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Engineering · Mechanical Engineering
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Problem No. 1 Derive the economic production quantity (EPO) formula assuming the production rate is m and the demand rate is D (m > D) and also sketch the profile of the inventory as function of time. In the EPO model considered above, it is generally assumed that the demand is satisfied unit by unit and hence production and consumption simultaneously occur during the period of production. However, in certain situations demand cannon be stratified during production time. In this scenario, the demand accumulated during the production time can be satisfied just immediately after the production is ended as back-order. Then, the demand accruing between the end of the current production run and the beginning of the next production run can be satisfied unit by unit as in the of the classical EPQ. For this scenario, sketch the inventory profile as fiunction of time and drive a new economic production quantity (EPO) formula. Use the following Notation D Number of units demanded per year, m-production rate (number of units that can be produced per year), vproduction cost per unit, r carrying charge S/

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