The chasing demand strategy was also proposed to productiuon department as to ke

Question

The chasing demand strategy was also proposed to productiuon department as to keep minimum inventory.

$10=production cost

$1,000= hiring cost

$500= firing cost

Total cost= (12,000 x $10)+(26 x 1,000)+(6 x 500)= $149,000

If you were to use a mathmatical modeling approach for optimal production strategy, wrtie the objective function of the model.

Month Demand Production Inventory # of workers Hired Fired Jan 1,000 1,000 0 10 0 Feb 400 400 0 4 6 Mar 400 400 0 4 Apr 400 400 0 4 May 400 400 0 4 Jun 400 400 0 4 Jul 500 500 0 5 1 Aug 500 500 0 5 Sep 1,000 1,000 0 10 5 Oct 1,500 1,500 0 15 5 Nov 2,500 2,500 0 25 10 Dec 3,000 3,000 0 30 5 Total 12,000 12,000 0 26 6

Explanation / Answer

Let Hi, Fi, and Ei be the hires, fires, and ending inventories in month-i; i=1,2,..,12. These are the decision variable.

Defined the following composite variables
Wi = Worker level in month-i = Wi-1 + Hi - Fi; i=1,2,..,12 given that W0 = workers preexisitng = 10
So, W1 = 10 + H1 - F1
W2 = W1 + H2 - F2 = 10 + H1 - F1 + H2 - F2
W3 = W2 + H3 + F3 = 10 + H1 - F1 + H2 - F2 + H3 - F3 and so on....
Pi = production in any month = 100*Wi

Minimize Z = Total cost = c*iEi + 10*iPi + 1000*iHi + 500*iFi
[Note: the cost of inventory holding is not given, so, I assume it to be 'c' for one unit ending inventory for single month]
Subject to,
Pi - (Ei - Ei-1) = Forecat of month-i

i.e.
100*(10+H1-F1) - E1 = 1000 (Jan)
100*(10+H1-F1+H2-F2) - E2 + E1 = 400 (Feb)
100*(10+H1-F1+H2-F2+H3-F3) - E3 + E2 = 400 (Mar)
-
-
-
100*(10+H1-F1+H2-F2+H3-F3+....+H12 - F12) - E12 + E11 = 3000 (Dec)

Hi, Fi, Ei >= 0; i=1,2,...,12

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Please provide c = a real number in order to solve this model in Excel.

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