Storage and Retrieval Cycle A storage and retrieval (S/R) cycle is - PowerPoint PPT Presentation

Storage and Retrieval Cycle • A storage and retrieval (S/R) cycle is one complete roundtrip from an I/O port to slot(s) and back to the I/O • Type of cycle depends on load carrying ability: – Carrying one load at-a-time (load carried on a pallet): • Single command • Dual command – Carrying multiple loads (order picking of small items): • Multiple command 145

Single-Command S/R Cycle • Single-command (SC) cycles: empty – Storage: carry one load to store slot for storage and return I/O empty back to I/O port, or slot empty – Retrieval: travel empty to retrieve slot to retrieve load and return with it back to I/O Expected time for each SC S/R cycle: d d port SC SC = + + = + t t t 2 t SC L U L U / v v 146

Industrial Trucks: Walk vs. Ride Walk (2 mph = 176 fpm) Ride (7 mph = 616 fpm) Pallet Jack Pallet Truck Walkie Stacker Sit-down Counterbalanced Lift Truck 147

Dual-Command S/R Cycle • Dual-command (DC): • Combine storage with a retrieval: store – store load in slot 1, travel empty I/O empty to slot 2 to slot1 slot2 retrieve retrieve load • Can reduce travel distance by a third, on Expected time for each SC S/R cycle: average d d DC DC = + + = + t 2 t 2 t 4 t DC L U L U / v v • Also termed task “interleaving” 148

Multi-Command S/R Cycle • Multi-command: multiple loads can be carried at the same time empty I/O • Used in case and piece retrieve order picking • Picker routed to slots – Simple VRP procedures can be used 149

1-D Expected Distance • Assumptions: 1-D Storage Region – All single-command cycles – Rectilinear distances I/O 3 9 X = 12 0 6 – Each slot is region used X X with equal frequency x = 2 L L (i.e., randomized storage) L L   X X X X ∑ ∑ ( ) = − = − TD i i 1   − 1 way  L 2 L  L 2 L • Expected distance is the = = i 1 i 1 + X  L L ( 1)  X ( ) = − average distance from L   L  2  2 L I/O port to midpoint of + − XL X X XL = = 2 2 each slot TD X − 1 way = = ED – e.g., [2(1.5) + 2(4.5) + − 1 way L 2 2(6.5) + 2(10.5)]/4 = 12 = = d 2( ED ) X − SC 1 way 150

Off-set I/O Port • If the I/O port is off-set from the storage region, then 2 times the distance 3 9 X = 12 I/O 0 6 of the offset is added the offset expected distance within the slots = + d 2( d ) X SC offset 151

2-D Expected Distances • Since dimensions X and Y are independent of each other for rectilinear distances, the expected distance for a 2-D rectangular region with the I/O port in a corner is just the sum rect = + of the distance in X and in Y : d X Y SC • For a triangular region with the I/O port in the corner: − + L L i 1    X X   X X  Y ∑ ∑ = − + − = TD i j        1-way  L 2 L   L 2 L    = = i 1 j 1 ( ) X 2 = + + 2 L 3 L 1 6 Y = y TD D 2 X 2 1-way = = + = → ∞ ED X X , as L 1-way + L L ( 1) 3 3 L 3 2 X I/O X   2   2 1 1 = x tri ( ) = = = + d 2 X 2 + X Y     X Y L SC    3  3 3 3 152

I/O-to-Side Configurations Rectangular Triangular X X TA TA X 0 0 X I/O I/O 1 = 2 TA X = 2 TA X 2 ⇒ = X TA ⇒ = = X 2 TA 2 TA ⇒ = d 2 TA 4 SC ⇒ = = d 2 TA 1.886 TA SC 3 153

I/O-at-Middle Configurations Rectangular Triangular X X TA/2 TA/2 TA/2 TA/2 0 X 0 X I/O I/O TA TA 1 = 2 = 2 X X 2 2 2 ⇒ = TA TA X TA ⇒ = = X 2 2 4 ⇒ = = d TA 1.333 TA SC 3 ⇒ = = d 2 TA 1.414 TA SC 154

