A solution to the capacitated lot sizing problem

Abstract

We study a capacitated dynamic lot sizing problem with special cost structure involving fixed setup cost, freight cost, production cost and inventory holding cost. The freight cost is proportional to the number of containers used. We investigate the problem in which the maximal production capacity in one period is integral multiple of the capacity of a container and reveal the special structure of the optimal solution. We transfer the lot sizing problem into a shortest path problem and propose a network algorithm to deal with it. The T-period problem is solved in O(T 4 ) effort by the network algorithm.

Analysis of a dynamic lot‐sizing problem with production capacity constraint

“…The following theorem (Theorem ) indicates the production points of the optimal solution. The proof of Theorem 1 has been shown in our previous work (Zhang et al., ). Theorem For the (i + 1, j)‐problem with mod(U, W) = 0, either there exists an optimal production plan such that for any t (), if then , and if there exists some m such that then for some n (n = 1, 2, …, U/W), or (2) there exists some k () such that …”

“…For convenience, we define The following theorem (Theorem 1) indicates the production points of the optimal solution. The proof of Theorem 1 has been shown in our previous work (Zhang et al, 2011).…”

An open Web-based integrated system for intelligent building

“…So, in the future, IBMS will be incorporated into the system of Internet of Things, as a basic unit for "The Digital City". The applications of the domestic Internet of Buildings have been carried out [4]. With the continuous investment in research, more comprehensive applications will be invented for general use.…”