A simulation approach for multi-stage supply chain optimization to analyze real world transportation effects

The cost effective management of a supply chain under stochastic influences, e.g. in demand or the replenishment lead time, is a critical issue. In this paper a multi-stage and multi-product supply chain is investigated where each member uses the (s,Q)-policy for inventory management. A bi-objective optimization problem to minimize overall supply chain costs while maximizing service level for retailers is studied. Optimal parameter levels for reorder points and lot sizes are evaluated. In a first step a streamlined analytical solution approach is tested to identify optimal parameter settings. For real applications, this approach neglects the dynamics and interdependencies of the supply chain members. Therefore a simulation-based approach, combining an evolutionary algorithm with simulation, is used for the optimization. The simulation-based approach further enables the modelling of additional real world transportation constraints. The numerical simulation study highlights the potential of simulation-based optimization compared to analytical models for multi-stage multi-product supply chains.

The members of a supply chain (SC) — a network of interconnected organizations — are linked by material, information and financial flows. The objective of supply chain management (SCM) is to produce value in form of products and services for the ultimate customer. SCM involves planning, design and control of materials, information and finance along the SC in an effective an efficient manner. Especially in the last years, SCM received a lot of attention in literature as well as practice. One source of complexity in SCM is given by the different stakeholders involved, e.g. manufacturers, suppliers, distributors, transporters and warehouses. Stochastic demand and divergent and convergent flows of materials determine another source of complexity in the SC planning process (Shah 2009; Stadtler 2015). Inside SCM, inventory management is a critical issue for success. The goal of successful SCM is to provide a high service level and simultaneously minimize operating costs such as inventory costs for capital tied up in raw material, work-in-progress and finished goods inventories, respectively. Therefore inventory model parameterization offers an interesting field of research (Axsäter 2015).

In this article an analytical approach is compared to a simulation-based optimization approach. For the analytical case a single-echelon (s,Q) policy is applied to all partners within the SC in order to determine appropriate levels for reorder point s and lot size Q. The optimal solution and parameters derived from the analytical approach are then re-evaluated in the simulation model. This first study leads to insights into how a practitioner’s solution of using analytical models and ignoring interdependencies in the SC performs in a complex setting. With the use of an evolutionary algorithm the parameters for reorder point s and lot size Q are optimized and the performance increase of incorporating the dynamics and dependencies between the SC members is evaluated. Note that the simulation-based optimization does not guarantee to find the global optimum solution for the studied SC structure. Nevertheless, the simulation-based optimization technique shows a significant potential to improve the performance in comparison to the iterative analytical approach. Also a detailed analysis of the different optimal parameters is presented. Furthermore, in a more realistic scenario the influence of the real world effect of having a truck load limit, i.e. the trucks are limited in size, is studied. Finally, in another scenario the truck load limit restriction is extended by modelling a mixed load opportunity where different products can be transported on the same truck. The focus of the paper is twofold. First, from a methodological aspect, the solution and parameter differences of the analytical and the simulation-based optimization approach are discussed. Second, concerning real world assumptions, the cost influence of these assumptions is investigated.

Multi-stage supply chain model

Figure 1: Multi-stage supply chain.

The multi-stage and multi-product SC, as illustrated in Figure 1, is modeled in AnyLogic simulation software and consists of a Manufacturer M, a Distribution Center DC and several Retailers Ri. The objective is to minimize overall costs while maximizing service level η for Retailers. Overall costs consist of inventory costs ch and also for SC optimization order/setup costs cs. Note that no backorder costs are incorporated within the cost function as service level η is maximized in the bi-objective optimization problem. Whereas overall costs C are summarized over all SC members, the service level η is only evaluated for Retailers that deliver their goods to customers, i.e. product availability to the customer.

Each member within the SC uses the (s,Q) policy per product for the inventory management. The parameters that are critical for the SC performance are reorder point s and lot size Q. Reorder point s specifies the decision in time, i.e. when to order, and lot size Q the decision on the amount of an order. Higher reorder point s reduces the probability of a stock out situation and therefore increases service level η, but also increases inventory costs. Higher lot size Q reduces the order costs because fewer orders are necessary, but simultaneously increase inventory costs.

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