The Indian auto-components industry has experienced healthy growth over the last few years. The auto-component industry of India has expanded by The auto-components industry accounts for 2. A stable government framework, increased purchasing power, large domestic market, and an ever increasing development in infrastructure have made India a favourable destination for investment. The Indian auto-components industry can be broadly classified into the organised and unorganised sectors. The organised sector caters to the Original Equipment Manufacturers OEMs and consists of high-value precision instruments while the unorganised sector comprises low-valued products and caters mostly to the aftermarket category.
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This paper presents a 0—1 programming model aimed at obtaining the optimal inventory policy and transportation mode for maintenance spare parts of high-speed trains. In addition, we analyse the shortage time using PERT, and then calculate the unit time shortage cost from the viewpoint of train operation revenue.
Finally, a real-world case study from Shanghai Depot is conducted to demonstrate our method. Computational results offer an effective and efficient decision support for inventory managers. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. As an energy-saving and environmentally friendly transportation mode, railways have attracted much attention in recent years.
The railway network, especially the high-speed railway HSR , has developed rapidly in China. For example, China had built a HSR network of 19, km by the end of [ 1 ]. According to the long-term plan released recently, the HSR network size is expected to reach 30, km in and 38, km in [ 2 ].
Along with construction of the HSR network, the demand for high-speed trains is increasingly strong. Ever since the Beijing-Tianjin high-speed rail line which is generally regarded as the first high-speed line in mainland China was put into operation in , the accumulative mileage of all high-speed EMU trains has reached more than 3.
Therefore, the ordering and inventory of overhaul spare parts for high-speed trains have been placed on the agenda. It is well known that high-speed EMU trains should be inspected and maintained after a pre-defined travel distance for safety reasons.
During the maintenance process, some worn components are replaced. Thus, EMU depots where EMU trains are overhauled should not only provide a range of inspection equipment but also stock a large number of spare parts. Clearly, excess inventory of spare parts will lead to high holding costs. In contrast, insufficient inventory yields a low service level and may impact on the maintenance process. Worse yet, a shortage of spare parts may delay putting the EMU trains into service on schedule, which can lead to vast economic losses [ 4 , 5 ].
Hence, determining how many spare parts should be stored in EMU depots has become an urgent scientific problem for the high-speed railway system [ 6 ]. This issue is even trickier for occasionally-replaced spare parts OSP that are required within an EMU overhaul process because their demand is highly random, with little historical data and lacking in statistical samples. Transportation plays a major role in supply chain management.
If the transportation costs of EMU spare parts are low, and the parts can be delivered in time, a zero inventory strategy is worth pursuing. However, uncertainty always exists in the transportation and delivery process, and as a result, transportation time windows need to be considered when developing inventory strategies in practice.
As inventory and transportation are highly correlated [ 7 ], their joint optimization represents a critical and important task for inventory managers. Demand for spare parts is typically intermittent and lumpy, and forecasting the relevant requirements constitutes a very challenging exercise [ 8 ]. Croston [ 9 ] described a method of forecasting intermittent demand by using separate estimates of the size of demand, and of the demand frequency. The rules for setting the safety stock levels had also to be adjusted before consistent protection could be obtained against being out of stock.
Kamath and Pakkala [ 10 ] outlined a Bayesian approach to demand estimation for the cases of stationary as well as non-stationary demand, which was particularly useful for long planning horizons. Moreover, the bootstrap procedure was also widely used to address the intermittent demand [ 11 ]. In early literature, the demand of spare parts was primarily assumed to be normally distributed [ 9 ], geometrically distributed [ 12 ], or a gamma distribution [ 13 ].
However, these assumptions lack of empirical support. Syntetos et al. The results of their empirical investigation suggest that the negative binomial distribution NBD performs best in an inventory context, followed by the Gamma and Stuttering Poisson distribution.
Recently, maintenance policies have been considered when forecasting spare parts demand. On this basis, integrated demand forecasting and equipment maintenance models are proposed.
Wang and Syntetos [ 8 ] presented a novel idea to forecast service parts demand that relies upon the very sources of the demand generation process and compared it with a well-known time-series method. Subsequently, Wang [ 15 ] presented the joint optimization for both the inventory control of the spare parts and the preventive maintenance inspection interval.
Romeijnders et al. These maintenance-driven models provide better accuracy than traditional methods, and thus they are recommended for practical applications. The inventory control policies need to be developed once the spare parts demand is obtained. Because spare parts inventories differ from those of work-in-process and finished products, unique aspects of maintenance inventories have been considered in previous studies see the overview by [ 17 ].
Kocaga and Sen [ 18 ] studied an inventory system that consisted of two demand classes. The orders in the first class needed to be satisfied immediately, whereas the orders in the second class were to be filled in a given demand lead time. Selcuk [ 19 ] presented an adaptive base stock policy for a repairable item inventory control problem. A binary programming model was proposed and then an automated approach was presented to solve the model, in which each combination of policy parameters s , S for a spare part was represented by a column.
