A queueing approach to production-inventory planning for supply chain with uncertain demands: Case study of PAKSHOO Chemicals Company

Abstract In some industries such as the consumable product industry because of small differences between products made by various companies, customer loyalty is directly related to the availability of products required at that time. In other words, in such industries demand cannot be backlogged but can be totally or partly lost. So companies of this group use make-to-stock (MTS) production policy. Therefore, in these supply chains, final product warehouses play a very important role, which will be highlighted by considering the demand uncertainty as it happens in real world, especially in the consumable product industries in which demand easily varies according to the customer’s taste variation, behavioral habits, environmental changes, etc. In this article, an ( s , Q ) inventory system with lost sales and two types of customers, ordinary and precedence customers and exponentially distributed lead times are analyzed. Each group of demands arrives according to the two independent Poisson processes with different rates. A computationally efficient algorithm for determining the optimal values for safety stock as reorder level and reorder quantity for a multi-item capacitated warehouse is developed. The algorithm also suggests the optimal warehouse capacity. A Multi-item Capacitated Lot-sizing problem with Safety stock and Setup times (MCLSS) production planning model is then developed to determine the optimal production quantities in each period using optimal values computed by the first algorithm as inputs. Finally, the proposed production-inventory-queue model is implemented in a case study in PAKSHOO Chemicals Company and results are obtained and analyzed. Moreover, solving this problem can help to strategic decision making about supply chain decoupling point.

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