Defining inventory control points in multiproduct stochastic pull systems

Abstract

Multistage pull production systems have been widely implemented in recent years and constitute a significant aspect of lean manufacturing. One of the important considerations in such systems is identifying the control points, i.e. where in the multistage sequence to locate the output buffers. Allowable container/batch sizes, optimal inventory levels, and ability of systems to automatically adjust to stochastic demand depend on the location of these control points yet the issue of optimal location has not been widely addressed. This paper considers a multiproduct pull setting where part types compete with each other for common production resources. In this environment it is important to consider factors such as lead time variability and to include the corresponding queuing aspects into the model. Each workstation is modeled as a GI/G/1 queue. Waiting times spent by parts at workstations are approximated using a decomposition/recomposition algorithm. Necessary and sufficient conditions are provided for the optimality of a single control point. Conditions under which multiple control points are optimal are investigated along with the impact of product mix and utilization parameters on the number of control points. Analytical model results are validated by simulation.

Introduction

Extensive research has been carried out on pull control-based production systems as one aspect of lean manufacturing. However, the majority of this research has concentrated on determining the number of kanbans, with lesser emphasis placed on container sizes and product sequence in a just-in-time (JIT) shop. Askin and Krishnan (2006) developed conditions ensuring the optimality of a single buffer in a multistage pull system producing a single product type with known service times and deterministic lead times. However, while the issue of locating safety stock in multiechelon push production planning systems has been examined by several authors, little attention has been paid to the problem of locating buffers in a stochastic pull production system operating within a facility.

In this paper, the multiproduct, stochastic, pull environment is modeled. Service times and demand interarrival times are assumed to be random. Products flow in a serial manner through all stages, i.e. product merge/split issues are not considered. Because different product types may be present in the manufacturing system at a given time, the products compete with each other for the limited machine resources. This results in an increase in the mean and variance of production lead time at each stage as compared to single product models. The increase is due to the additional time spent by each part waiting for service. In serial systems, it is not necessary to implement controlled inventory buffers at all workstations. These controlled inventory buffers are referred to as control points in this study. We define a control section as the sequence of workstations between two control points. Within control sections, a push philosophy is incorporated. Once production is authorized by the removal of a container of parts from the control section's output buffer, a replenishment order is released to the first workstation in the control section. These orders then have authorization to flow through each stage of the control section until again reaching the output buffer, i.e. they are pushed through without waiting for a customer request. Each control section therefore operates as a CONstant Work In Process (CONWIP, Spearman et al., 1990) system. The objective of this paper is to determine where inventory buffers should be located in serial systems operating with demand-based pull control. A related question concerns determining the conditions under which it is optimal to use a CONWIP strategy with a single end-of-line inventory buffer. Thus the problem addressed may be viewed as determining the appropriate span for a CONWIP control system. We note that systems such as mixed model assembly lines operate as multiproduct serial systems with a single control section. A secondary consideration concerns determining the number of kanbans and container sizes that should be used in specific conditions. The system is modeled as a collection of GI/G/1 queues and the waiting times are approximated by a decomposition/recomposition technique modeled after Shantikumar and Buzacott (1981).

In the next section we review the relevant literature. A more formal problem statement is provided in Section 3 along with a solution methodology. Computational results are described in Section 4. Results are summarized and conclusions stated in Section 5.