A. STORAGE/ WAREHOUSE SPACE

A. STORAGE/ WAREHOUSE SPACE Question 1 A factory produces an item (0.5 x 0.5 x 0.5)-m at rate 200 units/hr. Two weeks production is to be containers size (1.8 x 1.2 x 1.2)-m. A minimum space of 100-mm is required between adjacent items. Determine the number of the containers. Question 2 30 different products of 300 loads each are stored in block stacked. Each load is 1.2-m tall and is puton 1.2 x1.2 x 0.15-m pallet. The receiving and shipping docks are to be located along one side of the warehouse with ceiling height of 6.5-m. 1.0-m aisles are required, since a counterbalanced lift trucks in the warehouse are to be used. Develop a layout for the warehouse. Assume any missing data. Question 3 Six products received in pallet load according to schedule in table below are to be stored on pallet rack. Each pallet opening is 1.2 x 1.2 x 1.4-m. The rack is constructed of 5-cm tubular stock. The warehouse ceiling height is 5.5-m. How much space is required to store on pallet racks? Question 4 Six products are to be stored using block stacked. The pallet size, number of pallet, and height of pallet load are given in the table below. The receiving and shipping docks are to be located along one side of the warehouse with ceiling height of 6.5-m. 4.0-m aisles are required, since a counterbalanced lift trucks in the warehouse are to be used. Develop a layout for the warehouse. Assume any missing data. Question 5 Find the space area 14 products are to be stored according the data given below. Develop the warehouse layout, assuming the following:- a- The receiving and shipping docks are to be located at the middle point of north and south faces of the warehouse with a main aisle form north to south with width 4.8-m. b- Each product is block stacked 3 high and 2 rows form wall to main aisle. c- A clearance between product types is 2.0-m. d- Pallet size for all loads of products is 1.0 x 1.2 x 0.15-m. e- Each load is 1.2-m tall. Question 6 Six items are to be stored according the data given below in a storage. The storage layout arrangement is to be as shown in the figure below with aisles width are 3.8-m. Door A serves as receiving dock and door B serves as shipping dock. Determine: - f- The number of sections required for each item. 1 Products 1 2 3 4 5 6 Quantity received/month 400 500 600 800 700 500 Unit load Size, m. 1.2x1.2x.15 1.2x0.9x.125 1.1x1.0x.15 1.2x1.2x.25 1.0x1.0x.15 1.2x1.2x.15 Load height, m. 1.2 1.0 1.5 0.9 1.2 0.9 Products 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Quantity received/month 300 200 10 400 6000 40 200 9000 50 500 80 400 7000 700 Unit load at receipt 1 4 1 1 6 1 1 4 1 1 1 1 6 5 Average order size for shipping 2 4 1 4 2 8 6 4 2 8 6 4 2 4

g- The best storage arrangement. h- The size of the storage. Item A B C D E F Quantity received, unit/month 400 300 250 350 500 300 Average units Received /Trip 50 80 10 20 100 175 Average units shipped/trip 1 3 5 2 5 4 size of a SKU (section), units 50 100 50 50 50 100 A B Question 7 Six items are to be stored according the data given below in a storage. The storage layout arrangement is shown in the figure below with aisles width are 4.8-m. Door A serves as receiving dock and door B serves as shipping dock. 100 units of B fill one storage section (bay). Determine: - a- The number of sections required for each item. b- The best storage arrangement c- The size of the storage. A Item A B C D E F Unit received 200 600 200 300 500 250 Receiving Trip 50 100 20 20 100 25 Average unit shipped 1 3 5 2 5 5 Unit size 0.5B B 0.33B 0.5B B B B Question 8 Deep lane storage is used for storing a soft drink product. The dimensions of the unit load are 1.2 x 1.0-m. The flue clearance is 0.36-m, the rack is 0.15-m wide, the clearance between a load and the rack is 0.1-m, and the aisle width is 2.5-m. seven tiers of storage are used. 400 pallet loads of a product are to be stored. Determine the depth of storage row for the following: - a) Using continuous approximation. b) Using enumeration, when the quantity of loads to be stored is reduced to 35. Question 9 Materials are stored on 1.05 x 1.2 x 0.15-m pallets in selective pallet double deep racks. In each rack opening, two pallet loads are stored side by side with 12.5-cm clearance between loads and two pallet loads are stored back to back. Also In each rack opening, the load stored on the pallet is 1.125-m high and a clearance of 12.5-cm is used between load and a vertical rack member. Each vertical rack member is 0.15-m. Question 10 In an opening, the load in the first-depth position just touches the load in the second-depth position. Pallets are placed on 0.1-m load beams, including the bottom load. There is a clearance of 0.1-m between the top of each load and the load beam above it. A 2.5-m aisle (load to load) and a flue spacing (back to back between loads in the second-depth position) of 0.3-m are used. The rack has 5 tiers of storage. Loads do not overhang the pallet. Compute the storage space utilization assuming the loads in the second-depth position are full and the loads in the first-depth position are half full. Question 11 Materials are stored on 0.9 x 1.2 x 0.15-m pallets in selective pallet one deep racks. In each rack opening, two pallet loads are stored side by side with 0.1-m clearance between loads. Also In each 2

