Lot streaming models with a limited number of capacitated transporters in multistage batch production systems

Abstract

This paper presents a more general mathematical programming model to solve a lot streaming problem in multistage batch production systems in which transportation activities are involved. The purpose of the proposed mathematical programming model is to find the optimal start time, the optimal number of transfer batches, and the optimal allocation of variable transfer batches that minimize the total cost, including the makespan cost and the transportation cost. Two efficient heuristic procedures are developed due to the large amount of computational time required to solve the proposed mathematical programming model. A practical application of the two proposed heuristic methods is demonstrated to show their real-world usefulness. We also recommend the best appropriate heuristic method that can be chosen by a production manager under a certain premise. An experiment consisting of two phases was conducted to further verify the excellent performance of the two proposed heuristic methods.

Introduction

In recent years, the importance of reducing the manufacturing lead time (MLT) and decreasing work-in-process (WIP) inventories has been widely recognized in the manufacturing sector. Hence, some techniques (e.g., just-in-time (JIT), cell manufacturing, and optimized production technology (OPT), which was initiated by Goldratt [1]) have been used to achieve the above-mentioned important goals. Lot streaming, which was first introduced by Reiter [2], is a technique in OPT that splits a processing batch (i.e., a lot) into several transfer batches (i.e., sublots). Then, operations can be performed in different manufacturing stages simultaneously, and thus production can be accelerated. As stated by Kropp and Smunt [3] and Ronen and Starr [4], lot streaming is one of the effective methods for compressing MLT and reducing WIP inventories in general multistage batch production systems.

To determine appropriate lot streaming policies, a number of issues must be carefully considered and are discussed below. The first issue is what objective (e.g., the time or the total cost) should be chosen by production managers. Considering from the viewpoint of the characteristics of each objective mentioned above, the literature on modeling the lot streaming problem can be divided into two categories. One category concentrates on time models. Some researchers, such as Kropp and Smunt [3], Truscott [5], Baker and Pyke [6], Trietsch and Baker [7], Chen and Steiner [8], [9], Glass and Potts [10], and Kalir and Sarin [11], have devoted themselves to determining the optimal allocation of sublots for the single-product case. On the other hand, some time models developed by Vickson and Alfredsson [12], Cetinkaya [13], and Vickson [14] aim to determine both the optimal allocation of sublots and the optimal production sequence for the multiple-product case. The objective functions of the time models based on a time-related performance measurement criterion (e.g., the makespan or the mean flow time) are minimized. Another category deals with cost models that only consider the single-product case since multiple-product problems are extremely intractable. The purpose of solving a cost model is to determine the optimal processing lot size and/or the optimal number of sublots that minimize the total cost (see, for example, Szendrovits [15], Goyal [16], Graves and Kostreva [17], and Ranga et al. [18]).

The second issue is whether transportation activities between stages are involved in multistage batch production systems. Two kinds of activities are needed to complete production. One is manufacturing activities that involve a series of operations that alter the physical form of WIP in different stages. Another is complementary activities, including setup and transportation, that are not part of the finished goods but are necessary to complete production. Setup can be divided into attached setup and detached setup. Attached setup sets up a machine that requires a certain minimum number of units (usually one unit received from the immediately upstream stage) to be available when setup is started. Detached setup is performed before any unit arrives at the machine. Transportation further involves sublot transportation activities and empty transporter return activities. Therefore, the total time required to complete a processing lot is the sum of the total setup time, the total production time, the total sublot transportation time, and the total empty transporter return time. As far as we know, few studies on time models have considered the influence of transportation activities on the makespan. For the sake of model simplicity, in the literature, these times associated with transportation activities have been neglected or incorporated into the processing times. In practice, however, the makespan is significantly influenced by these times associated with transportation activities. Furthermore, the extent to which these activities affect the makespan depends on the number of transporters. Consequently, this issue was only discussed by Truscott [5] and Trietsch and Baker [7]. Truscott [5] presented a zero–one mixed integer programming (ZOMIP) model and proposed an algorithm based on the branch-and-bound method to solve the segmental adjacent-stage lot streaming problem, where only a single transporter was considered. Additionally, an efficient algorithm was developed by Trietsch and Baker [7] to solve the two-stage lot streaming problem, where multiple transporters were included, but the setup time was excluded.

On the other hand, while almost none of the existing cost models elaborately explore the effect of transportation activities on the total cost, for the convenience of model derivation, these activities have merely been transformed into a transportation cost by multiplying the number of sublots by a unit cost (see Goyal [16] and Graves and Kostreva [17]). Ranga et al. [18] proposed a cost model in which the setup time, the waiting time, and the sublot transportation time that was part of the makespan were considered. They also transformed the makespan into a cost.

The third issue is what types of sublots should be allocated in multistage batch production systems. The allocation of sublots also has a significant impact on the makespan or the total cost. Determining sublot allocation involves three types of sublots: equal sublots, consistent sublots, and variable sublots. More detailed descriptions of these three types of sublots have been given by Trietsch and Baker [7, p. 1068]. It is well recognized that the makespan based on the allocation of variable sublots is shorter than that based on the allocation of equal sublots or consistent sublots since both equal sublots and consistent sublots are special cases of variable sublots. To date, almost all the reports in the literature have only considered the allocation of equal sublots (see Trietsch and Baker [7], Kalir and Sarin [11], Szendrovits [15], Goyal [16], Graves and Kostreva [17], Ranga et al. [18], and Baker and Jia [19]) or consistent sublots (see Kropp and Smunt [3], Truscott [5], Baker and Pyke [6], Trietsch and Baker [7], Chen and Steiner [8], [9], Glass and Potts [10], Vickson and Alfredsson [12], Cetinkaya [13], Vickson [14], and Baker and Jia [19]).

Our paper differs from those of Truscott [5] and Trietsch and Baker [7] in four ways: (1) We deal with a more general multistage production system rather than the segmental adjacent-stage production system considered by Truscott [5] and the two-stage production system studied by Trietsch and Baker [7]. (2) We consider multiple transporters instead of a single transporter as assumed by Truscott [5]. (3) The allocation of variable sublots is explored for the first time in this paper. (4) We consider attached setup and detached setup simultaneously.