Example 3: Handling Requirements Pallet loads will be unloaded at the receiving dock of a warehouse and placed on the floor. From there, they will be transported 500 feet using a dedicated pallet truck to the in-floor induction conveyor of an AS/RS. Given a. It takes 30 sec to load each pallet at the dock b. 30 sec to unload it at the induction conveyor c. There will be 80,000 loads per year on average d. Operator rides on the truck (because a pallet truck) e. Facility will operate 50 weeks per year, 40 hours per week empty transport load Receiving Dock 500 ft AS/RS 155

Example 3: Handling Requirements 1. Assuming that it will take 30 seconds to load each pallet at the dock and 30 seconds to unload it at the induction conveyor, what is the expected time required for each single- command S/R cycle? = = d 2(500) 1000 ft/mov SC   d 1000 ft/mov 30 SC = + = +  t 2 t 2 min/mov  SC L U / v 616 ft/min  60  2.62 = = 2.62 min/mov hr/mov 60 (616 fpm because operator rides on a pallet truck) 156

Example 3: Handling Requirements 2. Assuming that there will be 80,000 loads per year on average and that the facility will operate for 50 weeks per year, 40 hours per week, what is the minimum number of trucks needed? 80,000 mov/yr = = r 40 mov/hr avg 50(40) hr/yr = +   m r t 1   avg SC     2.62 = + = + 40 1  1.75 1         60    = 2 trucks 157

Example 3: Handling Requirements 3. How many trucks are needed to handle a peak expected demand of 80 moves per hour? = r 80 mov/hr peak = +   m r t 1   peak SC     2.62 = + = +   80 1 3.50 1       60     = 4 trucks 158

Example 3: Handling Requirements 4. If, instead of unloading at the conveyor, the 3-foot-wide loads are placed side-by-side in a staging area along one side of 90-foot aisle that begins 30 feet from the dock, what is the expected time required for each single-command S/R cycle? . . . Receiving 0 3 6 84 Dock 87 X = 90 offset = 30 ft = + = + = d 2( d ) X 2(30) 90 150 ft SC offset   d 150 ft/mov 30 SC = + = +  t 2 t 2 min/mov  SC L U / v 616 ft/min  60  1.24 = = 1.24 min/mov hr/mov 60 159

Estimating Handling Costs • Warehouse design involves the trade-off between building and handling cost. • Maximizing the cube utilization of a storage region will help minimize building costs. • Handling costs can be estimated by determining: 1. Expected time required for each move based on an average of the time required to reach each slot in the region. 2. Number of vehicles needed to handle a target peak demand for moves, e.g., moves per hour. 3. Operating costs per hour of vehicle operation , e.g., labor, fuel (assuming the operators can perform other productive tasks when not operating a truck) 4. Annual operating costs based on annual demand for moves. 5. Total handling costs as the sum of the annual capital recovery costs for the vehicles and the annual operating costs. 160

Example 4: Estimating Handing Cost = = = Expected Distance: d 2 TA 2 20,000 200 ft SC d SC = + Expected Time: t 2 t SC L U / v 200 ft = + = 2(0.5 min) 2 min per move TA = 20,000 200 fpm = Peak Demand: r 75 moves per hour peak I/O = Annual Demand: r 100,000 moves per year year ⇑  t  SC Add 20% Cross aisle: = + = =   Number of T rucks: m r 1 3.5 3 trucks     peak 60   ′ = × TA TA 1.2 t SC = + Handling Cost: TC mK r C 2 = 20,000 ft hand truck year labor 60 ⇑ 2 = + 3($2,500 / tr-yr) 100,000 ($10 / hr) Total Storage Area: 60 = + = $7,500 $33,333 $40,833 per year ′ * ⇒ * ⇒ D L D ( ) TA 161