Truck Shipment Example: Periodic

Transcription

1 11. Continuing with the example: assuming a constant annual demand for the product of 0 tons, what is the number of full truckloads per year? f 0 ton/yr ton/ TL (full truckload ) max f 0 n 3.77 TL/yr, average shipment freuency max Why should this number not be rounded to an integer value? 116

2 1. What is the shipment interval? t yr/tl, average shipment interval n f 0 How many days are there between shipments? day/yr t day/tl n 117

3 13. What is the annual full truckload transport cost? r d 53 mi, r $ / mi FTL r $0.3961/ ton-mi max TC f r d n rd wd, w monetary weight in $/mi FTL FTL 3.77(.40643)53 $4, 14.56/yr What would be the cost if the shipments were to be made at least every three months? t max 3 1 yr/tl nmin 4 TL/yr 1 t TC max n, n rd FTL min max max 3.77, (53) $5,151.13/yr 118

4 Independent and allocated full truckload charges:, c ( ), FTL UB LB r d max 0 Transport Charge for a Shipment TL LTL TL 3 TL Transport Charge ($) MC /000 Independent Allocated Truckload Allocated Full-Truckload Shipment Size (tons) 119

5 Total Logistics Cost (TLC) includes all costs that could change as a result of a logistics related decision TLC TC IC PC TC transport cost IC PC inventory cost IC IC IC cycle pipeline safety purchase cost Cycle inventory: held to allow cheaper large shipments Pipeline inventory: goods in transit or awaiting transshipment Safety stock: held due to transport uncertainty Purchase cost: can be different for different suppliers 10

6 14. Since demand is constant throughout the year, one half of a shipment is stored at the destination, on average. Assuming that the production rate is also constant, one half of a shipment will also be stored at the origin, on average. Assuming each ton of the product is valued at $5,000 and loses 5% of its value after 3 months, what is a reasonable estimate for the total annual cost for this cycle inventory? IC cycle v (annualcost of holding one ton)(average annual inventory level) ( vh)( ) unit value of shipment ($/ton) h inventory carrying rate, the cost per dollar of inventory per year (1/yr) average inter-shipment inventory fraction at Origin and Destination shipment size (ton) 11

7 Rate (h) = sum of interest + warehousing + obsolescence rate Interest: 5% per Total U.S. Logistics Costs Warehousing: 6% per Total U.S. Logistics Costs Obsolescence: default rate h annual = 0.3 h obs 0. Hourly vs Annual: h hour = h annual /H = 0.3/000 = (H =operhr/yr) High FGI cost: h h obs, can ignore interest & warehousing Estimate h obs using percent reduction interval method: given time t h when product loses x h percent of its original value v, find h obs x h t v x vh t x h t h obs h h obs h h obs, and h th Example: If a product loses 5% of its value after 3 months: 3 xh 0.05 th 0.5 yr hobs 0. h t 0.5 h x h h obs 1

8 Average annual inventory level 1 1 (1)

9 Inter shipment inventory fraction alternatives: O D Batch Production Immediate Consumption

10 Reasonable estimate for the total annual cost for the cycle inventory: IC cycle where vh (1)(5,000)(0.3) $45, / yr 1 1 at Origin + at Destination 1 v $5,000 unit value of shipment ($/ton) h 0.3 estimated carrying rate (1/yr) = FTL shipment size (ton) max 15

11 15. What is the annual total logistics cost (TLC) for these fulltruckload TL shipments? TLC TC IC FTL nrd FTL vh cycle 3.77(.40643)53 (1)(5,000)(0.3) , , $50, / yr 16

12 16. What is the minimum possible annual total logistics cost for independent TL shipments, where the shipment size can now be less than a full truckload? f f TLCTL( ) TCTL( ) IC( ) ctl( ) vh rd vh dtlctl( ) * frd 0(.40643)53 0 TL ton d vh (1)5000(0.3) f TLC rd vh * * TL( TL) * TL TL 0 (.40643)53 (1)5000(0.3) , , $7, / yr 17

