Multi-site integrated production-distribution planning with trans-shipment: a fuzzy goal programming approach

In multi-site (parallel) manufacturing systems, each selling region (SR) is usually allocated to a specific manufacturing site (MS) in order to minimise the transportation costs, simplify the planning process, etc. However, such manufacturing systems usually encounter great drawbacks in terms of over-achievement or under-achievement of the forecasted demand due to isolation of the MSs. To cope with this drawback, this paper proposes a novel framework for preparing an optimal aggregate production plan by interconnecting the MSs through lateral trans-shipment. In the presence of fluctuating and dynamic demands, we apply some classic strategies including the inventory holding, back-ordering, and additional capacity options (i.e. overtime and changing workforce level) as well as lateral trans-shipment of products among MSs as the feasible strategies undertaken. Maximising the total profit and minimising the manufacturing lead time are considered as two managerial goals. Due to ambiguousness of some critical parameters as well as vagueness of objectives' target values, a fuzzy goal programming (FGP) approach with imprecise goal hierarchy is developed for modelling the aggregate production-distribution planning (APDP) problem with trans-shipment. The proposed FGP model is then converted to an equivalent crisp one by combining the two recently developed fuzzy programming approaches. An illustrative example inspired by a real case study is provided to show the usefulness and applicability of the proposed model.