Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources

Abstract

We consider the problem of allocating demand that originates from multiple sources among multiple inventory locations. Demand from each source arrives dynamically according to an independent Poisson process. The cost of fulfilling each order depends on both the source of the order and its fulfillment location. Inventory at all locations is replenished from a shared production facility with a finite production capacity and stochastic production times. Consequently, supply lead times are load dependent and affected by congestion at the production facility. Our objective is to determine an optimal demand allocation and optimal inventory levels at each location so that the sum of transportation, inventory, and backorder costs is minimized. We formulate the problem as a nonlinear optimization problem and characterize the structure of the optimal allocation policy. We show that the optimal demand allocations are always discrete, with demand from each source always fulfilled entirely from a single inventory location. We use this discreteness property to reformulate the problems as a mixed-integer linear program and provide an exact solution procedure. We show that this discreteness property extends to systems with other forms of supply processes. However, we also show that supply systems exist for which the property does not hold. Using numerical results, we examine the impact of different parameters and provide some managerial insights.production-inventory systems, optimal demand allocation, make-to-stock queues, facility location

A Review on Long Distribution Channel‟s Problems

“…Most of the current distribution network studies use parameters based on the customer service level, which is service coverage area such as the number of distribution centres and the inventory level with minimum total costs [5], [8], [15], and [16]. However, only a limited number of researchers consider delivery time with minimum total costs or consider all parameters such as inventory level, lead time, service coverage areas, and costs simultaneously [15]- [17].…”

“…The structure of distribution network configuration in the current research studies are mainly described as a system that consists of single or multi-production plant, multi-distribution center and multi-retailer [5], [8], [16], [38]- [42]. Multi-tier distribution considerably applied in long distribution channels have the same prime objective of warehouses to fulfill customer requirements in terms of demand quantity and lead time in wider market areas [9].…”

“…Multi-tier distribution considerably applied in long distribution channels have the same prime objective of warehouses to fulfill customer requirements in terms of demand quantity and lead time in wider market areas [9]. Adding extra warehouses should be decided by considering the trade-off of some variables because using more warehouses will increase costs of inventory, carrying and warehousing while on the other hand will reduce transportation costs [8]- [14]. Transportation and logistics costs become critical components because products are distributed in a long distance with various vehicles and transited in many sites with different capabilities [34].…”

“…Determining the right number of facilities and locations in the selection of a distribution network configuration is essential policy for mostly every company and supply chain [5]- [7]. This policy is challenging due to some conflicting aspects such as warehouse and transportation costs [8].…”

A two‐echelon inventory‐location problem with service considerations

“…Eskigun et al [17], Eskigun et al [15], and Sourirajan et al [36] study different supply chain network design problems with stochastic lead times. Finally, Benjaafar et al [2] study the problem of locating facilities and managing inventory in a single-echelon system. All of the articles discussed in this paragraph utilize approximate or exact queuing formulas to model congestion in stochastic lead times.…”