This paper addresses the storage assignment problem in a mixed-shelves warehouse. In a mixed-shelves warehouse, a stock-keeping unit（SKU）is assigned to several storage locations, and many kinds of SKUs are assigned in neighboring areas. Such an arrangement can reduce the length of the picking tour when many different orders, each involving small amounts for each SKU, are to be filled. However, locating SKUs in several storage areas makes it difficult to decide the best position for each SKU. Moreover, when the pickers pick an SKU for an order, they must decide where to start, and which storage locations should be visited in order to ensure the shortest picking tour. In this paper, we first propose a mathematical model for the mixed-shelves problem. We then propose two methods to obtain approximate solutions to the problem. The first method uses a two-step approach in which we first decide the best SKU pairs to assign to the same storage area and then determine the best position for these SKU pairs. The other method consists of three steps. The first step decides the SKU pairs, the second decides the storage location assignment, and the third decides the routing. To produce the best solution, a simulated annealing-based algorithm for the assignment problem is proposed. A numerical experiment is conducted to verify the effectiveness of the two proposed methods relative to the exact method for solving the proposed mathematical formulation, especially for large size datasets.

The present study discusses an extended problem of assembly line balancing with fractional task allocation. Fractional task allocation means that a task will be executed on one of paired consecutive stations. A fractional value gives the allocation ratio of the task on the upstream station against the downstream station. A mixed-model assembly line is assumed to accept the fractional allocation of a single task. Under the condition of mixed-model assembling, the duration of each task depends on the model. Therefore, buffer stations are necessary between stations to absorb the duration variation. However, preparing a buffer incurs a fixed cost, and thus it is a realistic assumption that the number of available buffers is limited. Therefore, examining the exact timing that a job arrives at each station and the buffer required is necessary to generate a feasible assembly schedule. The present study presents a mixed-integer programming model that includes three types of decisions; the allocation of tasks at each station, including a task with fractional allocation, the assignment of buffers, and the generation of a feasible assembly schedule. The objective is to minimize the cycle time under the given number of stations. Numerical experiments were conducted for problem instances with two and five models. Solutions support fractional allocation under the conditions of (i) there is a task that has a longer processing duration than the cycle time, and (ii) the model that involves such a task has a higher demand ratio.

This paper proposes a new inventory control technique for dual-channel supply chains. In dual-channel supply chains, both a retail channel and a direct channel via a website exist. In previous studies, Takahashi et al. (2011) proposed a new inventory control technique for dual-channel supply chains by using a switching point that starts and stops for production and delivery. However, using a linear function for switching, reductions in inventory cost and lost sales costs can be expected. Therefore, in this paper, the authors propose an inventory control method using linear functions for dual-supply chains and and prove its effectiveness using numerical experiments and comparing results with those of a previous study conducted by Takahashi et al. (2011).