rack opening, the load stored on the pallet is 1.25-m high and a clearance of 0.1-m is used between load and a vertical rack member (upright truss). Each vertical rack member is 0.075-m. Question 12 Pallets are placed on 0.1-m load beams except the bottom load, which is stored on the floor. There is a clearance of 0.075-m between the top of each load and the load beam above it. A 2.5-m aisle (load to load) and flue spacing) of 0.35-m between loads is used. The rack has 4 tiers of storage. Loads do not overhang the pallet. Compute the storage space utilization. Question 13 30-pallet loads pf a product with dimensions 1.0 x 1.2-m. are to be stored. Several storage design are investigated based on the following: - a- Alternative A; The loads are block stacked 3 high. With block stacking an 0.2-m clearance between lanes is required. A 4.8-m aisle is required since; a counterbalanced lift truck in the warehouse is to be used. b- Alternative B; Storage rack can be used to achieve 5 high storage, rack flue space of 0.25-m, horizontal clearance of 0.1-m, and 0.075m upright rack member dimensions are to be used for the rack alternatives. Determine the storage method that minimizes a annual cost, assuming a uniform withdrawal rate. The annual costs for various storage alternatives are as follow: - Alternative Block stacking Single-deep pallet rack Double-deep pallet rack Deep lane storage Cost, SR/m 2 250 270 280 310 Question 14 Block stacking is used for the storage of unit loads paper products (1.25 x 1.35-m). A clearance of 0.2-m is provided between storage rows. The storage aisle is 3.75-m wide. The product is stacked 4 level high in the warehouse. 40 loads of a particular product have been received. a- By using enumeration, determine the depth of the storage rows that will minimize the average amount of loads. Assume uniform depletion over the life forty loads. b- By using a continuous approximation, what row depth would minimize the average amount of floor space? Question 15 Deep lane storage is used for storing a soft drink product. The dimensions of the unit load are 1.2 x 1.0-m. The flue clearance is 0.36-m, the rack is 0.15-m wide, the clearance between a load and the rack is 0.1-m, and the aisle width is 2.5-m. Seven tiers of storage are used. 200 pallet loads of a product are to be stored. Determine the depth of storage row for the following:- a- Using continuous approximation. b- Using enumeration, when the quantity of loads to be stored is reduced to 35. Question 16 1.5 x 1.2-m loads is blocked stacked 5-high using 3.0-m wide aisle. 100 unit loads of a product are received; a safety stock level of 15 unit loads is desired. In this case, suppose 15 units loads of the previous lot of the product are in the warehouse at the time of receipt the current lot. Due to the random nature of demand for the product, the probability distribution for the amount of the particular lot of product in inventory is given as follows: 3

