7. Consider conducting putaway and retrieval simultaneously in a warehouse. The putaway process is that an employee brings a loaded pallet to its corresponding storage location from a workstation (1), and moves back to the workstation (2). The retrieval process is that an employee moves towards a storage location to fetch a pallet (3), and brings it back to the workstation (4). Assume that there is only one employee, who can carry at most one pallet when moving. There are a finite set of putaway assignments S and a finite set of retrieval assignments S. All assignments need to be fulfilled by the employee, and each assignment i corresponds to a pallet storage location, where i E S US. The warehouse network is a fully-connected map, and let dij denote the walking distance between the storage locations of assignment i and j, and d, denote the walking distance between the workstation and the storage location of assignment i. For a map, we have following conditions: dij dj,i, Vi, j E S U S U {*}, i j, and di,j di,k + dk.j, Vi, j, k S U S U {*}, i j k. = a) If the employee finishes all putaway and retrieval assignment one by one separately, how long is the total walking distance C? (5 points) b) If the employee pairs putaway assignment i with retrieval assignment j, how long would the walking distance be reduced by? (5 points) c) Suppose the employee can freely pair any putaway assignment with any retrieval assignment. Formulate an integer programming model to minimize her total walking distance. (Hint: a matching problem) (10 points) Movement with pallet: Movement without pallet: Movement with pallet: Movement without pallet: Putaway Retrieval Process Process Workstation 7. Consider conducting putaway and retrieval simultaneously in a warehouse. The putaway process is that an employee brings a loaded pallet to its corresponding storage location from a workstation (1), and moves back to the workstation (2). The retrieval process is that an employee moves towards a storage location to fetch a pallet (3), and brings it back to the workstation (4). Assume that there is only one employee, who can carry at most one pallet when moving. There are a finite set of putaway assignments S and a finite set of retrieval assignments S. All assignments need to be fulfilled by the employee, and each assignment i corresponds to a pallet storage location, where i E S US. The warehouse network is a fully-connected map, and let dij denote the walking distance between the storage locations of assignment i and j, and d, denote the walking distance between the workstation and the storage location of assignment i. For a map, we have following conditions: dij dj,i, Vi, j E S U S U {*}, i j, and di,j di,k + dk.j, Vi, j, k S U S U {*}, i j k. = a) If the employee finishes all putaway and retrieval assignment one by one separately, how long is the total walking distance C? (5 points) b) If the employee pairs putaway assignment i with retrieval assignment j, how long would the walking distance be reduced by? (5 points) c) Suppose the employee can freely pair any putaway assignment with any retrieval assignment. Formulate an integer programming model to minimize her total walking distance. (Hint: a matching problem) (10 points) Movement with pallet: Movement without pallet: Movement with pallet: Movement without pallet: Putaway Retrieval Process Process Workstation
