Retail replenishment, the decision of how much stock to send from distribution centres and plants to the outlets that sell it, is a natural application of the transportation model of operations research (OR), yet published applications differ widely in rigour and reporting quality. This literature-based analytical study reviews fifteen studies on transportation-type models for retail distribution and examines two applications in depth: a two-source, four-dealer transportation problem for a Malaysian furniture distributor (Tuan Hassan & Masrom, 2022) and an integer programme that plans daily pallet dispatch from a distribution centre to twenty stores of a Brazilian retail chain (Santos Cruz et al., 2016). For each paper we extract the real-life context, objective function, constraints, assumptions, solution method and reported results, and then re-solve the published models independently in Python (SciPy/HiGHS). Both optima reproduce exactly: RM50,605.21 for Paper 1 and 342 pallets for Paper 2. The audit nevertheless finds that Paper 1's headline saving of 78.91% rests on a baseline its data do not produce (50.7% on its own stated rule, 8.7% against its North-West Corner plan), and that its reduced-cost example confuses a basic variable's cost range with a reduced cost. Paper 2's text reports 427 pallets dispatched where its own tables give 342, and its full-load constraint makes three of the twenty stores impossible to serve. Extending the models, we find that each extra unit of 5-ton lorry capacity saves RM3.12, that under ±20% lane-cost variation the fixed Paper 1 plan loses 2.2% on average against re-optimisation and changes in 63% of draws, and that allowing partial loads in Paper 2 serves every store while still dispatching 349 pallets. A hypothetical store-to-store example shows that lateral transfers cut total cost by 44% and that a minimum-lot rule costs 0.6% when modelled but 18% when imposed after optimisation. We conclude with reporting, validation and modelling recommendations for retail replenishment studies.

Keywords: transportation problem; linear programming; integer programming; retail replenishment; distribution planning; sensitivity analysis; operations research