Two components of a supply chain with a significant impact on its performances are inventories and transportation costs. Mutual dependences between the activities of inventory allocation and vehicle routing have recently motivated some authors to model them simultaneously. This practical and challenging logistical problem is known as the integrated Inventory Routing Problem (IRP). The IRP assumes application of vendor management inventory (VMI) concept where suppliers determine an order quantity and the time of its delivery. The IRP is usually formulated and solved under the assumptions of deterministic consumption and delivery times which, in turn, provide an opportunity of obtaining a solution of the problem regardless of its NP hardness, even in this simplified form. However, since fuel consumption is stochastic in its nature, delivery plans based on a deterministic assumption, particularly covering longer planning periods, may introduce certain problems in real life applications, imposing shortages, higher inventories levels, or even the necessity of changing delivery routes. This paper presents a simulation approach to the analysis of the applicability of deterministic IRP solution to real life stochastic fuel consumption and delivery process. The applicability of deterministic IRP solutions to stochastic problems with planning periods of different lengths is analyzed through observing different process performances. From obtained results it can be concluded that solutions based on deterministic consumption can be applied in stochastic IRP by applying and balancing two additional measures: emergency deliveries and safety stocks.

In this study, we consider a production lot-sizing and scheduling problem found in the fruit juice production industry from an enhanced inventory management perspective. The problem can be classified as a P2SMM (two-stage multi-machine lot-scheduling) problem. We extended the classical P2SMM problem by incorporating an additional inventory management aspect of finished products to reflect a possible real-life case problem, specifically regarding the shelf-life concept and limited warehouse capacity, with a possibility of outsourcing the warehousing demand to a third-party logistics company. We developed the mixed integer linear programming (MILP) model to fully represent the considered problem (due to the NP-hard nature of the problem, only small-scale instances could be solved to optimality), and the hybrid variable neighborhood search with linear programming (VNS/LP) model to solve both small and real-life large-scale problem instances. The goal of the developed models is to minimize total costs that consist of the cost of backordering, the cost of planned minimum and maximum stock level violation, the cost of warehouse capacity overflow, the costs of production setup time and unused available production time. The main idea of the VNS/LP model is to solve the scheduling segment of P2SMM (the production sequence) via a VNS heuristic, and the lot-sizing segment of P2SMM via the linear programming (LP) model. Based on the results from five variants of the problem setup, a potential decision maker can have an overview of the impact of different important input parameters (production time costs, warehouse capacity and costs, inventory related costs and production demand) on the total cost of a production process and improve its efficiency in changing conditions.

In order to increase the efficiency of the order-picking process, warehouses are forced to find ways to adopt to constantly intensifying changes in the assortment and quantities of stored products. Accordingly, we present a methodology that deals with such a problem at a tactical level by defining the optimal size and an allocation of products within the order-picking area of the most typical order-picking setting. The methodology combined two methods, dynamic programming and simulation modelling, with the aim of taking advantages of their positive features. In that sense, the optimal allocation of products for different sizes of the order-picking zone were obtained by the dynamic programming approach. Afterwards, the influence of a demand’s seasonality and variations were treated by the simulation model, so that the more realistic performances of the system were captured for the optimal allocation of products. The methodology was tested on the retailer data with significant week seasonality. The obtained results confirmed the practical applicability of the methodology in real systems, while the sensitivity analysis of results showed that special attention and effort should be given to the determination of costs related to the engagement of order-pikers, storage equipment and unit replenishment during a planning period.