# Inventory Cost Captures time-value of holding product Captures time-value of holding product Perishability, theft, opportunity cost of cash, insurance,

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Inventory Cost Captures time-value of holding product Captures time-value of holding product Perishability, theft, opportunity cost of cash, insurance, shrinkage, obsolescence Perishability, theft, opportunity cost of cash, insurance, shrinkage, obsolescence Usually 10-15% for electronics Usually 10-15% for electronics Value of good*interest rate*time Value of good*interest rate*time

Exercise DC 100 miles 100 miles 100 miles 60 miles 40 miles 50 miles 50 miles Fuel economy: 10 mpg Driver wages: \$15/hour Ignore depreciation of vehicle, insurance Speed of vehicle: 25 mph Price of fuel: \$2.50 per gallon Value of goods in a truck: \$100,000 Interest rate: 6% per year Time spent at DC: 3 days Handling cost at DC: \$50 per truck Ignore rent, operating cost of DC Calculate one way transportation cost and one way inventory cost.

Cost Comparison TransportationInventoryHandlingTotal Direct3(\$60+\$25)=\$2553(\$2.74)=\$8.22\$0\$263.22 DC (3 days) (\$36+\$15)+2(\$30+\$12.50)+(\$24+\$10)=\$170\$4.93+2(\$1.37)+\$1.10+3*(\$49.32)=\$156.73\$150\$476.73 DC (1 days) (\$36+\$15)+2(\$30+\$12.50)+(\$24+\$10)=\$170\$4.93+2(\$1.37)+\$1.10+\$49.32=\$58.09\$150\$378.09

Hypothetical curves Shipment frequency cost transportation inventory total Minim cost shipment frequency We will identify the optimal when we talk about distribution systems

Cumulative Number of Items Diagram time cumulative number of items Production (rate D’) shipments arrivals Consumption (D’) An item is a fixed quantity of infinitely divisible quantity (e.g. person, parcel, case of beer) tmtm H Consider units on area

Cumulative Number Diagram Good for one origin/one destination problems Good for one origin/one destination problems Identify production and consumption rates Identify production and consumption rates Items waiting to be shipped Items waiting to be shipped Shipment times Shipment times Shipment sizes Shipment sizes Items waiting to be consumed Items waiting to be consumed Total wait time from production to consumption (if FIFO) Total wait time from production to consumption (if FIFO) Headway (H) Headway (H) Travel time Travel time Units Units Storage space proportional to max accumulation is D’H Storage space proportional to max accumulation is D’H

Network Structures Trade-off inventory cost and transportation cost Trade-off inventory cost and transportation cost Milk-run Milk-run Hub and spoke (distribution center) Hub and spoke (distribution center) Direct Shipping Direct Shipping

No DC cost Reduce lead times Higher transportation expense Good if fully loaded trucks or timely goods Store goods to pool inventory risk Trade-offs in size as more demand can be pooled, but then farther from destination Not stored for a significant length of time Sorted, consolidated, shipped out directly Use different containers Requires high volume warehousecrossdocks

Exercise DC 100 miles 100 miles 100 miles 60 miles 40 miles 50 miles 50 miles Inventory Pooling What is the inventory held in the system without the distribution center? What is the inventory held in the system with the distribution center?

Inventory Aggregation Store 1 Store 2 Store 3 Average demand 10 units/day 20 units/day 30 units/day Standard deviation of demand 2 units/day 4 units/day 6 units/day Calculate number required on hand if held at 3 stores, central facility. Online retailers as well as traditional retailers Typically increases transportation cost (think outbound, but who pays?)

Inventory Management Improve service level Improve service level Reduce logistics cost Reduce logistics cost Cope with randomness and seasonality Cope with randomness and seasonality Speculate on price Speculate on price Overcoming inefficiencies in managing the logistics system Overcoming inefficiencies in managing the logistics system

Distribution Systems Prof. Anne Goodchild Spring 2009

Distribution systems One to one One to one One to many One to many Many to one Many to one Many to many Many to many

1-1 Distribution Examples Port to rail head drayage Port to rail head drayage Small in scale and/or scope Small in scale and/or scope Decisions: Decisions: Shipment frequency Shipment frequency Route (this is typically a function of the network and travel times) Route (this is typically a function of the network and travel times) Shipment times Shipment times