Inventory level 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 Probability, % 12 2 2 2 2 2 2 2 2 4 4 4 6 6 6 8 8 8 8 10 Determine the lane depth for block staking that minimize the average amount of floor space over the lifetime of a lot of particular product in question. a- Use continuous approximation based on uniform demand. b- Using enumeration, determine a local minimum near the solution obtained in part (a) Question 17 A storage system is to be designed for storing 1.5 x 0.95-m pallet loads of a wide variety of products. The storage alternatives are as follows: Block stacking A counterbalanced lift truck will be used. The resulting design parameters are: - 4.0-m aisle width, 0.25-m clearance between storage rows, and 4-high storage of products Deep lane storage An S/R machine will be used. The design parameters are: - 1.8-m aisle width, 0.3-m flue space, 0.077-m clearance between the load and the rack, and 8-high storage Pallet rack Singledeep Double-deep Triple-deep A narrow-aisle lift truck will be used. Two loads are stored side-by-side on a common load beam. The design parameters are: - 2.5-m aisle width, 0.3-m flue space, 0.127-m clearance between the load and the rack, 0.127-m rack member, and 6-high storage a- Based on a lot size of 25, determine the average amount of floor space required for block stacking with the row depth that minimizes the average amount of floor space, measured in m 2. Solve the row depth Using enumeration. b- Solve a) for deep-lane storage, but determine the lane depth Using continuous approximation; round-off the lane depth to nearest integer value. c- Based on a lot size of 25, determine the average amount of floor space required to store the product using single- deep pallet rack. Express answer in m 2. d- Solve part c) using double- deep pallet rack. e- Solve part c) using triple- deep pallet rack. Question 18 Considering storage (42 m 35 m) with storage bays of (7 m 7 m). The storage is served by two shipping docks (1, 2) located at north of the storage and two receiving docks (3, 4) located at the south of the storage at equal distance between bays. The storage is used to store five products (A, B, C, D, E). The data for number of bays requirement and daily activity are given in Table (2). All movement within the storage is performed by left back using single command cycle and traveling at constant velocity. Determine the dedicated storage arrangement:- a- When equal load rate for shipping and receiving doors are assumed. b- When 40/60 % load rate for shipping and receiving doors are assumed. 4

Product No. Of bay required Daily shipment Daily received A 5 25 25 B 6 5 5 C 10 10 10 D 5 15 15 E 4 5 5 Question 19 An existing storage layout arrangement is shown in the figure below with aisles width are 2.4-m for one-way aisles and 4.8-m for two-way aisles. Each bay is 6.0 x 6.0-m. Door A and B serve as receiving and shipping docks respectively. Three items are to be stored according the data given in the table below. Determine the layout that will minimize the expected travel distance. Two way Item A B C Area, m 2 576 792 216 Load Rate 300 400 500 A 50% One way One way Two way Two way One way B 50% Question 20 A warehouse with bay of (10m x10m) is available to store four different types of products in dedicated bays according the flow data and area required are given in Table (20). The warehouse has two equally shared shipping docks (1, 2) located at east side and two equally shared receiving docks (3, 4) located at the south side at equal distance between bays. Determine the layout that minimizes the average distance traveled. Question 21 A warehouse (20m 20m) with storage bays of (4m 4m) is to be considered for storing five products (A, B, C, D, E). A shipping and receiving dock is located at center of the east side. The data for area requirements and daily activities are given in Table (21). Determine the dedicated warehouse arrangement. Product Question 22 A warehouse with bay of (10m x10m) is available to store five different types of products in dedicated bays according the flow data and area required are given in Table (22). The warehouse has two equally shared docks located at top north -east side and bottom South west side at equal distance of the bay. Determine the layout that minimizes the average distance traveled. Table (20) Product Area, m 2 Weekly Load rate A 800 400 B 1200 800 C 600 600 D 1000 400 Table 21 Load Movement/month A 400 80 B 300 96 C 200 64 D 150 64 E 200 80 Required Area, m2 Table (22) Product Area, m 2 Weekly Load rate A 800 400 B 1000 800 C 600 600 D 900 400 E 700 500 5

