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Q. 11.S5

DETERMINING STORAGE LOCATIONS IN A WAREHOUSE. Erika Marsillac manages a warehouse for a local chain of specialty hardware stores. As seen in Figure S11.3 , the single-aisle rectangular warehouse has a dock for pickup and delivery, along with 16 equal-sized storage blocks for inventory items.

The following table shows: (1) the category of each item stored in the warehouse, (2) the estimated number of times per month (trips) that workers need to either store or retrieve those items, and (3) the area (number of specialized blocks) required to store the items. Erika wishes to assign items to the storage blocks to minimize average distance traveled.

 ITEM MONTHLY TRIPS TO STORAGE BLOCKS OF STORAGE SPACE NEEDED Lumber 600 5 Paint 260 2 Tools 150 3 Small hardware 400 2 Chemical bags 90 3 Lightbulbs 220 1

APPROACH $\blacktriangleright$ For each item, calculate the ratio of the number of trips to blocks of storage area needed. Rank the items according to this ratio, and place the highest -ranked items closest to the dock.

Verified Solution

SOLUTION $\blacktriangleright$ The following table calculates the ratio for each item and ranks the items from highest to lowest. Based on the ranking, items are assigned to the remaining blocks that are as close to the dock as possible. (Where applicable, given a choice between two equidistant blocks, items should be placed next to items of the same type rather than across the aisle from them.)

 ITEM TRIPS/BLOCKS RANKING ASSIGNED BLOCKS Lumber 600/5 = 120 4 6, 7, 8, 9, 10 Paint 260/2 = 130 3 3, 5 Tools 150/3 = 50 5 11, 12, 13 Small hardware 400/2 = 200 2 2, 4 Chemical bags 90/3 = 30 6 14, 15, 16 Lightbulbs 220/1 = 220 1 1

INSIGHT $\blacktriangleright$ This procedure allocates items with the highest “bang-for-the-buck” first. The “bang” (value) here is the number of trips. Because we want to minimize travel, we would like to place items with high-frequency visits near the front. The storage space represents the “buck” (cost). We want items that take up a lot of space moved toward the back because if they were placed near the front, we would have to travel past their multiple blocks every time we needed to store or retrieve an item from a different category. This bang versus buck trade-off is neatly accommodated by using the trips/blocks ratio (column 2 of the solution table). In this example, even though lumber has the highest number of trips, the lumber takes up so much storage space that it is placed further back, toward the middle of the warehouse.

LEARNING EXERCISE $\blacktriangleright$ Order frequency for paint is expected to increase to 410 trips per month. How will that change the storage plan? [Answer: Paint and small hardware will switch storage locations.]

RELATED PROBLEMS $\blacktriangleright$ S11.18, S11.19, S11.20