• Journal of Korean Institute of Industrial Engineers
• /
• v.24 no.1
• /
• pp.157-165
• /
• 1998

This paper considers the single-product production and transportation problem with discrete time, dynamic demand and finite time horizon, an extension of classical dynamic lot-sizing model. In the model, multiple freight container types are allowed as the transportation mode and each order (product) placed in a period is shipped immediately by containers in the period. Moreover, each container has type-dependent carrying capacity restriction and at most one container type is allowed in each shipping period. The unit freight cost for each container type depends on the size of its carrying capacity. The total freight cost is proportional to the number of each container type employed. Such a freight cost is considered as another set-up cost. Also, it is assumed in the model that production and inventory cost functions are dynamically concave and backlogging is not allowed. The objective of this study is to determine the optimal production policy and the optimal transportation policy simultaneously that minimizes the total system cost (including production cost, inventory holding cost, and freight cost) to satisfy dynamic demands over a finite time horizon. In the analysis, the optimal solution properties are characterized, based on which a dynamic programming algorithm is derived. The solution algorithm is then illustrated with a numerical example.

• The Journal of the Convergence on Culture Technology
• /
• v.8 no.6
• /
• pp.655-660
• /
• 2022

This paper analyzes the problem of the economic order quantity (lot size) of a retailer in a two-stage supply chain consisting of a supplier, a retailer(distributor), and a customer. In this two-stage supply chain, the supplier permits the retailer to defer payment for a certain fixed period of time for the purchase cost to be paid by the retailer as a price differentiation strategy with his competitor. In addition, in the case of customer goods such as food and grain, it is common to see that end-customer demand is generally depend on the level of inventory displayed by the retailer. From this perspective, this paper analyzes the inventory problem of retailers under the assumption that the supplier may allow a certain period to suspend payments for the purchase of goods and the end customer demand is a function of the retailer's inventory level increasing with size. In this regard, we need to analyze how much the length of the grace period for product purchase costs affect the retailer's lot-sizing policy. Therefore, we formulate the retailer's annual net profit and analyze the effect of the length of credit period on the retailer's inventory policy numerically.

• The Journal of the Convergence on Culture Technology
• /
• v.9 no.6
• /
• pp.257-262
• /
• 2023

As part of their marketing policy, some suppliers allow retailers a period of credit in anticipation of increasing demand for the products they supply. The opportunity to defer payments on products through credit transactions has the effect of reducing retailers' inventory investment costs, and as a result, retailers determine selling prices in anticipation of increased demand from buyers. This study aims to analyze the inventory model that determines the retailer's selling price and EOQ(Economic Order Quantity) under the assumption that the buyer's demand is an exponentially decreasing function of the retailer's selling price in the credit transaction supply chain consisting of suppliers, retailers, and buyers. The products supplied for problem analysis include the case of deteriorating products that deteriorate over time, and the effect of the credit transaction period, the index of price elasticity and the degree of deterioration on the retailer's selling price and EOQ is analyzed.

• Korean Chemical Engineering Research
• /
• v.45 no.3
• /
• pp.249-257
• /
• 2007

The periodic square wave (PSW) model was successfully applied to the optimal design of a batch-storage network. The network structure can cover any type of batch production, distribution and inventory system, including recycle streams. Here we extend the coverage of the PSW model to multitasking semi-continuous processes as well as pure continuous and batch processes. In previous solutions obtained using the PSW model, the feedstock composition and product yield were treated as known constants. This constraint is relaxed in the present work, which treats the feedstock composition and product yield as free variables to be optimized. This modification makes it possible to deal with the pooling problem commonly encountered in oil refinery processes. Despite the greater complexity that arises when the feedstock composition and product yield are free variables, the PSW model still gives analytic lot sizing equations. The ability of the proposed method to determine the optimal plant design is demonstrated through the example of a high density polyethylene (HDPE) plant. Based on the analytical optimality results, we propose a practical process optimality measure that can be used for any kind of process. This measure facilitates direct comparison of the performance of multiple processes, and hence is a useful tool for diagnosing the status of process systems. The result that the cost of a process is proportional to the square root of average flow rate is similar to the well-known six-tenths factor rule in plant design.