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the presentation for my talk at ORBEL \'09
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A NOTE ON « THE SINGLE-VENDOR SINGLE-BUYER
INTEGRATED INVENTORY PROBLEM WITH QUALITY IMPROVEMENT AND LEAD TIME REDUCTION »
dr. ir. Sofie Van Volsem
Department of Industrial Management
Ghent University, Belgium
ORBEL 09
6 feb 2009
Leuven
Integrated inventory problem
Strategic supplier –
buyer relation
Min JTEC = TECvendor +
TECbuyer
Investments possible:
Improve quality or
reduce lead time
Buyer-vendor coordination (Goyal and Gupta, 1989)
2
Literature3
Porteus (1986): relationship between quality and lot size in EOQ models
Liao and Shyu (1991): crash cost, probabilistic inventory model with lead time a unique decision variable
Integrated vendor-buyer inventory problem has received a lot of attention, but focus is primarily on the production / shipment schedule and models don’t account for imperfect quality
Lead time assumptions:4
Shorter lead time results in:
Lower safety stock
Reduction of stock-out losses
Improvement of customer service
level
Quality: assumptions5
In classical EOQ models a fixed (generally perfect) quality level is implicitly assumed
More recent EOQ/EPQ models neglect possible buyer-vendor cooperation to improve joint management policy
The model by Ouyang et al. (2006)6
=vendor-buyer integrated inventory
model
Discrete imperfect production process, can
be improved by extra capital investment
Lead time is controllable and
reducible by adding crash costs
Ouyangs conclusions7
A lower JTEC can be achieved through lead time reduction and quality improvement
When there is an investment option for improving the process quality, it is always advisable to invest
Modeling random yield8
Specifying a distribution for the time in which the process remains in control, after which the process is out of control
A distribution for the overall fraction of defective units
Modeling defects as a Bernouilli process, where each unit is defective with probability p
Out-of-control probability9
While producing a product, the production process can go out-of-control with probability and stay o-o-c for the remainder of the lot
The expected # of defectives in a lot of size Q is given by:
↘This is approximated by Ouyang et al. by Q2/2
Joint total expected cost per unit of time:
10
0 0.2 0.4 0.6 0.8 1
Critique on o-o-c probability function11
Reliability: bathtub curve
Relation with lot size: industry evolution is towards smaller lot sizes, even “lot size of 1”
Porposed alternative failure model12
Production process operatingwith known defect rate:
x<Q1 : u(x) = ω
x>Q1 : u(x) = ω + δ (x-Q1)
General investment function: I(p): 0 ≤ p ≤ 1 = scaling factor, reducing the defect rate function to:
I(1)=0
I’(p)<0
Solution procedure:13
p
I(p)
0>p 1
Optimization of setup cost reduction14
Propositions:
for a deteriorating process, the marginal value of setup cost reduction is higher for:
1. Smaller setup cost Av
2. Larger holding cost hv
3. Larger repair cost s
4. Faster deteriorating process (larger u’(x))
Optimization of process quality improvement
15
Propositions:1. The optimal run length Q* is decreasing in p
2. The rate of change in optimal cost as a funtion of p is given by the repair cost per unit time:
3. For a deteriorating process (u’(x)>0), the marginal value of process improvement is larger for greater Av
and smaller hv .
4. The marginal value of process improvement can increase or decrease with the repair cost s, and the total number of defects can increase or decrease with the quality scaling factor p.
Proposed algorithmic solution procedure17