13 Including the minimum charge and maximum payload restrictions: * TL f max rd, MC TL frd min, max vh vh What is the TLC if this size shipment could be made as an allocated full truckload? f r TLC r d vh f d vh * * * * AllocFTL( TL) * TL FTL TL TL TL max (1)5000(0.3) , , $18,11.8 / yr vs. $7, as independent PP TL 18

14 17. What is the optimal LTL shipment size? f TLCLTL( ) TCLTL( ) IC( ) cltl( ) vh * LTL arg min TLC ( ) ton LTL Must be careful in picking starting point for optimization since r LTL PPI LTL d s s s ,000, , ft 3 d,000,000 s 19

15 18. Should the product be shipped TL or LTL? * * * LTL LTL LTL LTL LTL TLC ( ) TC ( ) IC( ) 3, , $38,10.00 / yr TLC LTL $ per year TC LTL TLC TL TC TL IC Shipment weight (tons) 130

16 19. If the value of the product increased to $85,000 per ton, should the product be shipped TL or LTL? TLC LTL TLC LTL $ per year TLC TL $ per year IC TC LTL TC TL IC TLC TL TC TL TC LTL Shipment weight (tons) Shipment weight (tons) (a) $5000 value per ton (b) $85000 value per ton 131

17 Better to pick from separate optimal TL and LTL because independent charge has two local minima: * 0 arg min TLC ( ), TLC ( ) TL LTL! * f 0 arg min c0( ) vh 13

18 0. What is optimal independent shipment size to ship 80 tons per year of a Class 60 product valued at $5000 per ton between Raleigh and Gainesville (assuming the same carrying rate)? * 0 3 arg min TLC ( ), TLC ( ) ton * * 0 LTL 0 TLC ( ) $4,86.33 / yr TLC ( ) TL s 3.16 lb/ft TL LTL 133

19 1. What is the optimal shipment size if both shipments will always be shipped together on the same truck (with same shipment interval)? d d, h h, f f f ton s agg 1 agg 1 agg 1 fagg fagg aggregate weight, in lb f lb/ft 3 aggregate cube, in ft f1 f 0 80 s s agg 3 1 f f 0 80 v v v 85, $1, 000 / ton * TL faggrd 100(.3953)53 v h (1)1000(0.3) agg ton 134

20 Summary of results: 135

21 Location and Transport Costs Monetary weights w used for location are, in general, a function of the location of a NF Distance d appears in optimal TL size formula TC & IC functions of location Need to minimize TLC instead of TC FTL (since size is fixed at max payload) results in only constant weights for location Need to only minimize TC since IC is constant in TLC m m fi TL i i i i i i1 i1 i( x) TLC ( x) w ( x) d ( x) vh ( x) rd ( x) vh ( x) m m fi firdi( x) 1 rdi( x) vh firdi( x) vh i1 frd i i( x) vh i1 vh vh m m fi FTL i max i i max FTL i1 max i1 TLC ( x) rd ( x) vh w d ( x) vh TC ( x) constant 136

22 FTL Location Example Where should a DC be located in order to minimize 36.5 transportation costs, given: 1. FTLs containing mix of products A and B shipped PP from DC to customers in Winston Salem, Durham, and Wilmington. Each customer receives 0, 30, and 50% of total demand tons/yr of A shipped FTL PP to DC from supplier in Asheville tons/yr of B shipped FTL PP to DC from Statesville 5. Each carton of A weighs 30 lb, and occupies 10 ft 3 6. Each carton of B weighs 10 lb, and occupies 4 ft 3 7. Revenue per loaded truck mile is $ 8. Each truck s cubic and weight capacity is,750 ft 3 and 5 tons, respectively Asheville 50 Statesville Winston-Salem Greensboro Durham RaleighWilmington

