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,
𝑃𝑖 = 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑛 𝑖𝑡ℎ 𝑚𝑜𝑛𝑡ℎ
𝑆𝑖 = 𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 𝑜𝑓 𝑖𝑡ℎ 𝑚𝑜𝑛𝑡ℎ
Then the formulated Linear programing is,
Minimize Z = $49𝑃1 + $45𝑃2 + $46𝑃3 + $47𝑃4 + $1.50 ∗ ቀ120+𝑆1
2 + 𝑆1+𝑆2
2 + 𝑆2+𝑆3
2 +
𝑆3+𝑆4
2 ቁ
Subject to,
𝑃1 ≤ 500
𝑃1 + 120 − 𝑆1 = 420
𝑃2 ≤ 520
𝑃2 + 𝑆1 − 𝑆2 = 580
𝑃3 ≤ 450
𝑃3 + 𝑆2 − 𝑆3 = 310
𝑃4 ≤ 550
𝑃4 + 𝑆3 − 𝑆4 = 540
𝑃𝑖 ≥ 400 𝑎𝑛𝑑 𝑆𝑖 ≥ 50
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,
𝑃𝑖 = 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑜𝑛 𝑖𝑡ℎ 𝑚𝑜𝑛𝑡ℎ
𝑆𝑖 = 𝑆𝑎𝑓𝑒𝑡𝑦 𝑠𝑡𝑜𝑐𝑘 𝑜𝑓 𝑖𝑡ℎ 𝑚𝑜𝑛𝑡ℎ
Then the formulated Linear programing is,
Minimize Z = $49𝑃1 + $45𝑃2 + $46𝑃3 + $47𝑃4 + $1.50 ∗ ቀ120+𝑆1
2 + 𝑆1+𝑆2
2 + 𝑆2+𝑆3
2 +
𝑆3+𝑆4
2 ቁ
Subject to,
𝑃1 ≤ 500
𝑃1 + 120 − 𝑆1 = 420
𝑃2 ≤ 520
𝑃2 + 𝑆1 − 𝑆2 = 580
𝑃3 ≤ 450
𝑃3 + 𝑆2 − 𝑆3 = 310
𝑃4 ≤ 550
𝑃4 + 𝑆3 − 𝑆4 = 540
𝑃𝑖 ≥ 400 𝑎𝑛𝑑 𝑆𝑖 ≥ 50
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Subject
Mathematics