An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

An MILP approximation for ordering perishable products with non-stationary demand and service level constraints

“…Several extensions of Tarim and Kingsman's model exist. Rossi et al (2011b), Tarim et al (2011) proposed efficient and complete special purpose algorithms. Tempelmeier (2007) used Tarim and Kingsman's model as a basis to formulate different types of service-level constraints.…”

A reformulation for the stochastic lot sizing problem with service-level constraints

“…The objective function (12) minimizes the sum of expected total costs over all possible replenishment cycles (as defined in (11)) while conditioning on both fixed and incremental cost components by means of the binary variable X ij and the order-up-to level S ij . Constraints (13), (14), and (15) regulate the flow conservation. More specifically; (13) states that if there is a cycle that starts at period i, then there must be a successive cycle that ends at period i − 1, (14) ensures that there must be one cycle starting at the very first period, and similarly, (15) guarantees that the last cycle must end at the very last period.…”

“…As opposed to the special-purpose algorithms in the literature (see [9,13]), the reformulation is a deterministic equivalent MIP model. As such, it has http://dx.doi.org/10.1016/j.orl.2014.01.010 0167-6377/© 2014 Elsevier B.V. All rights reserved.…”

“…Tarim and Kingsman [15], Tempelmeier [16], and Rossi et al [8] adapted this formulation to take into account different service measures. Recently, Rossi et al [9] and Tarim et al [13] developed computationally efficient specialpurpose algorithms where an optimal solution is obtained by iteratively solving a relaxed version of the problem that is formulated and solved as a shortest-path problem.…”

Adaptive Strategies for Accelerating the Convergence of Average Cost Markov Decision Processes Using a Moving Average Digital Filter

“…An elegant way to find the optimal control actions for each state is provided by the classical value or policy iteration algorithms [1][2][3][4][5][6][7][8][9][10][11]. The value iteration (VI) algorithm is arguably the most popular algorithm, in part because of its simplicity and ease of implementation.…”