Coordinating Failed Goods
Collecting Policies and Repair
Capacity Policies in the
Maintenance of Commoditized
Capital Goods
Henny P.G. van Ooijen
J. Will M. Bertrand
Nasuh C. Büyükkaramikli
OUTLINE
• Background
•
•
•
•
Commoditized systems
Repair shop
Collecting policies
Capacity policies
• Model
• Computational study
• Conclusions
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2012
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COMMODITIZED SYSTEMS
• High number of end users
• Low technological/financial barriers -> easy entry
of repair market
• Short term availability of substitutes (e.g. by
leasing)
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2012
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REPAIR SHOP
• Repair shop (Maintenance Service Provider)
• Maintenance service for commoditized systems
− failure due to (sub-)system failure
• Defective systems are replaced by rented systems for a
fixed time
• Responsible for downtime
• Repair shop characteristics
− capacity of the shop determines the speed of repair;
capacity level: the processing rate
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2012
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Collecting Policies
• Immediate collection
• Periodic collection (milk run)
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Capacity Policies
• Availability based policy:
• There is always a fixed amount of capacity available
• Usage based policy
• Periodic capacity contract
− A specific amount of capacity is available at the
start of a period
− Only paid for in proportion to the hours the
capacity is used during the period
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Research Question
• For what environments does periodic collection
whether or not in combination with a usage based
capacity policy lead to “overall” benefits?
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Problem
• Given
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An overall failure rate λ,
transportation costs tc
capacity costs (permanent cp, contingent cc)
machine downtime costs B
system rental costs (hτ),
a capacity sell-back ratio R,
minimize total costs by decisions on:
• transportation policy
• capacity policy
− terms of the capacity contract (level, period length)
• rental period L
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2012
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Model I: tranportation costs
• Immediate collection:
E TCi    * tc * 2 * 0.367 A
• Periodic collection
e  D D 
E TC p D   ( 
* 0.75 * An  1 * tc ) / D
n!
n 0

n
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2012
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Model II: capacity costs
• Availability based:
• Repair shop: M/M/1
e      L
c p      h L  B
   
• Usage based:
• Repair shop: DX/M/1
𝒄𝒄 = 𝒄𝒑 +
∆
𝟏+α
cc  c p R  c p 1  R   * h  D  L  ETPCD   B  ( x  L) f Sd ( x | C)dx
D
2

xL

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COMPUTATIONAL STUDY (I)
• Cost price system:
• Normalized arrival rate:
defects
• System renting cost:
• Downtime cost:
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Capacity costs:
Sell-back parameter:
Transportation costs:
Area size:
€ 200.000
λ=1 per time unit (week/day)
h=€11, €15, €20 per hour
B=€5000, €10000, €20000
per unit down per week
cp= €2400 per unit
R=0.2, 0.5, 0.8
€90, €120 per hour
300.000 sqm, 1.000.000 sqm
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COMPUTATIONAL STUDY (II)
• Immediate collection, availability based capacity

Periodic collection, availability based capacity
• Immediate collection, availability based capacity

Periodic collection, usage based capacity
% Cost savings: (TRC*i – TRC*p)/TRC*i
•
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RESULTS (I)
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RESULTS (II)
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CONCLUSIONS (I)
• Transportation point of view: periodic collection always
leads to benefits; benefits increase with increasing λ
• Also customer related aspects included: positive effects
are canceled out by extra rental
• Also MPS aspects included:
• Availability policy: decrease positive effects due to bursty
arrival pattern (unless a high λ)
• Usage policy: benefits can be obtained for smaller values
of λ (λ = 1: up to 38% cost reduction)
some cost parameter instances: loss in
savings (up to 126%)
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2012
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CONCLUSIONS (II)
• Usgae based policy often outperformed by the
availability based policy
• % savings increase with increase in α
• The higher Δ the lower the % savings
• The higher hτ the lower the % savings
• In most cases the system chooses the shortest
possible period length  indicates importance of
fast response to the system state
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2012
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