1 / 19

Delivery Lead Time and Flexible Capacity Setting for Repair Shops with Homogenous Customers

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

antranig
Download Presentation

Delivery Lead Time and Flexible Capacity Setting for Repair Shops with Homogenous Customers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. OUTLINE • Introduction & Motivation (give some spoilers) • Literature Review • Model & Assumptions • Setting the Scene for Flexibility

  3. 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

  4. 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.

  5. 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?

  6. 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)

  7. 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

  8. 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)

  9. 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)

  10. 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

  11. 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

  12. 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+

  13. 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))

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

More Related