Question 6.1. What is a unit-load warehouse and why is it easier to layout than others?
Question 6.2. For each of the following, explain whether the description makes the SKU more or less appropriate to be stored in pallet rack rather than stacked on the floor, and why.
1. A pallet of this SKU is fragile.
2. A pallet of this SKU is heavy.
3. Pallets of this SKU can be stacked safely almost to the ceiling.
4. A pallet of this SKU is strong and square.
5. There are never more than two pallets of this SKU in the warehouse.
6. Each case of this SKU is dense and so, to keep the pallet from being too heavy,it is loaded only one meter high.
Question 6.3. Why is it generally better to centrally locate receiving and shipping doors.
Question 6.4. When is a cross aisle valuable? When are angled aisles valuable?
Question 6.5. Explain why it is almost always preferable to orient aisles parallel to a line connecting receiving to shipping.
Question 6.6. Consider the two ways of orienting aisles on the floor plan shown in Figure 6.14. Assume that for each layout receiving is located at the bottom of the figure and shipping at the top. Which is the more efficient layout and why? How would your answer change if both receiving and shipping were located at the bottom? (Answer: The one on the left is more efficient in both cases.)
Figure 6.15: Question 6.7: Should a cross-aisle be located close to receiving/shipping or far?
Question 6.7 (K. R. Gue). Where is the best place for a single cross-aisle in a unit-load warehouse such as shown in Figure 6.15? Assume that all operations are dual-cycle,all locations are equally likely to be used, and that both receiving and shipping are at the bottom of the figure. What if receiving and shipping are on opposite sides? How would your answers change if the challenge were to locate several cross-aisles?
Question 6.8. Figure 6.16 shows the layout of a distributor of spare parts. The left side of the warehouse is pallet rack and cantilever rack. Receiving is on the bottom left and shipping is on the bottom center of the figure. Critique this layout.
Question 6.9. Under what circumstances are deep lanes appropriate? What advantages and disadvantages accrue for deeper lanes?
Question 6.10. Suppose you have 100 pallets of SKU A and 100 pallets of SKU B.Pallets of SKU A may be stacked 4 high while, because of fragility, pallets of SKU B may be stacked only two high. Which one should have deeper lanes if they are floorstacked? How much deeper? (Answer: SKU B by a factor of √
2)
Question 6.11. Suppose you are laying out a floor stack area with an aisle 14 feet (4.3 meters) wide to accommodate forklift trucks. All pallets are 48 by 40 inches (1200 by 1000 mm) and are stored with the 40-inch side facing the aisle. Assume that each SKU experiences demand that is constant and is reordered once each inventory cycle as below.
A. For each SKU, compute a space-efficient lane depth.
B. Compute a single, common lane depth that will be space-efficient for the set of SKUs. (Answer: 4 pallet positions)
Figure 6.16: Question 6.8: Critique this layout of a service parts distribution center.
Question 6.12. Suppose you are laying out a floor stack area that will be a single pallet position deep. The aisle will be 2 pallets wide. Assuming that demands are constant, which SKUs will give the best space utilization in this area? (Answer: Those with no more than two columns to be stored)
Question 6.13. Consider a collection of pallets of paint of various kinds. Each SKU will be floor-stacked 4 pallets high. Which SKUs are best stored in the area of the warehouse with lane depth of 3 pallet positions and an aisle 3-pallets wide?
Question 6.14. Prove Theorem 6.3, which establishes the optimal lane depth for pallet flow rack. Hint: You must also charge for aisle space behind the flow rack, for restocking.
Question 6.15. True or false: Faster-moving product should be stored in deeper lanes. Explain your answer.
Question 6.16. Why cannot high space utilization be guaranteed simply by storing product in sufficiently deep lanes?
Question 6.17. What is “honeycombing” and why is it a problem for warehouses? What techniques or tools can be used during the phase of warehouse design to reduce horizontal honeycombing? Vertical honeycombing?
Question 6.18. For a given set of SKUs and fixed aisle width, which type of storage would likely have the greater lane depth when optimized for space efficiency: floor storage or pallet flow rack? Why?
Question 6.19. Suppose that you have planned a layout for floor storage with one global, optimal lane depth for your SKUs. Subsequently you learn that inventory levels will be half of what you had expected; how does this change the optimal lane depth? (Answer: reduced by a factor of 1/
√
2)
Question 6.20. Consider a SKU with pallets so short that a stack of two can be stored within a single pallet opening in rack. How would you estimate the average number of visits per storage location generated by such a SKU? How can you continue to use the formula for optimal lane depth for such a SKU?
Question 6.21. Why do you suppose single-deep rack also called “selective rack”?
Question 6.22. Selective (single-deep) rack can never provide utilization of floorspace in a real warehouse exceeding which value: 25%? 33%? 50%? 66%? 75%? 100%? Explain why your answer is the best choice.