Question 23 A warehouse with bay of (10m x10m) is available to store five different types of products in dedicated bays according the flow data and area required are given in Table (23). The warehouse has two equally shared docks located at center of east and west sides at equal distance of the bay. Determine the layout that minimizes the average distance traveled. Table (23) Product Area, m 2 Weekly Load rate A 1000 550 B 1200 900 C 800 700 D 1000 500 E 800 600 Question24 A warehouse (25m 25m) with storage bays of (5m 5m) is to be considered for storing six products (A, B, C, D, E, F). At the east side and west side sides of the warehouse, a shipping and receiving dock is located. The data for area requirements and daily activities are given in Table (524). Determine the dedicated warehouse arrangement. Question 25 Storage is to be considered for storing six products Table (25) (A, B, C, D, E). The storage bays of (5m 5m). Two Product Load Movement/month Required Area, m2 A 200 175 docks serve the storage and both are used for B 220 100 shipping and receiving. Dock (D1) is located at C 160 150 center of the west side of the storage and dock (D2) D 100 100 is located at center of the east side. The data for E 160 125 area requirements and daily activities are given in Table (25). Determine:- i- The dedicated storage arrangement. Assuming load rate at the docks D1, D2 is 40/60% respectively. [6 marks] ii- Area and Layout of storage, all movement within the storage is performed by lift-truck. Assume any missing data. [2 marks] Question 26 The inventory demand and replenishment of three products are as shown in table (26). Determine: Table (26) Table (24) Product Load Required Movement/month Area, m2 A 600 75 B 300 125 C 400 75 D 450 75 E 200 125 F 300 75 Period 1 2 3 4 5 6 7 8 9 10 11 12 Products A 12 24 20 16 12 24 20 16 12 24 20 16 B 24 18 12 6 36 30 24 18 12 6 36 30 C 9 6 12 9 6 12 9 6 12 9 6 12 a) Randomized storage and dedicated storage sizes. b) If the products to be stored on pallet rack. Each pallet opening is 1.2 x 1.2 x 1.4-m. The rack is constructed of 5-cm tubular stock. The warehouse ceiling height is 5.5-m. How much space is required to store on pallet racks? 6

Question 27 The inventory demand and replenishment of three products are as shown in table (27). a. Determine Randomized storage and Dedicated storage sizes. b. If the products to be stored on pallet rack. Each pallet opening is 1.2 x 1.2 x 1.45-m. The rack is constructed of 10-cm tubular stock. The warehouse ceiling height is 6-m. develop the store layout. Question 28 Table (28) gives the inventory demand and replenishment of four products. Determine: a) Randomized storage and dedicated storage sizes. b) Number of racks for each type of storage, If the products to be stored on pallet rack. Given the following data: Each pallet opening is 1.15 x 1.15 x 1.4-m. The rack is constructed of 10-cm tubular stock. The number of rack opening on the floor is 10. The warehouse ceiling height is 6-m. c) The storage layout and the required space. Question 29 Table (29) gives the inventory demand and replenishment of four products. Products Determine: a) Randomized storage and dedicated storage sizes. b) Number of racks for each type of storage, If the products to be stored on pallet rack. Given the following data: 7 Table (27) Inventory level in a warehouse Period 1 2 3 4 5 6 7 8 9 10 11 12 A 20 17 14 11 8 5 20 17 14 11 8 5 Products B 12 9 6 3 36 33 30 27 24 21 18 15 C 4 12 8 4 12 8 4 12 8 4 12 8 Table (28) Inventory level in a warehouse Period 1 2 3 4 5 6 7 8 9 10 11 12 A 30 25 20 15 10 5 30 25 20 15 10 5 B 28 22 16 10 40 34 28 22 16 10 40 34 Products C 5 15 10 5 12 8 4 15 10 5 15 10 D 16 5 60 49 38 27 16 5 60 49 38 27 Table (29) Periods 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 24 22 20 18 16 14 12 10 8 6 4 2 24 22 20 13 16 14 12 10 8 6 4 2 2 12 9 6 3 36 33 30 27 24 21 18 15 12 9 6 3 36 33 30 27 24 21 18 15 3 2 8 6 4 2 8 6 4 2 8 6 4 2 8 6 4 2 8 6 4 2 8 6 4 4 12 8 4 24 20 16 12 8 4 24 20 16 12 8 4 24 20 16 12 8 4 20 20 16 5 11 10 9 8 7 6 5 4 3 2 1 24 23 22 21 20 19 13 17 16 15 13 13 12 6 12 9 6 3 24 21 18 15 12 9 6 3 24 21 13 15 12 9 6 3 24 18 18 15

