11

Logistics Systems AnalysisMid-Term Review

John H. Vande Vate

Spring, 2001

22

Subjects Covered• Supply Chain Costs

– Holding• Waiting• Rent

– Moving • Handling• Transport

• EOQ– Trade off Holding and Moving Costs– cQ + d/Q minimized with Q = d/c

33

Subjects Covered• Project

– Inventory Analysis– Modeling

• Inventory Analysis– At the Plant

• Shipments of size Q to DC– Inventory at plant per shipment: (Q/2)*(Q/P)

– Shipments per year: D/Q

– Total Inventory: (Q/2)*(D/P) + Q/2

– EOQ: minimize fD/Q + h(Q/2)*(1+D/P)

– Q* = (2fD/h)P/(P+D)

44

Project • Inventory Analysis

– Plant to Warehouse• Inventory at plant per shipment: (Q/2)(Q/P)

• Shipments per year: unknown

• Shipments generated by DC served through warehouse: D/Q

• Total Plant inventory per DC served through warehouse: (Q/2)(D/P)

• EOQ to warehouse:

Q* = (2fDw/h)P/(P+Dw) but what’s Dw?

55

Warehouse Inventory• Inbound

– Q/2 from each plant that serves it

• Outbound– “Option” or mix of items shipped together

– Total Demand at warehouse for Assembly: DO

– “Production Rate” of Option at Warehouse: DO

– Inventory per shipment to DC: (Q/2)(Q/DO)

– Shipments per year: D/Q

– EOQ: min fD/Q + h(Q/2)(1 + D/DO)

Q* = (2fD/h)DO/(DO +D) but what’s DO?

66

Outbound Inventory to DC• Inventory per shipment to DC: (Q/2)(Q/DO)

• Shipments per year: D/Q

• Inventory per year: (Q/2)(D/DO) if served with this option

• DO= Sum of Demands at DC’s served with this option

• If Shipment size Q for this option is relatively constant across the DC’s

• Total Outbound Inventory Cost for the Option is (average Q/2)*[Do we serve any DC with this option?]

77

Modeling “Rules”

• Use meaningful (helpful) names

• Comment extensively

• Keep data and model separate

• Keep model general where possible

88

“Finance”

• Capital Utilization influences financial performance

• Total Capital influences Capital Utilization

• Inventory Levels contribute to Capital

• Cash-to-Cash Cycle influences Capital

• Value of Inventory Savings

99

1-1 Distribution• Extension of EOQ to variable demand

– Simple formula for headways:H(t) = (2Fixed/cD’(t))

– Estimate of Total Cost– Reconstructing implementable headways

t D'(t) D(t) H(t) Integral of H(t)t*t h Integral of H(t)1 0.119608 0.598042 4.08916 4.08916 1 52 0.119608 1.196084 4.08916 8.17832 4 53 0.119608 1.794126 4.08916 12.26748 9 54 0.054771 2.067982 6.042807 18.31029 16 55 0.054771 2.341839 6.042807 24.35309 25 56 0.054771 2.615695 6.042807 30.3959 36 3 6.0428077 0.382124 4.526317 2.287771 32.68367 49 3 8.3305798 0.382124 6.436939 2.287771 34.97144 64 3 10.618359 0.382124 8.34756 2.287771 37.25922 81 2 12.90612

10 0.946519 13.08016 1.453618 38.71283 100 2 14.3597411 0.946519 17.81275 1.453618 40.16645 121 1 15.8133612 0.946519 22.54535 1.453618 41.62007 144 1 17.2669813 0.975312 27.42191 1.432 43.05207 169 1 18.6989814 0.975312 32.29847 1.432 44.48407 196 1 20.1309815 0.975312 37.17503 1.432 45.91607 225 2 21.5629816 0.753098 40.94052 1.629631 47.5457 256 2 23.1926117 0.753098 44.70601 1.629631 49.17533 289 2 24.8222418 0.753098 48.47149 1.629631 50.80497 324 2 26.4518719 0.727394 52.10846 1.658174 52.46314 361 2 28.11005

1010

Models for Variable Demand

• Correct Models– Relate decision whether or not to ship with

volume shipped– Q[t] Ship[t]*Remaining Demand

• Better Models– Do not aggregate constraints– Q[s, t] Ship[s]*Demand in Period t

1111

Location

• Different Objectives– Item-miles– miles– max distance– …

• Two varieties of models– Do we locate here or not?– What is the position of the facility?

1212

Location

• Measures of Distance– Rectilinear– Euclidean

• Iterative scheme for locating a single facility using Euclidean Distances

• Extension to locating several facilities– Locate– Allocate