A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times, nonlinear purchase and shortage cost functions

• Published in: European journal of operational research 2013-10, Vol.230 (1), p.26-41
• Main Authors: Mirzapour Al-e-hashem, S.M.J., Baboli, A., Sazvar, Z.
• Format: Article
• Language: English
• Subjects: Aggregate production planning; Air pollution; Computer Science; Cost analysis; Demand; Demand uncertainty; Green principles; Greenhouse effect; Greenhouse gases; Integer programming; Lead time; Linear programming; Mathematical models; Mathematical problems; Nonlinear shortage cost; Operations Research; Production planning; Quantity discount; Shortages; Stochastic models; Studies; Supply chain management; Supply chains
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2013.03.033

•Quantity discount is considered to encourage the producer to order more quantities.•Interrelationship between lead time, transportation cost, and GHGs is considered.•Demand uncertainty is assumed to follows a pre-specified distribution function.•Shortages are penalized by a generic nonlinear multiple breakpoint function.•The concepts of GHG emission and waste management are incorporated into the model. In this paper we develop a stochastic programming approach to solve a multi-period multi-product multi-site aggregate production planning problem in a green supply chain for a medium-term planning horizon under the assumption of demand uncertainty. The proposed model has the following features: (i) the majority of supply chain cost parameters are considered; (ii) quantity discounts to encourage the producer to order more from the suppliers in one period, instead of splitting the order into periodical small quantities, are considered; (iii) the interrelationship between lead time and transportation cost is considered, as well as that between lead time and greenhouse gas emission level; (iv) demand uncertainty is assumed to follow a pre-specified distribution function; (v) shortages are penalized by a general multiple breakpoint function, to persuade producers to reduce backorders as much as possible; (vi) some indicators of a green supply chain, such as greenhouse gas emissions and waste management are also incorporated into the model. The proposed model is first a nonlinear mixed integer programming which is converted into a linear one by applying some theoretical and numerical techniques. Due to the convexity of the model, the local solution obtained from linear programming solvers is also the global solution. Finally, a numerical example is presented to demonstrate the validity of the proposed model.