الگوریتم هیوریستیک برای اندازه پویاو حمل و نقل مسئله چند محصول

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped by some containers in the period and the total freight cost is proportional to the number of containers used. It is also assumed that backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the transportation policy that minimizes the total costs, which consist of production cost, inventory holding cost, and freight cost. Because this problem is NP-hard, a heuristic algorithm with an adjustment mechanism is proposed based on the optimal solution properties. The computational results from a set of simulation experiment are also presented.

The dynamic lot-sizing model (DLSM) has stemmed from the work of Wagner and Whitin (1958). The majority of DLSMs have not considered any production–inventory problem incorporating transportation activities. These days, the issue of transportation scheduling for shipping products (or delivering orders) by proper transportation modes at right time becomes significantly important in production (or distribution) management, or in import and export activities. Each company manufactures multiple products and uses a freight container as a transportation unit to ship its manufactured products to customers, which may lead to the managerial decision problems: production rates for each product, container types used, loading policy in containers, the number of containers used, etc. This provides us with a motivation to consider the optimal lot-sizing and shipping problem incorporating production–inventory and transportation functions together. Several articles have studied the extended works of the classical DLSM. Lippman (1969) studied two deterministic multi-period production planning models; monotone cost model and concave model. Hwang and Sohn (1985) dealt with a DLSM in which the transportation mode and the order size for a deteriorating product were simultaneously considered. However, they considered no capacity restriction on the transportation mode. Lee (1989) considered a DLSM allowing multiple set-up costs including a fixed charge cost and a freight cost, where a fixed single container type with limited carrying capacity is considered and the freight cost is proportional to the number of containers used. This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. In the problem, each order (product) placed in a period is immediately shipped by some containers in the period and the total freight cost is proportional to the number of containers used. It is also assumed that backlogging is not allowed. The problem extends the work of Lee (1989) to the multi-product problem. The objective of this study is to simultaneously determine the lot-sizes and the transportation policy that minimizes the total costs which consist of production cost, inventory holding cost, and freight cost.

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and a single container type are simultaneously considered. Because this problem is NP-hard, a heuristic algorithm with an adjustment mechanism is proposed based on the optimal solution properties. To evaluate the performance of the heuristic, we present the computational results from a set of simulation experiment. The result shows that in an average sense, the heuristic offers good solutions within 4.47% in comparison with the optimal solution for small-sized test problems having less than or equal to 8 periods and within 1.78% in comparison with the best solution for given test problems. Also, the result shows that the heuristic is faster than CPLEX package for all factors, T (planning horizon), M (the number of items), W (the load size), and becomes more efficient as T and M increase, respectively. These results show that the heuristic can efficiently work on same large-sized problems in a real world. However, simulation experiments are required to test the efficiency of the proposed heuristic for more large-sized problems. Further research will consider an extension of the problem where the loaded space size per unit for each product is inhomogeneous and various container types are allowed to employ together in each period