Question 6.23. Which method of storage makes empty pallet positions more quickly available, thereby increasing storage capacity: floor storage or rack storage? Explain.
Question 6.24. Explain why a warehouse with only one or two pallets of each of many SKUs is likely to prefer rack to floor storage.
Question 6.25. Consider a unit-load warehouse that is rectangular, of dimension m×n (with m >> n). If it is to be laid out with receiving and shipping on opposite sides, is it more efficient to run aisles parallel to the long or the short side of the warehouse?Why? What if receiving and shipping were on the same side?
Question 6.26. In Section 6.2.2 we estimated the “convenience” of a storage location by the forklift travel from receiving to the location plus that from the location to shipping. We did not explicitly account the unloaded travel (“dead-heading”) that the
forklift must make after storing a pallet in the location or delivering the pallet to shipping. How might this additional travel affect our analysis? Assume that we load and ship full trailers in the mornings and that we receive and unload full trailers in the afternoons.
Question 6.27. Suppose that we want to store all the SKUs of each customer together in a pallet-in, pallet-out warehouse. The SKUs of which customer are candidates for the most convenient locations? Explain.
• That customer who has the most pallets in the warehouse
• That customer whose pallets we receive and ship in the greatest quantities
• That customer whose product represents the greatest dollar-volume when we account for the value of the product
• That customer whose shipments into the warehouse are the largest
• That customer whose shipments out of the warehouse are the largest
• That customer whose SKUs achieve the greatest annual turns
• It is impossible to tell
• None of the above
Question 6.28. Consider two SKUs moving through a unit-load warehouse. Every Monday morning 100 pallets of SKU A are shipped out and in the afternoon 100 new pallets of SKU A arrive. Every other Monday, 10 pallets of SKU B are shipped out and in the afternoon 10 pallets arrive. On average there are 500 pallets of SKU A on-hand and 20 pallets of SKU B.
• Which SKU has priority for storage in the most convenient storage locations under FIFO?
• How would your answer change if the FIFO requirement were dropped?
Question 6.29. Consider three pallet locations A, B, C, for which the total time to travel from receiving to the location to shipping is 1, 2 and 2 minutes, respectively.Through these locations flow two SKUs, x and y, which you must manage in a strict
FIFO manner. Every three days one pallet of SKU x is shipped out in the morning and one pallet arrives in the afternoon and is put away. Every two days one pallet of SKU y is shipped out in the morning and one pallet arrives and is put away. You maintain a constant inventory of one pallet of SKU x and two pallets of SKU y on-hand at all times.
A. If you are using a policy of dedicated storage, what is the assignment of SKUs to storage locations that minimizes average labor? (Justify your answer.) What is the corresponding average minutes per day spent moving these products?
B. What is the smallest sustainable value of average minutes per day spent moving these SKUs if you adopt a policy of random storage? Does it make any difference where the SKUs are stored initially?
C. What is the best way of assigning pallets to storage locations if you are permitted to drop the FIFO requirement? Would this save any labor? If so, how much; if not, why not?
D. How would your previous answers change if the pallets of SKU y arrive in batches of two every four days? Assume the pattern of shipping is unchanged.Question 6.30. Label each of the following as true or false, and explain your answer.
For a unit-load transshipment warehouse
• Space is better utilized if the pallet expected to depart soonest is stored in the most convenient location.
• Labor is reduced if the pallet expected to depart soonest is stored in the most convenient location.
• Space is better utilized if the SKU expected to depart soonest is stored in the most convenient location.
• Labor is reduced if the SKU expected to depart soonest is stored in the most convenient location.
• Space is better utilized if the pallet expected to depart soonest is stored in the location closest to shipping.
• Labor is reduced if the pallet expected to depart soonest is stored in the location closest to shipping..
Question 6.31 (Exploration). Consider a unit-load warehouse with regular, patterned input stream of arriving pallets and output stream of departing pallets, as in the previous question. Explore how, under a policy of random storage, the disposition of SKUs in the warehouse organizes itself.
Question 6.32 (Harder). Suppose you are free to choose two lane depths for floor storage: One region of the warehouse will be devoted to deep lane storage and one to shallower storage.
• Prove the following: When the number of columns of each SKU greatly exceeds any candidate lane depth then, if a particular SKU belongs in the deeper lane storage, any SKU with more columns also belongs in the deeper lane storage.
• How can you use this fact to decide where to store the SKUs?
• How can you use this fact to choose the best two values for lane depth?
• Generalize to three or more lane depths.
Question 6.33 (Exploration). Build a simulation model to study the effect of lane depth on warehouse performance. Measure especially the effect on space utilization, labor, and observance of FIFO.
