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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
2
OUTLINE
• Background• Commoditized systems• Repair shop• Collecting policies• Capacity policies
• Model
• Computational study
• Conclusions
February 2012
3
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)
February 2012
4
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
February 2012
5
Collecting Policies
• Immediate collection• Periodic collection (milk run)
February 2012
6
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
February 2012
7
Research Question
• For what environments does periodic collection whether or not in combination with a usage based capacity policy lead to “overall” benefits?
February 2012
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Problem
• Given • 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
February 2012
9
Model I: tranportation costs
• Immediate collection:
• Periodic collection
February 2012
AtTCE ci 367.0*2**
0
/)*1*75.0*!
(n
c
nD
p DtnAn
DeDTCE
10
Model II: capacity costs
• Availability based:• Repair shop: M/M/1
• Usage based:• Repair shop: DX/M/1
February 2012
L
p
eBLhc
Lx
Sppc dxCxfLxBD
DETPCL
DhRcRcc
d)|()(
2*1
11
COMPUTATIONAL STUDY (I)
• Cost price system: € 200.000• Normalized arrival rate: λ=1 per time unit
(week/day) defects• System renting cost: h=€11, €15, €20
per hour• Downtime cost: B=€5000, €10000,
€20000 per unit down per week
• Capacity costs: cp= €2400 per unit• Sell-back parameter: R=0.2, 0.5, 0.8• Transportation costs: €90, €120 per hour• Area size: 300.000 sqm, 1.000.000
sqm
•
February 2012
12
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
• February 2012
13
RESULTS (I)
February 2012
14
RESULTS (II)
February 2012
15
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%)February
2012
16
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
February 2012