The article considers of a single-vendor single-buyer joint pricing and lot sizing model in which the vendor’s production process is imperfect. The market demand is a function of the buyer’s selling price. The vendor’s unit production cost is assumed to be a
function of lot size of each shipment to the buyer. This paper simultaneously determines shipment size, unit selling price of the buyer, vendor’s annual set-up cost, reliability of the production process and total number of shipments per lot from the vendor to the buyer. The expected annual total profit function is derived and signomial geometric programming technique is used to find the optimal solutions for different preferences of objective functions. The solution procedure is illustrated by a numerical example.
Sensitivity analysis is also carried out to investigate the effects of changes of parameter-values on the optimal decisions.
Optimal policy for a vendor-buyer inventory system with price-dependent demand, production cost discount and reliability consideration: A geometric programming approach
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