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Abstract
Supply chain scheduling addresses the coordination of machine and delivery scheduling of two or more supply chain stages. The aim is to improve supply chain performance measured in total logistics costs or the supply chain makespan, for example. However, the potential for improvement has never before been quantified, so this relatively new and ambitious field of study has not yet been properly justified. If performance improvements would barely compensate for the cost of coordination, supply chain scheduling would be expendable. This paper deals with a supply chain consisting of four stages. Focusing on the supply chain makespan, eight scheduling scenarios are compared by means of a numerical study. The simplest scenario is characterised by separate scheduling of all stages. The most promising scenario is a joint scheduling approach that treats the supply chain as a flow shop. In the other six scenarios, different subsets of stages coordinate their schedules. Joint supply chain scheduling of all stages significantly outperforms the other seven scenarios. This result holds for the case with a single machine as well as for two identical parallel machines at each stage. Owing to the complexity of some of the scheduling problems to be tackled in the experiments, the numerical study is based on small-size instances with only five jobs so that it can be solved using a commercial optimisation software. Hence, a simpler two-stage supply chain with a single machine at each stage is investigated to obtain results for large-size instances. Since the shortest processing time priority applied at the first stage leads to permutation schedules which on average result in near-optimum makespans, a joint supply chain coordination approach based on Johnson's algorithm turns out to be unreasonable especially when considering the cost of coordination.
Notes
The bullwhip effect, which was discovered by Simon Citation(1952) and Forrester Citation(1958), describes the amplification of demand variability further up the supply chain. A company exhibits the effect if it purchases materials and components more variably with regard to quantities and time intervals than it sells its products. Several reasons for this phenomenon are listed by Lee et al. (Citation1997a, Citationb), who popularised the name ‘bullwhip effect’, and Moyaux et al. Citation(2007). Cachon et al. Citation(2007) and Bray and Mendelson Citation(2012) provide empirical evidences.
Double marginalisation describes a problem of inefficient pricing in monopoly chains. If each supply chain stage sets its product price individually, only focusing on its own profit, under certain circumstances the sum of profits is lower than the total supply chain profit resulting from a central optimisation approach (Cournot Citation1897, Spengler Citation1950, Machlup and Taber Citation1960, Tirole Citation1988).
If the focus of this paper was on a supply chain organised as a pull system, due date-related dispatching rules such as the earliest due date priority would be more suitable than the shortest processing time (SPT), longest processing time (LPT), and first come first served (FCFS) rule which do not consider due dates agreed on with customers.