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Optimization of Production and Inventory Management for Acme Manufacturing Using Linear Programming

Optimizes production and inventory using linear programming.

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    Optimization of Production and Inventory Management for Acme Manufacturing Using Linear Programming Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next four months is shown in the following table along with the expected production costs and the expected capacity for producing these items. Month 1 2 3 4 Demand 420 580 310 540 Production Cost $49.00 $45.00 $46.00 $47.00 Production Capacity 500 520 450 550 Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory (estimated by averaging the beginning and ending inventory levels each month). Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. They also want to maintain a safety stock of at least 50 units per month. Acme wants to determine how many of each appliance to manufacture during each of next four months to meet the expected demand at the lowest possible total cost. 1. Formulate a Linear Programming model for this problem Let, 𝑃 𝑖 = π‘ƒπ‘Ÿπ‘œπ‘‘π‘’π‘π‘‘π‘–π‘œπ‘› π‘œπ‘› 𝑖𝑑 β„Ž π‘šπ‘œπ‘›π‘‘ β„Ž 𝑆 𝑖 = π‘†π‘Žπ‘“π‘’π‘‘π‘¦ π‘ π‘‘π‘œπ‘π‘˜ π‘œπ‘“ 𝑖𝑑 β„Ž π‘šπ‘œπ‘›π‘‘ β„Ž Then the formulated Linear programing is, Minimize Z = $49 𝑃 1 + $45 𝑃 2 + $46 𝑃 3 + $47 𝑃 4 + $1 . 50 βˆ— ቀ 120 + 𝑆 1 2 + 𝑆 1 + 𝑆 2 2 + 𝑆 2 + 𝑆 3 2 + 𝑆 3 + 𝑆 4 2 ቁ Subject to, 𝑃 1 ≀ 500 𝑃 1 + 120 βˆ’ 𝑆 1 = 420 𝑃 2 ≀ 520 𝑃 2 + 𝑆 1 βˆ’ 𝑆 2 = 580 𝑃 3 ≀ 450 𝑃 3 + 𝑆 2 βˆ’ 𝑆 3 = 310 𝑃 4 ≀ 550 𝑃 4 + 𝑆 3 βˆ’ 𝑆 4 = 540 𝑃 𝑖 β‰₯ 400 π‘Žπ‘›π‘‘ 𝑆 𝑖 β‰₯ 50

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