The Stochastic Dynamic Inventory Policy With Fixed Costs

The main goal of enterprise operations management is to reduce cost and improve efficiency,which is also the source for strengthening competitiveness of enterprises.Thus,operations management is extremely important in enterprise management.A commonly used method for lowering cost and increasing efficiency is to optimize enterprise's inventory decisions.However,when making operations decisions in practice,an enterprise usually incurs fixed costs independent of decision variables(e.g.,tolls as a part of transportation costs,and so on).An enormous amount of research on the operations policy has been studied by academia,yet most of which has ignored fixed costs.Morover,cost structures,demand classes and customer returns in different enterprises are various.Therefore,this dissertation would carry out a special investigation on dynamic inventory policy with fixed costs in production,retailing and service enterprises.First,a single product,periodic-review inventory problem faced by a manufacturer is considered.The manufacturer's replenishment cost is piecewisely linear and concave,and demand includes two sources: a deterministic one that must be satisfied in the current period and a random one that can be backordered or lost.Based on this,a multi-period inventory model with concave replenishment costs and two demand sources is developed.For the special demand case,a generalized(s,S)policy is shown optimal.Finally,the structure of the optimal replenishment policy is tested and effects of deterministic demand on the optimal policy are analyzed by numerical experiments.For a fixed and convex variable replenishment cost,a stochastic dynamic inventory model with two demand sources is built,the strong(K,c,q)-convexity of optimal value functions is shown and this property is applied to characterize the optimal production policy.From this,it is found that it is optimal to produce and the produce-up-to level increases with the initial inventory level when the initial inventory level is below the deterministic demand.Numerical study shows that the deterministic demand may not be satisfied and the structure of the policy is obviously different with the optimal one when the constraint that the deterministic demand must be satisfied is ignored.This suggests that the manufacturer needs to consider effects of the deterministic demand.In the case where e-commerce retailers allow their customers return goods,a multi-period joint replenishment and price model is considered with customer returns and fixed replenishment costs,where the quantity of returns is proportional to satisfied demand.In the general demand case,the optimal policy is an(s,S,p)policy for the single-period problem and is partially characterized for the multi-period problem.And in the special demand case,a stronger characterization of the optimal policy is made.On the basis of the characterization,a heuristic policy is proposed.Numerical results show that the heuristic is approximately optimal;and when the initial inventory level is low/high enough,both the optimal replenishment level and price vary monotonically with the fixed cost and return rate.For service enterpirises(taking a vehicle sharing service system for example),the dissertation observes that the fixed repositioning cost is important in practice.Based on this observation,a multi-period two-region dynamic repositioning model with fixed repositioning costs is developed.Incorporating fixed costs leads to a non-convex optimization problem,complicating the related analysis.Thus,the dissertation partially characterizes the optimal policy by applying properties of the optimal value function.And then based on this characterization,an easy-toimplement heuristic policy for the multi-period problem is designed.Finally,by numerical experiments,the approximate optimality of the heuristic policy is tested and the effects of the fixed cost on the optimal policy and total cost are obviously found.