An integrated replenishment and production control policy under inventory inaccuracy and time-delay

Highlights

• We model the robust control problem a production/inventory system with inaccurate inventory records and time-delay.

• A simplified optimal replenishment and production control policy is constructed based on dynamic programming.

• A robust replenishment and production control policy is developed based on the probability distribution of inventory level.

• Numerical experiments indicate that the proposed robust policy performances well in hedging against inventory inaccuracy.

Abstract

Inventory inaccuracy has a significant negative impact on the performance of raw materials replenishment and production control. It usually leads to high inventory holding cost or large backlog penalty. To hedge against it, we investigate a replenishment and production control problems for a multiple machines and multiple product-types production/inventory system with inventory inaccuracy. The objective is to minimize the average production cost, including the inventory holding cost and the backlog penalty. In addition to inventory inaccuracy, the lead-time of raw materials replenishment and the unreliability of machines are also taken into consideration. In light of the principle of dynamic programming, a simplified optimal replenishment and production control 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, a conditional expectation-based replenishment and production control policy is developed based on the fundamental structure of the simplified optimal replenishment and production control policy, and the conditional probability of the physical inventory level. Numerical experiments are conducted to examine the performance of the proposed policy for hedging against inventory inaccuracy, and sensitivity analysis is carried out to study how the parameters of the production/inventory system and the proposed policy affect the average production cost.

Introduction

In enterprise resource planning (ERP) or supply chain management (SCM) systems, the inventory records of raw materials, work-in-process (WIP), or final goods inventory might deviate from their real quantities. DeHoratius and Raman (2008) show that the inaccuracy of inventory record happens due to theft, miscounting, misplacing, deteriorating, etc. It has been reported in literature that inventory inaccuracy may worsen the performance of inventory management and production control. For example, French (1980) finds that the WIP inventory inaccuracy distorts the effectiveness of materials requirement planning (MRP) system. Disney et al. (2000) show that the WIP inventory inaccuracy in a shop floor causes a time-delay in the WIP feedback loop in the production and inventory control system, which makes it difficult to construct a good control policy. Kang and Gershwin (2005) point out that a very severe out-of-stock may be caused by a very small rate of undetected stock loss. DeHoratius and Raman (2008) report that inaccuracies cost retailers as much as 10% of their profit.

Therefore, for a production/inventory system, inventory inaccuracy has a significant negative impact on the performance of raw materials replenishment and production control. However, existing research on replenishment and production control usually focuses on the system whose inventory data is completely accurate. The replenishment and production control problem for a production/inventory system with inventory inaccuracy has not been investigated sufficiently. So it is necessary to develop a robust replenishment and production control policy that can hedge against the negative impact of inventory inaccuracy, or in other words, that is insensitive to the inaccurate records of inventory. We have focused on this issue for recent years. Wang and Yu (2012) investigate the robust production control problem for a single machine and single part-type manufacturing system with inaccurate WIP inventory, and propose a robust policy that is insensitive to the observation error of inventory. Chan and Wang (2014) extend this research to the case of multiple machines and multiple product-types manufacturing system, but without considering the lead-time of replenishment. Wang and Chan (2015) study the robust replenishment and production problem for a single-stage production/inventory system with inventory inaccuracy and lead-time for replenishment, which, however, only produces one type of product. In this paper, we extend the research on the optimal replenishment and production control problem under inventory inaccuracy to a more complicated situation and propose a new solution. The main differences between this paper and the previous three works (Wang and Yu, 2012, Chan and Wang, 2014, Wang and Chan, 2015) are on the following three aspects:

• Refined model. In the previous three works, inventory inaccuracy is modeled as observation error, i.e., the observed inventory equals the physical inventory plus the observation error at any time. Inventory inaccuracy is assumed to be independent over time horizon. In this situation, the difference between the recorded inventory and the physical inventory level may change sharply from one period to another, which is not realistic. In this paper, a new model is provided, in which we assume that inventory inaccuracy occurs due to theft, misplacing, damage, etc., and that the events resulting in inventory inaccuracy only affect the physical inventory but are not reflected in the inventory record. Moreover, in this paper, we consider the accumulation of inventory inaccuracy, which is more realistic.

• More complicated system. The system studied in this paper is more complicated than those in our previous works. Compared to Wang and Yu (2012) and Wang and Chan (2015), in which only one type of product is manufactured, in this paper we consider an inventory/production system that orders and consumes multiple kinds of raw materials and produces multiple types of products on multiple machines. Compared to Chan and Wang (2014), in which lead-time for replenishment is not considered, in this paper the lead-time for replenishment is also taken into consideration. Therefore, in this paper, we investigate a production/inventory system with multiple product-types, multiple machines, lead-time for replenishment, and inaccurate inventory record.

• New solution. In the previous works, the robust production control policy generates the production rate (i.e., the decision variable) only based on the inventory record. This idea works based on an unrealistic assumption that the discrepancy between the inventory record and the physical inventory is independent from one period to another. Since more realistic factors are considered and new mathematical model is constructed in this paper, the idea of the previous works does not work any more. We develop a new solution and construct a new replenishment and production control policy based on the conditional expectation of the physical inventory level, which is not difficult to estimate.

The rest of this paper is organized as follows: In Section 2, a literature review of existing research is given. In Section 3, we develop the mathematical formulation of the problem of optimal replenishment and production control for a multiple machines and multiple product-types production/inventory system under inventory inaccuracy and time-delay. In Section 4, a new conditional expectation-based replenishment and production control policy is proposed for such a system. In Section 5, numerical experiments are conducted to examine the performance of the proposed policy. In Section 6, main contributions of this research are summarized and some problems for future research are presented.