Multi-Echelon Inventory Control with Consideration of Emissions and Service Differentiation

An increased focus on sustainability and initiatives towards green supply chains raises new challenges for efficient inventory control. This doctoral thesis addresses the consequences some of these initiatives have on the modelling of inventory systems and the resulting policy variables. The overall research objective for the doctoral thesis can be stated as:To design mathematical models for evaluation and control of multi-echelon distribution systems with stochastic demand, in order to develop efficient methods for inventory control, with emphasis on the impact of various initiatives towards green supply chains. More specifically, this includes emissions related to system design decisions and service differentiation.This doctoral thesis consists of four scientific papers preceded by a summarizing introduction. Common for all papers is that they focus on inventory control in divergent multi-echelon inventory systems with one central warehouse supplying an arbitrary number of retailers or local warehouses. The research provides methods for determining control variables for efficient control in the different settings analysed in Papers I - IV, respectively. From a methodological perspective, the research belongs to the inventory control area in the field of operations research/management science.Paper I considers a situation where customers have an acceptable waiting time for which they are willing to wait for a requested item, but it is critical not to exceed it. This type of time limits may be present in for example spare part inventory systems in the food industry where it is crucial to repair broken-down machines before the product perishes. Thus, a time based service level or a non-linear backorder cost reflecting this is considered. The backorder cost structure is extended to include general backorder costs as a function of the customers' waiting time. Paper I presents an exact method for finding optimal base-stock levels to minimize the total system cost under a service constraint or using a backorder cost. Furthermore, the model allows for quantification of emissions due to production waste from perished products as a consequence of delayed deliveries.Paper II extends Paper I by allowing for emergency replenishments to prevent perishable products from going to waste because the acceptable waiting time is exceeded. The emergency replenishments are assumed to be faster than normal replenishments but at the cost of more emission intense transports. The model allows for emissions from production waste and the added emissions from the emergency replenishments to be quantified and compared.Paper III presents efficient heuristics for finding optimal reorder levels and shipment intervals in an inventory system with time based shipment consolidation and lumpy demand. Shipments from the central warehouse is dispatched periodically to the retailers at fixed time intervals as a means to increase the utilization of the transports. Thereby the number of transports needed is lowered with the aim to reduce the connected costs and emissions. Both a fill rate constraint model as well as a backorder cost model is considered. The aim of the presented heuristics is to be applicable to real life inventory systems, and they are tested for this with good results.Paper IV considers a setting with direct customer demand present not only at the retailers but also at the central warehouse. This type of inventory system may be found in an omni-channel distribution system with online sales, and it accentuates the need for service differentiation at the central warehouse. A heuristic for setting reorder points throughout the system and to decide how much stock to reserve at the central warehouse for the direct customer demand in order to achieve efficient control of the system is developed. The heuristic is designed to be implementable in practice, and it is evaluated using real life data from two different companies showing good results.To summarize, this doctoral thesis provides mathematical models and develops efficient methods for inventory control with consideration of emissions and service differentiation