به حداقل رساندن "زمان انجام سفارش" در سیستم تک پردازنده چندمحصولی: مقایسه سیاست های حلقوی

The supply chain under consideration is a two-echelon system consisting of a retailer and a manufacturer. The N different products face stochastic demand at the retailer and are produced using a shared facility at the manufacturer. Production changeover involves setup time that is significantly higher than the processing time. A cyclic polling model with exhaustive limited service policy from the networking literature is applied to the supply chain problem and the service limit values are obtained to minimize the lead time. Mathematically the exhaustive service policy gives least value, but in practice we can set the service limit to values near the stability condition and obtain similar results. Other cyclic policies that take into consideration either the minimum lot size or the production quantity band or the idle time between cycles are also studied. These are tested for different values of plant utilization and a comparison is drawn through simulation. Limitations of the model are discussed and possible extensions identified.

In this paper we consider a two-echelon supply chain system with stochastic demand for N different products at the retailer. All the products are produced by a manufacturer using a single processor with limited capacity. Each product type has its own set of parameters like setup time, processing time and arrival rate. The setup time of a product is usually much larger than its processing time. The manufacturer and the retailer share the point of sale information. For every unit sold at the retailer the corresponding order for the product gets accumulated at the manufacturer in the queue corresponding to that product. These queues are processed by the processor in a cyclic order. The demand at the retailer is stochastic and the transportation time is assumed to be negligible. This type of problem is termed as stochastic economic lot scheduling problem (SELSP). A detailed review on SELSP is provided by Sox et al. (1999). The deterministic version of this problem is NP hard (Hsu, 1985) and is widely studied, but not yet solved in general (Markowitz et al., 2000). We are interested in comparing the various cyclical policies from the standpoint of the manufacturer in reducing the lead time of the overall system. In today's supply chain, the retailers are willing to share the point of sale information with the higher echelons which can provide significant benefits to all the players. We have limited our scope to a retailer–manufacturer supply chain, where the manufacturer has to decide on his production schedule based on the real time information provided by the retailer. We do not get into the problem of determining the optimal quantities to be held by the retailer since, for a given service level, it can be determined using methods available in the literature. As such, the production scheduling of multiple products on a single machine with significant setup time is a classic problem of production planning. The stated problem has a wide range of industrial applications, which include glass manufacturing, injection molding, metal stamping, paper production, semi-continuous chemical processes and production of consumer products like detergents, bar cakes, toothpastes, etc. The practical benefit for the manufacturer is higher plant utilization and the retailer can maintain lower inventory for same level of customer service. In case of multiple retailers having Poisson demand for each of their products, the analysis still holds with the compound Poisson distribution for the demand of products at the manufacturer.

In this paper, waiting time computations available in networking literature have been suitably modified and applied in a supply chain environment having similar characteristics. Our experiments show that the waiting time estimations do not hold when the setup times are large. However, the model is effective in estimating service limits for each product queue so as to imitate the performance of exhaustive policy. It has been observed from the simulation that there is no considerable increase in waiting time beyond a threshold of ki. Determination of ki's is very helpful in evaluating wide range of policies. For the retailer, it helps to determine the safety stock and base stock level, and for the manufacturer, it guides to have a production plan that is easy to implement. The various assumptions, and hence the approximations, adopted from the networking literature are the clear limitations of the system. On the positive side, it helps to estimate ki's analytically without any complex algorithm and holds over a wide range of conditions. Future work can be concentrated on modeling this system by removing the approximations, but that may lead to the system being intractable. A comparison can be done with other polling policies as to what is best suited under the given set of conditions. One can also look at having different policies for the different queues within the polling model.