Transcript Supply Contracts with Total Minimum Commitments

Supply Contracts with Total
Minimum Commitments
Multi-Product Case
Zeynep YILDIZ
Outline
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Introduction
Traditional inventory models
Literature review for single product
Advantages of multi-product contracts
Literature review for multi-products
Model
Results and conclusion
Introduction
“According to Davis (1993) discussing HP’s
supply chain management problem: The real
problem with such a confusing network is the
uncertainty that plagues it. This uncertaintyobserved on a daily basis as late deliveries,
machine breakdowns, order cancellations,
and the like –leads to increased inventories.
In fact, inventory exists more or less as a
simple insurance against uncertainty”
Moinzadeh and Nahmias
Traditional Inventory Models
• Type of supply contracts with no commitments-Graves
et al.
• The classical newsvendor inventory problem
• Optimality of a base stock policy (Arrow, Karlin & Scarf,
1958)
• Total quantity purchased is unknown to the supplier
• Order previous period’s demand
• Uncertainty of demand directly passes to the supplier
• (s,S) policy, the variance of orders is even higher than
with a base stock policy (Moinzadeh & Nahmias)
• Bullwhip effect
Supply Contracts
“ However, in practice, many contracts
impose some restrictions on the buyer.
Usually, this takes form of commitments
by the buyer to purchase certain
minimum quantities”
Bassok and Anupindi, 1997
Literature review-Single Product
• Bassok and Anupindi (1997) analyzed a
single product contract where the
supplier offers discounts for a total
minimum quantity commitment
• They extended this single product
contract to allow for upper limits on the
total volume purchases that qualify for
discounted prices
Bassok and Anupindi, 1998
Literature review-Single Product
• Anupindi and Akella (1997) studied a class of
contracts that require the buyer to commit, at
the beginning of the planning horizon, to
purchase a certain minimum quantity in every
period of the horizon
• Reduce variance in order process to supplier
• Moinzadeh and Nahmias (1996) studied
continuous review model in which the buyer
makes a firm commitment to purchase a
certain minimum quantity at regular time
intervals
Bassok and Anupindi, 1998
Advantages of Multi-product Contracts
Supplier Base
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Increase total volume of business and market share
Increase market presence for higher priced products
Increase competitiveness
Ensure firm business for a finite horizon
Reduce order processing costs – packing(unpacking),
administrative and shipping costs
• Increase savings from manufacturing costs
• less setups
• larger production runs (especially if highly product specific)
• Product/process commonality in production
• FMS
Advantages of Multi-product Contracts
Buyer Base
• Small number of suppliers and closer cooperation
• Improved quality
• Improved service
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Greater assurance of supply
Pooling purchases-higher discount rates
Reduction in order processing costs
Associated risks
• Committing more than required-flexibility
• Increase in inventory holding costs-discounts
Literature review-Multi Product
• Sadrian and Yoon (1994)
• Problem of flexible procurement plan and changes in forecasted
demand and budget
• Procurement Decision Support System
• Multi-product multi-supplier contracts with discounts on total
dollar amount of sales volume
• Deterministic environment
• All product discount
• “minimize the total discounted purchasing cost, how many of
each product should be purchased from which supplier and
under which purchasing strategy, subject to fully satisfying the
demands, providing the required flexibility in the purchasing
plan, distributing the quantities to be purchased among several
suppliers in acceptable proportions, and possibly limiting the
total number of suppliers”
• Optimum product-supplier combinations under demand,
commitment, market share and maximum number of suppliers
constraints
Literature review-Multi Product
• Bassok and Anupindi (1998)
• Multi-period multi-product dynamic program
• Price discounts for total minimum dollar volume commitments
with flexibility
• Stochastic environment
• Optimal solution is complex
– Constrained dynamic program
– Allocation problem and decision in this period affects future
decisions
• Property of the optimal policy
• Approximations, order policy assumptions and uniform discount
policy
• Upper bound and lower bound for multi-product
small gap
• Computational study
– Demonstrate error because of approximations is small
– Managerial insights (effects of commitment, #of products on costs )
• Mean dollar volume commitments works quite well
Literature review-Multi Product
• (Qt,Mt)=
(0,0)
if It≥S∞
(S∞-It,0)
if S∞-KtL<It<S∞
(KtL,0)
if St-KtL<It<S∞-KtL
(St-It,0)
if St-KtU<It≤St-KtL
(KtU,0)
if Stm-KtU<It≤St-KtU
(KtU, Stm-KtU-It) o.w.
Where F(S∞)=/+h,
and, St is the base stock level in period t for a standard (N-t+1)
period newsboy problem with per unit order cost at c and,
Stm is the base stock level for a standard newsboy problem
with per unit order cost cr
Bassok&Anupindi,1998
Literature review-Multi Product
• Bassok and Anupindi (1998)
• Multi-period multi-product dynamic program
• Price discounts for total minimum dollar volume commitments
with flexibility
• Stochastic environment
• Optimal solution is complex
– Constrained dynamic program
– Allocation problem and decision in this period affects future
decisions
• Property of the optimal policy
• Approximations, order policy assumptions and uniform discount
policy
• Upper bound and lower bound for multi-product
small gap
• Computational study
– Demonstrate error because of approximations is small
– Managerial insights (effects of commitment, #of products on costs )
• Mean dollar volume commitments works quite well
Model-Basic Assumptions
• Demand
• Deterministic or Stochastic
• Correlation
– =0
– >0
– <0
Sadrian&Yoon, Bassok&Anupindi
decrease in savings from pooling
increase in savings and synergy
• Lead-time
• Instantaneous deliveries
• Fixed lead-times
• Setup cost
• Negligible
• Fixed
Model-Basic Assumptions
• Zero salvage value can be relaxed (Bassok and
Anupindi,1998)
• Flexibility
• With adjustments(upwards, upwards&downwards)
• Without adjustments
• Discount Schedule
• All units
• Restricted to commitments
• Identical or product specific (Katz, Sadrian&Tendick,1994)
• Purchasing of extra units
• Random market prices (proposed in Bassok&Anupindi,1998)
Model-Intuitions
• Useful for real cases
• Relaxation of some assumptions result
in more complex and intractable model
• Complex models cannot be useful to
implement and run
• Small gap between actual model and
assumptions (Bassok & Anupindi,1998)
Results
• Coefficient of variation of demand
• Decreases with increasing flexibility
• Commitments
• Increases with the CV of demands for the same level of
flexibility
• Percentage of error
• Additional cost due to committing the mean dollar
volume compared to optimum does not exceed 0.60%
• Flexibility
• Increases with CV of demands but very small compared
to no flexibility
Bassok and Anupindi,1998
Conclusions
• Discounts for commitments on product
basis (Katz, Sadrian&Tendick, 1994)
• Multiple suppliers and product specific
constraints (Bassok&Anupindi, 1998)
Multi-Product Multi-Supplier Model
• Sadrian and Yoon
Multi-Product Multi-Supplier Model
• Sadrian and Yoon
Multi-Product Multi-Supplier Model
• Sadrian and Yoon
CjDj and assume
demand is stochastic
with fj(.) and Fj(.)
and use the mean
value
Introduce initial
inventory and
inventory balance
equation
Thank You
Q&A