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Delivery Lead Time and Flexible Capacity Setting for Repair Shops with Homogenous Customers. N.C. Buyukkaramikli 1,2 J.W.M. Bertrand 1 H.P.G. van Ooijen 1 1- TU/e IE&IS 2- EURANDOM. OUTLINE. Introduction & Motivation (give some spoilers) Literature Review Model & Assumptions

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delivery lead time and flexible capacity setting for repair shops with homogenous customers

Delivery Lead Time andFlexible Capacity Setting forRepair Shops with Homogenous Customers

N.C. Buyukkaramikli1,2

J.W.M. Bertrand1

H.P.G. van Ooijen1

1- TU/e IE&IS 2- EURANDOM

outline
OUTLINE
  • Introduction & Motivation (give some spoilers)
  • Literature Review
  • Model & Assumptions
  • Setting the Scene for Flexibility
introduction motivation
INTRODUCTION & MOTIVATION
  • After Sales Services become more important (Cohen et. al, HBR 2006)
  • For Capital Goods  maintenance
    • Corrective
  • Area of Interest: Capital Goods which are commoditized to some extent:

Construction Eq.

Trucks

Forklifts

introduction motivation1
INTRODUCTION & MOTIVATION
  • Commoditized Capital Goods Environment
    • Numerous users
    • Rental suppliers available
    • Maintenance
      • Hiring a substitute machine during repair

One of the biggest Forklift Supplier & Service Provider in the Benelux Area that has numerous customers (Hypothetically at )

Repair Shop & Rental Store are nearby

Upon a failure  a substitute forklift from the rental store can be hired for a fixed amount of time.

introduction motivation2
INTRODUCTION & MOTIVATION

RESEARCH QUESTIONS

Given the availability of exogenous rental suppliers:

  • How should the repair shop capacity & hiring duration decisions be given?

Integrated vs. Non-integrated systems

2. What is the role of Lead Time Performance Requirements in the coordination of these decisions?

3. How can one make use of capacity flexibility in this environment?

literature review
LITERATURE REVIEW
  • Surveys on Maintenance:
    • Pierskalla and Voelker (1976), Sherif and Smith (1982), Cho and Parlar (1990), Dekker(1996), Wang (2002)
  • Flexible Capacity Management in Machine Interference Problem:
    • Crabill(1974), Winston(1977,1978), Allbright (1980)
  • Capacity Flexibility Management in Repairable-Item Inventory models:
    • Gross et al. (1983,1987), Scudder (1985), De Haas (1995)
  • Lead Time Management
    • Duenyas and Hopp (1995), Spearman and Zhang (1999), Elmaghraby and Keskinocak (2004)
model assumptions

m/c

m/c

m/c

m/c

m/c

m/c

m/c

m/c

m/c

subs.m/c

subs.m/c

subs.m/c

MODEL & ASSUMPTIONS

Repair Shop

......

.......

m/c

m/c

Resupply Time

.......

.......

.......

.......

L units of time

Exogenous Rental Supplier for substitute m/c

model assumptions1
MODEL & ASSUMPTIONS

Instantaneous Shipment from/to the Repair shop & the Rental Store

Failures ~Poisson (λ) (w.l.o.gλ = 1failure per week.)

Each failure  a random service time at the repair shop

Repair Shop ~ a single Server Queue

Capacity of the Repair shop= Service Rate (interpreted as the weekly working hours)

We pay h$during L units of time to the rental supplier, (non-refundable)

If (resupply time) > L we loose B$per unit time until the repaired machine is returned (B>h)

model assumptions2
MODEL & ASSUMPTIONS

Repair Shop’s Total Costs per unit time:

RSTC(µ) = K + cp µ.

K: Capacity unrelated costs

cp : Wage factor

Repair Shop: cost -plus (C+) strategy for determining price per repair

p(µ) = RSTC(µ)/λ + α .

µSojourn time distribution (density) function , Fµ(.), (f µ(.))

Given µ and L, total cost during downtime cycle TCDT (µ, L)

(B > h)

model assumptions3
MODEL & ASSUMPTIONS

INTEGRATED DECISION MAKING:

Assumptions:

Minimize TCDT (µ, L) when all info. is available(K, cp, h, B, λ, α, Fµ(.), fµ(.))

(1)

Special Case: Jointly Convex when M/M/1Fµ ~ Exponential(µ-λ)

Is Integrated Decision Making Realistic?