23 FTL Location Example Asheville DC 35% Statesville Winston- Salem TC w d i i ($/yr) ($/mi-yr) (mi) w f r n r i i FTL, i i i ($/mi-yr) (ton/yr) ($/ton-mi) (TL/yr) ($/TL-mi) Durham Wilmington r r FTL, i ($/ton-mi) max max, n f fagg (750 r $ / TL-mi, fagg fa fb ton/yr, sagg lb/ft, max 5, fa f B (750) sa sb 3 30 s1 3 lb/ft, max min 5, 4.15 ton f3 0.0 fagg 96, n3 6.69, w3 6.69() f1 100, n1 4.4, w1 4.4() DC 4 f fagg 144, n , w () (750) s 30 lb/ft, max min 5, 5 ton f fagg 40, n , w () f 380, n 15., w 15.() W W 146, 73 w i : Asheville Statesville Winston-Salem Durham Wilmington < 73 * (Montetary) Weight Losing: w 79 w 67 n 39 n 33 in 78 > 73 in out in out Physically Weight Unchanging (DC): f 480 f 480 out 138

24 FTL Location Example Include monthly outbound freuency constraint: Outbound shipments must occur at least once each month Implicit means of including inventory costs in location decision t max 1 1 yr/tl nmin 1 TL/yr 1 t TC max n, n rd FTL n n n min max max 6.69, 1 1, w 1() 4 max 10.04, 1 1, w 1() 4 max 16.73, , w 16.73() W W 160, 80 w i : Asheville Statesville Winston-Salem Durham Wilmington < < > 80 * (Montetary) Weight Gaining: w 79 w 81 n 39 n 41 in in out in out Physically Weight Unchanging (DC): f 480 f 480 out 139

25 Transshipment Direct: PP shipments from Suppliers to Customers Transshipment: use DC to consolidate outbound shipments Uncoordinated: determine separately each optimal inbound and outbound shipment hold inventory at DC Cross dock: use single shipment interval for all inbound and outbound shipments no inventory at DC 140

26 Uncoordinated Inventory Average pipeline inventory level at DC: 4 O D 1 O, inbound 0 D, outbound Supplier Supplier Customer 3 Customer 4 141

27 TLC with Transshipment Uncoordinated: Cross docking: TLC TLC of supplier/customer i i * i arg min TLC ( ) * * i i TLC TLC 0 * t, shipment interval f c0() t TLCi () t vhf t t * * i i c ( t) independent transport charge as function of t O 0, inbound 0 D, outbound t arg min TLC ( t) TLC TLC t t i 14

28 TLC and Location TLC should include all logistics related costs TLC can be used as sole objective for network design (incl. location) Facility fixed costs, two options: 1. Use non transport related facility costs (mix of top down and bottom up) to estimate fixed costs via linear regression. For DCs, might assume public warehouses to be used for all DCs Pay only for time each unit spends in WH No fixed cost at DC Transport fixed costs: Costs that are independent of shipment size (e.g., $/mi vs. $/ton mi) Costs that make it worthwhile to incur the inventory cost associated with larger shipment sizes in order to spread out the fixed cost Main transport fixed cost is the indivisible labor cost for a human driver Why many logistics networks (e.g., Walmart, Lowes) designed for all FTL transport 143

29 Example: Optimal Number DCs for Lowe's Example of logistics network design using TLC Lowe s logistics network (016): Regional DCs (15) Costal holding facilities Appliance DCs and Flatbed DCs Transloading facilities Modeling approach: Focus only on Regional DCs Mix of top down (COGS) and bottom up (typical load/tl parameters) FTL for all inbound and outbound shipments ALA used to determine TC for given number of DCs IC = αvh max x (number of suppliers x number of DCs + number stores) Assume uncoordinated DC inventory, no cross docking Ignoring max DC to store distance constraints, consolidation, etc. Determined 9 DCs min TLC (15 DCs 0.87% increase in TLC) 144