The gardener problem with reservation policy and discount. (September 2018) - Sadralashrafi, Seyedeh Sara; Pasandideh, Seyed Hamid Reza; Niaki, Seyed Taghi Akhavan; Nahavandian, Mohammad Hossein
Graphical abstract: Highlights: A multi-product gardener problem with reservation policy (MPGR) is investigated. A discount rate is offered to those customers who make reservations. Extra demand is assumed due to the motivation received by the discount rate. Optimal order quantities and discount rate are found. MGPR is shown to provide greater expected profit than the one without a reservation policy. Abstract: The Newsboy problem has always been an important issue in inventory management. The multi-product newsboy problem with random yield and budget constraint named as the Gardener Problem is one of the novels and popular extensions of the newsboy problem. Different from the existing studies, this paper presents a multi-product gardener problem with reservation policy. Moreover, a discount rate is offered to those customers who are willing to make reservations. In addition to the demand from the original customers, extra demand is included in the model due to the motivation received by the discount rate. A solution algorithm namely the multi-product gardener problem with reservation policy (MGPRA) is proposed to obtain the optimal order quantities and discount rate in order to maximize the expected profit when the yield and demand are uniformly distributed. This solution algorithm is based on Newton's method and Lagrangian multipliers and solves the problem in unconstrained, constrained and tightly constraint cases. Examples are given to show not only can the MGPRA solve the problem under the constraint budget, but also it is able to solve the problem under tightly budget constraint, efficiently. In addition to the examples provided, the application of the multi-product gardener problem with reservation policy can obtain greater expected profit than the multi-product gardener problem without a reservation policy.