A Simulation and Genetic Algorithm Based Optimization of Closed – Loop Multi – Echelon Inventory System

Abstract

The objective of this research is to develop a Genetic Algorithm (GA) - based optimization approach for a multi - echelon closed - loop inventory system of items which are repairable in nature. In the context of the passenger transportation industry, engineering aggregates like engines, alternators, axles and tyres are representative examples of such systems. This research is motivated by the operations of the multi - echelon inventory system of a large public transport corporation with a fleet size of 9000 buses. For administrative control, the corporation is organized into l6 divisions and 130 depots. The weekly revenue of the corporation is Rs. 235 million. On an average 575 vehicles are off - road per day due to the non – availability of essential spares. The revenue loss per day on account of off - road vehicles alone is estimated to be Rs. 3.5 million. The non - availability of vehicles for operations poses several managerial challenges in maintaining network connectivity, schedules and consistency of operations. Often, conflicting objectives related to schedule frequency and network connectivity need to be managed. Disruptions would impact service levels adversely and defeat the purpose of the transport agency. The study discusses the context of the problem and the managerial issues, as well as key questions and describes the design, development, verification and validation for a simulation model. An attempt is also made to optimize the key inventory policy parameters, viz., the review periods and the base stock levels of the system by using GA. For the purpose of illustration, we consider the inventory of tyres. Tyres selected for rereading, at the depot level, are sent to the divisions. The accumulated tyres at each division are then sent to the rereading plant. After rereading, the tyres move from the rereading plant to the depots through the divisions. Several analytical models are reported in the literature along with varied assumptions. These include: 0 Demand represented by Poisson Process 0 (S-1, S) inventory policy 0 Continuous review inventory policy and batch replenishment of spares I Constant or stochastic transportation time between various echelons 0 Infinite repair capacity at the reconditioning facility 0 Negative exponential repair time for individual parts at the reconditioning facility 0 Constant or stochastic replenishment lead time Some of these assumptions are found to be restrictive in the context of the present problem. Thus, the available analytical models had limited use in our investigation. Hence, a simulation based optimization approach was adopted. The management of closed - loop multi - echelon inventory systems is a combination of several interlinked decisions. Our approach is comprehensive and can be generalized and applied to other problems in similar contexts. Specifically, we consider the following policy decisions while developing an optimization model: 0 Inventory of total tyres to be kept in the system 0 Inventory policy at various echelons 0 Distribution of spare tyres across echelons (both depots and divisions) We develop a simulation model customized to the specific context. The simulation model is verified and validated with the theoretical results on representative cases. A set of design experiments is used to optimize the total tyres in the system. We have adopted a two - stage modelling approach. In the first stage a comprehensive simulation model is developed for a periodic review base stock policy with assumptions reflecting the context. The choice of a periodic review ordering policy for this inventory system is motivated by several practical considerations related to transportation and logistics. The objective function considered is Minimizing Total Supply Chain Cost (TSC), which comprises of three cost elements - namely, the ordering cost, the holding cost and the shortage cost. The three cost elements, in turn; depend on the inventory policy parameters such as review periods and base stock levels at various echelons. The simulation model captures an extensive set of performance measures namely, the average on hand inventory, the backorders, the fill rates, the service levels, the ready rates and the lead time estimates at all echelons. For a given set of parameters (review periods and base stock levels), simulation is used to estimate the average on - hand inventory levels and the backorder levels at various echelons, which in tum gives the estimate for the TSC. In the second stage, a GA - based optimization approach is used. The GA implementation is based on simulation for a given set of policy parameters. The aim of the GA is to identify the optimal set of policy parameters for the system. The performance of the GA is compared to the appropriate lower bounds. A heuristic is also proposed to further improve the optimal solutions obtained by the GA. The main contribution of the present research is the design and development of an optimization approach based on simulation and GA. The simulation model captures real life assumptions and provides several performance measures to understand the complexities of the closed – loop inventory system. The approach (a combination of GA and simulation) can be generalized and applied in the context of a wide range of problem. Typically, the approach is applicable to the repairable parts inventory, related to industries with a heavy utilization of equipment’s, like the Chemical and the Petrochemical industries. Other areas of application include maintenance and repair of communication networks, refrigeration and air - conditioning equipment.