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In the J'ust-2'n-tirne context, parts are often processed by a single-unit production and conveyance system (called tiikko-nagashtii in Japanese) witheut conveyors.The U-shaped layout, ln which each mu!tifunction worker takes charge of several machines, has been introduced as an implementation of this concept/-Present}y the layout is gaining an increasing pepularity due to the low running cest.In this paper, first we deal with the U-shaped production line with a single multi-function We derive the overall cycie time of this line, and consider an optimal worker allocation problem that rrrtnimizes the overall cycle time when the number of workers is given. In particular, it is shown that the U-shaped Iayout is superior to the linear layout for lines with one or two workers.We also discuss the case where those processing, operation and walking times are stochastic.

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Purpose: Managing the inventory of spare parts is very difficult because of the stochastic nature of part’s demand. Also, only controlling the inventory of the spare part is not enough; instead, the supply chain of the spare part needs to be managed efficiently. Moreover, every organization now aims to have a resilient and sustainable supply chain to overcome the risk of facility disruption and to ensure environmental sustainability. This paper thus aims to establish a model of inventory-location relating to the resilient supply chain network of spare parts.Design/methodology/approach: First, applying queuing theory, a location-inventory model for a spare parts supply chain facing a facility disruption risk and has a restriction for CO2 emission, is developed. The model is later formulated as a non-linear mixed-integer programming problem and is solved using MATLAB.Findings: The model gives optimal decisions about the location of the warehouse facility and the policy of inventory management of each location selected. The sensitivity analysis shows that the very low probability of facility disruption does not influence controlling the average emission level. However, the average emission level certainly decreases with the increment of the disruption probability when the facility disruption probability is significant.Practical implications: Using this model, based on the cost and emission parameters and the likelihood of facility disruption, the spare part’s manufacturer can optimize the total average cost of the spare part’s supply chain through making a trade-off between productions, warehouse selection, inventory warehousing and demand allocation.Originality/value: Previous research focuses only on developing a framework for designing an efficient spare parts planning and control system. The inventory-location model for spare parts is not addressed in the sense of risk of facilities disturbance and emission. This research first time jointly considered the probabilistic facility disruption risk and carbon emission for modeling the spare part’s supply chain network.