Confidentiality concerns of the Repair Shop?

Reluctant to give repair time distribution…

Laws of Confidentiality Walls of Confidentiality

model assumptions4
MODEL & ASSUMPTIONS

DECOMPOSED DECISION MAKING:

Start from here

i.1

Lead Time Performance with Li & γ=h/B

P(S>Li )=γ

New Li

i i+1

i.2

Customer Side

Information available:

h, B

Decision to be Given:

L

Repair Shop Side

Information available:

cp, K, α, Fμ(.)

Decision to be Given:

μ

Min RSTC(µ)

s.t.

P(S>Li)=γ

Wall of

Confidentiality

Approximate

From HR(Li)

i.4

µ*(Li )

p(µ*(Li )),

HR(Li)=hazard rate @ Li

i.3

model assumptions5
MODEL & ASSUMPTIONS

DECOMPOSED DECISION MAKING:

Lead Time Performance Constraint reduces TCDT(L) to a single variable function

For general service times  exponential tail asymptotic (Glynn and Whitt (1994), Abate et al (1995)).

Total area can be derived from the hazard rate at L with µ*(L).

L* (integrated solution)can be reached with an arbitrary precision.

Further savings?  Capacity Flexibility

p(µ*(L))

γ=h/B

hL+

research question 2 setting the scene for capacity flexibility
Research Question 2Setting the Scene for Capacity Flexibility

Hire Immediately-Send Periodically

  • Each failed machine is sent to the repair shop only in equidistant points in time. (Period of length D)
  • However a substitute machine is hired immediately (until next period + L)
  • Time until next period ~ Uniform(0,D)
  • Repair Shop  D[X]/M/1,X~Poisson(λD) (Buyukkaramikli et al. (2009))
research question 2 setting the scene for capacity flexibility1
Research Question 2Setting the Scene for Capacity Flexibility

Negative Effects

  • Additional Hiring Time(hD/2)
  • Burstiness in the arrival pattern.

T=0

For small values of D, the

performance can be better

ρ=1.1, λ=1,

L:P(S<1) R:P(S<20)

T=3

T=5

setting the scene for capacity flexibility
Setting the Scene for Capacity Flexibility

Positive Effects

Recall that RSTC(µ) = K + cp µ

1. Savings in the fixed component due to economies of scale in transportation.

1

2

% Savings in K

1/(1+β1D)

(1-e-D) /D

D

4 failures in a period

1 truck

4 failures in a period

4 trucks

setting the scene for capacity flexibility1
Setting the Scene for Capacity Flexibility

Positive Effects

2. Certainty in arrival times : Once all the repairs are completed  idle (for sure!) at least until the next period.

  • Opportunity for capacity flexibility…
  • Agreement (with the union or individuals) on the Max. number of working hours per week (µ), payment for actual hours worked (λ)
  • Would cp be the same? (D=0) Compensating differentials?

D

after

before

Β2=0.1

Β2=0.25

Β2=0.5

decomposition method
Decomposition Method?

The Decomposed Method can be applied mutadis mutandis in this scheme, by updating the cost formulations:

RSTC(µ,D) = K/(1+β1D) +

p(µ,D) = RSTC(µ,D)/λ + α

decomposed decision making
DECOMPOSED DECISION MAKING:

D=0

D=5

D=4

D=3.5

D=3

D=2.5

D=2

D=1

D=1.5

D=0.5

D=4.5

Start from here

i.1

Lead Time Performance with Li & γ=h/B

P(S>Li )=γ

New Li

i i+1

i.2

Customer Side

Information available:

h, B,D

Decision to be Given:

L to minimize TCDT

Repair Shop Side

Information available:

cp, K, α, Fμ,D(.),D

Decision to be Given:

µto minimize RSTC

Min RSTC(µ)

s.t.

P(S>Li)=γ

Wall of

Confidentiality

Approximate

From HR(Li)

i.4

µ*(Li |D)

p(µ*(Li |D),D),

HR(Li)=hazard rate @ Li

i.3

conclusions
CONCLUSIONS
  • Maintenance Operations of a Commoditized Capital Goods Environment
    • Hiring a Substitute Machine Alternative
  • Decision Making Framework
    • Integrated vs. Decomposed
  • Setting the Scene for Strategic Capacity Flexibility
    • Periodic Customer Admissions
  • Applying Labor Economics Concepts

to OM models