An adjustable sample average approximation algorithm for the stochastic production‐inventory‐routing problem

Abstract

We consider a stochastic single item production‐inventory‐routing problem with a single producer, multiple clients, and multiple vehicles. At the clients, demand is allowed to be backlogged incurring a penalty cost. Demands are considered uncertain. A recourse model is presented, and valid inequalities are introduced to enhance the model. A new general approach that explores the sample average approximation (SAA) method is introduced. In the sample average approximation method, several sample sets are generated and solved independently in order to obtain a set of candidate solutions. Then, the candidate solutions are tested on a larger sample, and the best solution is selected among the candidates. In contrast to this approach, called static, we propose an adjustable approach that explores the candidate solutions in order to identify common structures. Using that information, part of the first‐stage decision variables is fixed, and the resulting restricted problem is solved for a larger size sample. Several heuristic algorithms based on the mathematical model are considered within each approach. Computational tests based on randomly generated instances are conducted to test several variants of the two approaches. The results show that the new adjustable SAA heuristic performs better than the static one for most of the instances.

Integrating production scheduling and transportation procurement through combinatorial auctions

“…It consists of transportation costs, either by the manufacturer's fleet or by the winning carrier, and the possible delivery-tardiness costs. Constraint (2) ensures that each order i has only one successor on the production line. Similarly, constraint (3) ensures that each order j has only one predecessor on the production line.…”

“…The bidding chromosome shows that there are two bidders or carriers. Assume that carrier 1 bids to deliver orders (6) and (6,2). Carrier 2 bids to deliver orders (5) and (5,7).…”

“…According to Figure 6 and based on the example in Section 3.1.3, offspring 1 shows that carrier 1 and carrier 2 win the delivery for order 6 and order 5, respectively. Additionally, offspring 2 shows that carrier 1 and carrier 2 win the delivery for order (6,2) and order (5,7), respectively. The bidding result of the offspring is adjusted to ensure that winning bids of different carriers do not contain identical orders.…”

“…Few studies belong to this category [28,34]. Some studies tackled different variants of the standard production-transportation problem with routing delivery [16,23,25,38,41,62]; some studies focused on developing approaches for its solution [2,5,32,33,43]; and some studies incorporated additional features within the problem, such as multi-objective optimization [31], uncertainty and robustness [17,53], and financial planning [3].…”

New advances and applications in deterministic and stochastic network optimization

“…Gugat et al propose a decomposition‐based method for solving mixed‐integer nonlinear optimization problems with “black‐box” nonlinearities. The method alternatingly solves a mixed‐integer linear master problem and a separation problem for iteratively refining the mixed‐integer linear relaxation of the nonlinear equalities.…”