost at entry and at exit (running).
• Production cost (running).
• Connection cost (Fixed)

Note It is possible that solution may not exist
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Minimisation
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Path relaxation approach

• Resolve two echelon problem for each pair of
  nodes using final demand.
• Consider the cost corresponding to these arcs as
  surrogate length.
• Solve the k-shortest path problem and compute the
  k-shortest path.
• For each shortest path, compute the real cost.
• If the relax path length is bigger than best real
  cost, stop.

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D1
D3
D2
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D1
D3
D2
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Demand
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Insertion of new project
1
2
3
1
2
3
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Problem data
1 (2, 1)
2 (5,1)
3 (2,0)
Solution
1
3
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Formulation
Min
s.t.

• An optimal algorithm is known for the above case.

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Simple assembly
Algorithm

• Computing two times Early start time Latest
  start time
• Select the common interval.

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Complex schedule
3
4
7
1
5
6
14
2
9
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12
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10
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Two approaches

• Simple- easy to program but time consuming.
• Little tidy difficult to program but on average
  performance is better.
• Both gives the optimal schedule.
• Worst case complexity is also same.

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Simple approach
1
14
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S1
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S2
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S3
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S4
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S5
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• For each assembly operation
• If the idle windows for two different lines are
  not the same then select the window which has
  higher lower limit (beginning time) and restart
  the calculation.
• If the windows are the same but starting time
  are different, then set the lower limit of this
  window as the greatest starting time of the two
  and restart the calculation.

If neither of the above case is present, then
the solution is optimal.
The algorithm converge towards an optimal
solution.
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Second approach

• Decompose the assembly into sub-assemblies.
• Solve the sub-assemblies.
• Coordinate the timing of sub-assemblies.

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• Recursive approach.
• Each time early start time (EST) and latest start
  time (LST) of assembly has to be computed.
• Advantage
• If the time lies between EST and LST then
  re-computation is not required.

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Second approach
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14
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WIP Control (Extension)
First case Number of finished jobs at the exit of
each machine is not limited in quantity but
limited by time.
Approach Introduce one virtual machine, following
the real machine with operation time 0 and
flexibility 0, T
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• Case 2
• Number of finished jobs are limited in time
  and in quantity too.
• Approach
• Introduce as many virtual machines as the
  number of finished jobs permitted.
• In both the cases, the algorithm presented
  before are applicable.

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Delivery date
Backlogging cost
Inventory holding cost
Instant of ordering
Delivery instant
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Three cots are to be considered I1, Inventory
cost between the arrival of first component and
last component. I2, Inventory cost between the
arrival of last component and the delivery
date. B, Backlogging cost if the last component
arrives after the delivery date.
Next
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is continuous and differentiable in R, 8
Basic property
1
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Propriété fondamentale

• Algorithme général
• Partir dune solution admissible.
• Chercher une solution admissible R1 du voisinage
  de R qui vérifié (1)
• Conserver ou rejeter R1 (recuit simulé)
• Retour à 2.

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• Algorithm
• Start with one feasible solution.
• (First feasible solution can easily be
  generated considering the same ordering time for
  all components.)
• 2. Define new solution R1 in the neighborhood of
  R that satisfies relation (1) (Use gradient
  method)
• 3. Conserve or reject R1 (Simulated annealing)
• 4. Go to 2.

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The behavior of cost I1 depends upon the density
function. The I1 may be convex or concave based
on the nature of density functions. Hence, with
an exact information of density functions an
specialize algorithm could have been devised.
With uniform densities, the problem can be solved
using gradient method only.
For general problem we proposed an approach based
on simulated annealing which looks, in each
iteration, for a closer solution which satisfies
the relation 1.
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Partnership formation A model
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Assumptions

• Customer is price sensitive.
• Average customer demand depleted as price
  increases.
• Customer demand is stochastic.
• Backordering cost at supplier is higher than at
  retailer.
• Inventory cost at supplier is cheaper than
  retailer.
• Inventory can be transferred between supplier
  and retailer in negligible time. In other words
  customer is ready to wait during the lead time.

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Example
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Model

• Each maintain a stock of Ip and Ir.
• Retailer pays for the holding and also pays for
  stock out.
• Supplier pays for holding and also pays for
  stock out. This stock out penalty goes to
  retailer (Compensation).
• Profit is shared according to their relative
  risk i.e. investment.

Objective is to maximize total benefit.
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• Fractional demand is given by f(wr), a concave
  function of selling price.

Fractional demand
Lost sell due to high price
Price wr
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Algorithm

• Take any starting price wr
• 2. Optimize Ip and Ir gt Ip and Ir , keeping Wr
  fix.
• Total profit function is convex w.r.t stocks and
  wr constant.
• 3. Optimize Wr, Ip and Ir are fixed.
• Combined profit function is concave w.r.t
  Wr.
• 4. Go to 2 until profit increases.

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Numerical illustration
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Continue
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Hot areas in SCM

• Dynamic pricing
• - Online bidding, (Ebay.com)
• - Price setting and discount for perishable
  goods in supermarket.
• - Customize pricing different prices for
  different customer segment.
• Inventory management in advance demand
  information sharing.