Order picking (OP) is a critical yet time-consuming and labor-intensive warehouse operation within the supply chain. In picker-to-part systems with high demand, pickers are exposed to fatigue due to the excessive repetition of picking activities, which results in high human energy expenditure. The literature indicates that energy expenditure depends on the picking activity and the worker’s attributes, such as pickers’ weight, gender, and age. Studies have shown that as the weights of individuals increase, the energy consumed for the same task increases. This study proposes a two-stage stochastic programming model that minimizes assignment and overtime costs while avoiding excessive fatigue levels for pickers by incorporating rest allowance into the picking tour time. In the first stage, the number of pickers required is decided. In the second stage, orders are assigned to pickers considering uncertain energy expenditure. The two-stage stochastic programming model is solved by the sample average approximation algorithm. Results show that both OP cost and the number of pickers required to fulfill an order increase when the picker’s weight exceeds 80kg. In allocating orders, pickers weighing less than 80kg should be assigned to orders with more items, such as those containing 4- or 5-items. Conversely, pickers weighing more than 80kg should be assigned to orders with fewer items, like those containing 2- or 3-items, to avoid fatigue side effects.

The product-mix planning and the lot size decisions are some of the most fundamental research themes for the operations research community. The fact that markets have become more unpredictable has increaed the importance of these issues, rapidly. Currently, directors need to work with product-mix planning and lot size decision models by introducing stochastic variables related to the demands, lead times, etc. However, some real mathematical models involving stochastic variables are not capable of obtaining good solutions within short commuting times. Several heuristics and metaheuristics have been developed to deal with lot decisions problems, in order to obtain high quality results within short commuting times. Nevertheless, the search for an efficient model by considering product mix and deal size with stochastic demand is a prominent research area. This paper aims to develop a general model for the product-mix, and lot size decision within a stochastic demand environment, by introducing the Economic Value Added (EVA) as the objective function of a product portfolio selection. The proposed stochastic model has been solved by using a Sample Average Approximation (SAA) scheme. The proposed model obtains high quality results within acceptable computing times.

This paper presents the problem of redesigning a supply network of large scale by considering variability of the demand. The central problematic takes root in determining strategic decisions of closing and adjusting of capacity of some network echelons and the tactical decisions concerning to the distribution channels used for transporting products. We have formulated a deterministic Mixed Integer Linear Programming Model (MILP) and a stochastic MILP model (SMILP) whose objective functions are the maximization of the EBITDA (Earnings before Interest, Taxes, Depreciation and Amortization). The decisions of Network Design on stochastic model as capacities, number of warehouses in operation, material and product flows between echelons, are determined in a single stage by defining an objective function that penalizes unsatisfied demand and surplus of demand due to demand changes. The solution strategy adopted for the stochastic model is a scheme denominated as Sample Average Approximation (SAA). The model is based on the case of a Colombian company dedicated to production and marketing of foodstuffs and supplies for the bakery industry. The results show that the proposed methodology was a solid reference for decision support regarding to the supply networks redesign by considering the expected economic contribution of products and variability of the demand.