Robust Integrated Replenishment,Production Control And Distribution Policy Under Inventory Inaccuracy

The control of a complete production/inventory/distribution system control usually contains three main stages:raw materials inventory management,production control and final goods distribution scheduling.Raw materials inventory,work-in-process inventory and final goods inventory exist at the three stages respectively.Inventory inaccuracy(i.e.,the discrepancy between the inventory record and the physical inventory level)does exist in the above three types of inventories and brings negative impact on the operation of materials requirements planning and supply chain management systems.Therefore,this dissertation aims to develop a robust integrated replenishment,production control and distribution scheduling policy to hedge against the negative impact on production/inventory/distribution system from inventory inaccuracy.The main contents of this dissertation are summarized as follows:1.For a raw materials inventory system with replenishment lead-time and inventory inaccuracy,the robust replenishment problem is studied.The objective of this problem is to minimize the average inventory holding cost,backlog penalty and the materials transportation cost.First,a recursive algorithm is developed to estimate the probability distribution of the physical inventory levels,based on which,a robust reorder-time/reorder-quantity(RTQ)policy is proposed.Theoretical analysis and numerical experiments reveal some managerial insights of the proposed RTQ policy and the classical(r,Q),(s,S)and(R,S)policies:(1)If there exist invisible stock loss and inaccurate inventory records,the inventory system will be trapped into the zero-service state(i.e.,the inventory level becomes less than or equal to zero with probability one)in finite time under the classical policies;however,under the proposed RTQ policy,if the probability distribution of inventory error is known exactly,the inventory system will never be trapped into the zero-service state and will keep a high service level even if no audit is made.(2)If the inventory record is accurate,the RTQ policy is nearly optimal,and its performance is close to the perfonnance of the(r,Q)policy with optimal parameters.(3)To hedge against the negative impact from inventory inaccuracy,except for making audits or employing RFID devices,robust replenishment policy can also be adopted without generating extra human resource and device investment.2.For multiple machines and multiple product-types manufacturing systems with inventory inaccuracy of work-in-process and final goods,the robust production control problem is studied.The objective of this problem is to minimize the average production cost,including the inventory holding cost and the backlog penalty.The problem is solved in two steps;firstly,in light of the principle of dynamic programming,a simplified optimal policy is constructed based on the assumption that the records of inventories are completely accurate.To overcome the shortcomings of the simplified policy in hedging against inventory inaccuracy,we develop a robust production control policy based on the fundamental structure of the simplified optimal production control policy,and the conditional mathematical expectation of the physical inventory level of work-in-process and final goods.Numerical experiments are conducted to examine the performance of the proposed conditional expectation-based robust production control policy(i.e.,the Robust Policy)by comparing to the simplified production control policy(i.e.,the Simplified Policy)under different hedging points.The results of the experiments show that the proposed Robust Policy usually outperforms the Simplified Policy.Sensitivity analysis is also carried out to evaluate how some important parameters,e.g.,the distribution of inventory error,and the machines failure rates influence the performance of the two policies.The results of sensitivity analysis show that the proposed conditional expectation-based robust production control policy outperforms the simplified replenishment and production control policy under the variation of system parameters.The research on this problem reveals that the proposed robust production control policy can significantly reduce the negative impact caused by inventory inaccuracy even if product types are very many and their quantities vary continuously.3.For distribution systems with replenishment lead-time and inventory inaccuracy,the robust inventory routing problem(IRP)is studied.Differing from the traditional IRPs,we take the lead-time for replenishment into consideration,which is determined by the routing decision.Therefore,the decisions of replenishment quantity and routing depend on each other.This problem is solved in two steps:(1)The IRP with replenishment lead-time and accurate inventory record is studied.For a simple case with one vendor and two retailers,it is proved that the structure of the optimal replenishment and routing policy is of a switching-curve type.In this policy,the state space,which is composed of the inventory positions of the two retailers,is divided into several domains;and for inventory positions in each domain,there exists an optimal order-up-to level.Since the optimal policy is difficult to realize in practice,a Myopic policy that is easier to implement is proposed and numerical experiments are conducted to examine the near-optimality of the Myopic policy.(2)The IRP with replenishment lead-time and inventory inaccuracy is studied.The problem is solved in three layers:the route optimization layer,the replenishment quantity optimization layer and the route evaluation layer.On the first layer,candidate routes are generated and optimized;on the second layer,the replenishment quantity of all the retailers is optimized for each candidate route;and on the third layer,the performance of each route is evaluated under the according optimal replenishment quantity,and the result of evaluation is fed back to the first layer.A robust delivery time/stage length/replenishment quantity algorithm is proposed to optimize the replenishment time and quantity.Finally,a genetic algorithm-based method is developed to optimize the delivery route.4.For production/inventory/distribution systems under inventory inaccuracy,the robust integrated replenishment,production control and distribution problem is studied.For solving this problem,first we build up the mathematical model of the whole system and construct the robust integrated replenishment,production control and distribution policy based on the aforementioned work.According to the probability distribution of the inventory levels in future periods,which is obtained by recursive estimation,the next distribution time and corresponding distribution quantity is predicted,which can be taken as the goal of the next production stage.It is proved that in this situation,the optimal production control policy is of a {0,?}-style.That is to say,the optimal productivity is 0 or the maximum production rate(?).In production process,the production start time and the probability distribution of raw materials consumption are obtained by a simulation-based method.This probability distribution can be used to make raw materials replenishment decisions.Numerical experiments show the feasibility of the policy.According to the sensitivity analysis of inventory inaccuracy,we find that under the proposed policy,when the magnitude of the inventory errors varies,although the parameters of the policy changes accordingly,the service levels of each process keep the same.This shows good robustness of the proposed policy.For the research on inventory inaccuracy,the main contributions of this dissertation are:(1)The research of replenishment problem under inventory inaccuracy is extended from the existing newsboy model to the general model with fixed cost and replenishment delay;moreover,a robust replenishment policy is proposed.(2)The production control problem under the inventory inaccuracy of work-in-process and finial goods is studied and a robust conditional expectation-based production control policy is proposed based on the conditional expectation of the physical level of work-in-process and final goods.(3)The inventory routing problem under inventory inaccuracy in final goods distribution is studied.Considering the non-ignorable transportation delay in distribution,the structure of the optimal inventory routing policy is proved and a robust inventory routing policy is proposed;(4)The integrated replenishment/production/distribution control problem under inventory inaccuracy is studied and a robust integrated control policy is proposed.The feasibility and robustness of the policy are examined in the numerical experiments.