1-1 Distribution Constant demand Constant demand Trade-off inventory and transportation cost: z=min v {(c h /D’)v+c f /v}, s.t. v { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/14/4248685/slides/slide_15.jpg", "name": "1-1 Distribution Constant demand Constant demand Trade-off inventory and transportation cost: z=min v {(c h /D’)v+c f /v}, s.t.", "description": "v

EOQ (economic order quantity) z=min v {Av+B/v+C} z=min v {Av+B/v+C} v*=sqrt{B/A} v*=sqrt{B/A} z*=2sqrt{AB} z*=2sqrt{AB} If v*>v max use v=v max If v*>v max use v=v max v* makes both of the terms in the objective function equal (motion cost = holding cost) v* makes both of the terms in the objective function equal (motion cost = holding cost) Why should these be equal? Why should these be equal?

Lot Size problem with Variable Demand D(t) gives cumulative number of items demanded between 0 and t D(t) gives cumulative number of items demanded between 0 and t D’(t) is variable demand rate D’(t) is variable demand rate Seek the set of times when shipments are to be received and the shipment sizes that will minimize sum of motion plus holding costs over some time period Seek the set of times when shipments are to be received and the shipment sizes that will minimize sum of motion plus holding costs over some time period With an infinite time horizon and constant demand this is the EOQ problem just discussed With an infinite time horizon and constant demand this is the EOQ problem just discussed

When holding cost close to rent Variable demand Variable demand Inventory cost negligible (big, cheap items) Inventory cost negligible (big, cheap items) Increases with maximum inventory accumulation Increases with maximum inventory accumulation Recall motion cost independent of shipment sizes and times (only dependent on total amount moved or average) Recall motion cost independent of shipment sizes and times (only dependent on total amount moved or average) Thus we want to choose times and sizes to minimize holding cost Thus we want to choose times and sizes to minimize holding cost V*= D(t max )/n, all equal minimizes cost V*= D(t max )/n, all equal minimizes cost cost/time=c r D(t max )/n+c f n/t max, find n by minimizing cost/time=c r D(t max )/n+c f n/t max, find n by minimizing

When rent is negligible Small, expensive items Small, expensive items Simple expression cannot be obtained unless D(t) varies slowly with t (CA method) Simple expression cannot be obtained unless D(t) varies slowly with t (CA method) Use numerical solution (e.g. dynamic programming) Use numerical solution (e.g. dynamic programming)

One to Many Distribution Movement of containers from the port to landside destinations Movement of containers from the port to landside destinations Delivery systems Delivery systems Decisions: Decisions: Network structure Network structure Fleet size (VRP and TSP) Fleet size (VRP and TSP) Shipment frequency Shipment frequency Use of an intermediate facility (minimizing logistics cost) Use of an intermediate facility (minimizing logistics cost)

Many to one distribution Export containers being delivered to a marine port Export containers being delivered to a marine port Collection systems Collection systems The same analytical methods can be used as with one to many distribution The same analytical methods can be used as with one to many distribution Decisions: Decisions: Network structure Network structure Fleet size Fleet size Shipment frequency Shipment frequency Use of an intermediate facility Use of an intermediate facility

Many to Many Distribution Global distribution of marine containers Global distribution of marine containers Collection and distribution systems Collection and distribution systems Decisions: Decisions: Network structure Network structure Coordination of inbound and outbound shipments Coordination of inbound and outbound shipments

Many to many distribution The problem can often, and should often, be broken down into pieces The problem can often, and should often, be broken down into pieces Inbound logistics (many to one) Inbound logistics (many to one) Outbound logistics (one to many) Outbound logistics (one to many) Be mindful of who is responsible for cost within the supply chain Be mindful of who is responsible for cost within the supply chain Most supply chains are not operated by the same entity Most supply chains are not operated by the same entity Use terminals to consolidate some of the flow Use terminals to consolidate some of the flow

Transshipment

Transshipment 1 Reduce line-haul cost through consolidation

Transshipment 1 Introduce levels of transshipment terminals These can be used on the collection side or the distribution side Consider the use of tiered airports in a hub and spoke system 2 2 Influence area

Influence Areas total outbound inbound terminal Cost per item delivered Size of influence area

Themes Scale Scale What part of the logistics system will you consider? What part of the logistics system will you consider? Typically determined by ownership and operating units but it depends on your goals Typically determined by ownership and operating units but it depends on your goals Consistency Consistency Logistics systems are more manageable Logistics systems are more manageable

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