Guajardo et al. The fitness of seven demand models to the data of about 21, items were studied. Topan et al. They also proved that the heuristic was asymptotically optimal in the number of parts. However, the above literature do not consider the transportation process in the supply chain management.
Indeed, impacts of transportation on the development of inventory policy lie on various aspects. For example, since different transportation modes correspond to different delivery time, to ensure the buyer can receive items within a given time window e. Otherwise, it may result in extra holding costs or shortage costs. Compared with independent inventory optimization, integrated inventory-transportation related considerations of the spare parts inventory problem is an area that has not received sufficient attention in the literature.
Qu et al. Kutanoglu and Lohiya [ 5 ] presented an optimization-based model to gain insights into the integrated inventory and transportation problem for a single-echelon, multi-facility service parts logistics system with time-based service level constraints.
Zhao et al. Jha and Shanker [ 26 ] investigated an integrated inventory problem with transportation in a single-vendor and multi-buyer divergent supply chain. The issue of transportation was addressed through vehicle routing in the model.
Amini and Ghodsi [ 7 ] addressed an integrated transportation and inventory problem in a two-stage supply chain, including suppliers and retailers, while considering the role of energy in terms of fuel's type selection.
Lee et al. However, above methods cannot be applied to our work directly since unique aspects should be considered in a high-speed railway system. Despite relatively rich literature on service spare parts demand forecasting and inventory policy development, few studies involve high-speed train maintenance parts. Some unique problems should be carefully examined for these parts when developing inventory policies, such as how to calculate the shortage cost caused by delay of train services and how to take into consideration of train maintenance strategies.
In this paper, we address the inventory-transportation integrated optimization problem from both aspects of theoretical analysis and practical application. Our contributions can be summarized as follows:. The remainder of this paper is organized as follows.
Section 2 presents the 0—1 programming model to address the integrated inventory-transportation problem, together with analysis of total costs of two basic inventory policies. Section 4 analyzes the shadow loss of absence from train operation service caused by the shortage of spare parts using PERT.
Section 5 demonstrates our method by a real-world example. Finally, conclusions and directions for future research are discussed in Section 6. There are various types of inventory policy, such as the reorder point policy, the fixed-time period method, and the just-in-time strategy. These policies can be roughly divided into two basic types: the advance order policy AOP and the temporary order policy TOP. The advance order policy states that in order to avoid being out of stock, items are stored in warehouses in advance, on the basis of materials consumption law.
In contrast, under the temporary order policy, items are ordered when needed. For each inventory policy, we consider three major transportation modes: rail, truck, and air transport. The aim of our study is to determine the optimal the most economical inventory policy as well as the optimal transportation mode. In this section, we propose a 0—1 programming model to address this integrated inventory-transportation optimization problem. Intended to achieve the minimal costs of inventory, the integrated inventory-transportation problem can be formulated as a 0—1 programming model as follows: 1 2 3 4 Objective Function 1 is the total costs of inventory.
Constraint 2 ensures that each inventory policy can only adopt one transportation mode. Constraints 3 and 4 are the binary restrictions on decision variables. Under the AOP, we consider the following costs: ordering cost, purchase price, inventory holding cost, transportation cost and in-transit inventory cost. In this way, the total cost derived from [ 28 ] of the AOP with transportation mode m can be expressed as follows. The five terms on the right side of Eq 5 are ordering cost, transportation cost, in-transit inventory cost, annual purchase cost, and annual holding cost, respectively.
In the TOP, items are ordered when they are needed; that is, there are no holding costs. However, stockouts may occur as the transportation process can sometimes be out of the time window. In fact, the TOP avoids the holding costs at the price of shortage costs. Please note that both annual purchase cost terms in the AOP and TOP are identical, which means they have no effects on the optimization process.
However, to highlight the total costs of inventory and without loss of generality, we still preserve the annual purchase cost term in the computational process.
Clearly, there are six candidate solutions of the 0—1 programming model, which means we can apply an enumeration method to solve it. In fact, for the AOP, without any doubt, we would adopt the least costly transportation mode; that is, the rail transport mode.
To calculate the total costs of inventory for each candidate solution, we need to first obtain the annual demand. To this end, we describe the detailed demand estimation method in Section 3. In addition, in the TOP, the shortage costs should also be obtained.
With respect to this point, a PERT is used to calculate the shortage costs from the perspective of train operation revenue in Section 4. Note that the order quantity Q m in Eq 5 is unknown.
To achieve minimal costs, we use the EOQ model to determine the optimal lot size: 7 By comparing the four corresponding objective values, the best inventory policy as well as the transportation mode can be obtained.
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