Each pallet opening is 1.15 x 1.15 x 1.4-m. The rack is constructed of 10-cm tubular stock. The number of rack opening on the floor is 10. The warehouse ceiling height is 6-m. c) The storage layout and the required space. Question 30 Five products are to be stored on a pallet rack system. The inventory data are given in table (30). Table (30) Inventory data for five products Period at which Maximum Replenishment Products Maximum Quantity Quantity is replenished Frequency, month A 80 Beginning of 3 rd month Every 4 B 30 Beginning of 4 th month Every 3 B 80 Beginning of 1 st month Every 6 D 60 Beginning of 2 nd month Every 4 E 30 Beginning of 4 th month Every 3 A) Determine Randomized storage and Dedicated storage sizes. (Hint: find the inventory levels at the twelve periods first assuming equal withdrawal). B) Find for dedicated storage the following: a. the number of number of racks opening in X, Y, Z direction of the storage, if the ratio of is given as Nx ; Ny ; Nz = 9 : 3 : 1 b. Find the total number of racks, if each rack has 9 opening in x directions. c. Find the layout and space of the storage for dedicated storage. Assume the following: every two racks are arranged back to back aisle width is 2.5-m, each pallet opening is 1.0 x 1.0 x 1.25-m. the rack is constructed of 25-cm tubular stock. Question 31 A new production plant is to be located along a street running north and south. The plant is to be 265m long and 165m wide. The property is 300m long and 235m deep. Four receiving docks are to be located in one rear corner of the plant and four shipping docks on the other rear corner. The trucks servicing the plant are all 18m. Sufficient truck buffer area must be planned for three trucks for both receiving and shipping. Draw a plot plan for the site. 8

B. RECEIVING AND SHIPPING SPACE Question 1 A hospital is to have two receiving docks for receipt the supplies, which immediately stored. 15m carriers are to serve the hospital. A narrow-aisle lift truck is to be used to unload the carriers. What will be the impact on space requirement if instead of 90 0 docks, 45 0 finger docks are utilized? Question 2 A company receives trucks that hold 5000 kg each. It takes to unload each truck 1.8 worker-hours. 10 minutes is allowed for the truck to leave and anther to pull in. If eight trucks are to be serviced at the busiest time of the day, Determine: - a- The number of docks. b- The required space of the dock area for size 16m x 3m truck. Assume any missing data. Question 3 Suppose the arrival pattern of the trucks follows a passion distribution with a mean of 2 trucks/hr and the service rate follows an exponential distribution with a mean of 2 trucks/hr. a- Find the number of docks needed so that a truck does not spent more than 30 minutes in the plants. b- If the truck cost is 200 SR/hr and dock operator is paid 40 SR/hr. What is the most economical dock size? c- If it is decided that a truck should not wait more than 10 minutes (ignore the constraint on the time spent by the truck) Question4 A company recieves trucks that hold 4500 kg each. It takes 1.5 worker-hour to unload each truck. 12 minutes is allowed for the truck to leave and anther to pull in. If eight trucks are to be serviced at the busiest time of the day, Determine:- a) The number of docks. b) The required space of the dock area for size 16m x 3m truck. Assume any missing data. Question 5 A company receives trucks that hold 4500 kg each. 4000 kg can be unloaded from the truck every hour and 15 minutes is allowed for the truck to leave and anther truck to pull in. If seven trucks are to be serviced at the busiest time of the day. Determine:- i. The number of docks. ii. Develop a layout of dock area and find the required space for size truck 16m x 3m. Assume any missing data. 9