Linear Programming: Solving Acme's Lowest Cost Problem

[iNCREDiBLE]

My assignment is to formulate a LP and find the optimal solution for the following problem:

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 the 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 the next four months to meet the expected demand at the lowest possible total cost.

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

I understand everything except the first sentence. Can someone please explain the meaning of the first sentence.

 

[geosonel]

My assignment is to formulate a LP and find the optimal solution for the following problem:

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 the 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 the next four months to meet the expected demand at the lowest possible total cost.

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

I understand everything except the first sentence. Can someone please explain the meaning of the first sentence.

total cost (each month) = production cost + inventory cost
first sentence refers to inventory cost calculation
build total cost equation month by month then add all months:
month #1:
production cost₁ = P₁*(49.00)
inventory cost₁ = (1/2)*(120 + (120 + P₁ - D₁))*(1.50) ...since currently have 120 in stock
etc
determine constraints based on capacity limits, minimum production goals, and safety stock requirement

 

[Gokul43201]

Doesn't the inventory level depend of whether delivery happens continuously or at the end of the month ? Or is this assumed by convention to be one or the other of the two ?

 

[iNCREDiBLE]

total cost (each month) = production cost + inventory cost
first sentence refers to inventory cost calculation
build total cost equation month by month then add all months:
month #1:
production cost₁ = P₁*(49.00)
inventory cost₁ = (1/2)*(120 + (120 + P₁ - D₁))*(1.50) ...since currently have 120 in stock
etc
determine constraints based on capacity limits, minimum production goals, and safety stock requirement

That really helped me out. Thank you a lot! :!)