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This paper proposes an extended linear programming model for the hybrid approach proposed by Byrne and Bakir (International Journal of Production Economics 59 (1999) 305) and Kim and Kim (International Journal of Production Economics 73 (2001) 165). In this new model the workload of jobs is sub-divided to introduce the unit load concept of JIT. While an optimum plan is sought, due to this unit load concept, the model takes account of the requirement of small lot sizes which is one factor of the JIT approach. The effective loading ratio (ratio of the output quantity to the input quantity) is modified by omitting the slack time for each job. This helps to ensure that correct quantity of product is produced in each period, thus minimising any excess inventory or backlogging. Omission of slack time will also improve equipment utilisation and throughput. A flexible capacity constraint is also introduced which takes into account the availability of resources based on their previous histories. The incorporation of the unit load concept and modification of resource requirements and constraints in the proposed LP formulation are expected to help to improve the planning model by reducing the level of WIP and total flow time.

Linear programming (LP) models for production planning have been well known for many years. A typical LP planning model has the objective of minimising the total cost (generally covering the production cost, inventory cost, shortages cost, etc.) over a fixed planning horizon. The usual constraints are inventory balances, production quantity, demand quantity and capacity constraints in each period of the planning horizon. Material requirement planning (MRP) systems are widely used in production planning. Billington et al. (1983) presented mathematical programming formulations for the general MRP planning problem, together with a method to reduce the problem size. However, the complexity of real production systems makes it difficult for MRP systems to deal with the real characteristics of system demand. Segerstedt (1996) further developed the models of Billington et al. (1983) and identified the issue of scheduling constraints, which can lead to infeasibility of mathematical solutions. To overcome some of these difficulties the hybrid solution approach, which gives the advantages of both analytical and simulation solution procedures has been proposed and investigated by Byrne and Bakir (1999) and Kim and Kim (2001). This paper describes an extended LP model for the hybrid approach proposed by Byrne and Bakir (1999) incorporating JIT concepts.

This paper has presented a new LP formulation for use with the hybrid approach presented by Byrne and Bakir (1999) and Kim and Kim (2001). This new formulation incorporates features allowing JIT-like aspects of manufacturing to be better represented. The preliminary results presented here indicate that the new formulation may give some benefits over those previously adopted. Further investigation, incorporating the LP model with simulation in the complete hybrid procedure, is expected to identify further benefits which would make the procedure easier to apply in many modern manufacturing systems which incorporate aspects of the JIT approach.