Question

Demand requirements for an enterprise over the next 8 months are given below. The Stockout cost of lost sales is $100/unit. The inventory holding cost is $20 per unit per month. The manager is considering a plan, which begins in January with 200 units on hand and keeps the workforce stable at 1600 units per month. Maximum overtime of 20% at an additional cost of $50 per unit is permissible. The warehouse can only store a maximum inventory of 400 units.

Calculate the cost of this plan. Discuss the usage of overtime in your plan identifying the selection of quantity and timing of overtime.

Answer 1

There are two options that can be explored in this case.

Option-1: Use overtime up to a maximum of 20% of 1600 = 320 only when there is stock-out happening in a period without the overtime. This means no overtime when there is ending inventory available in a period.

Month	Demand	Production	Overtime	Total output	Ending Inventory	Stockout
					200
Jan	1,400	1,600	0	1,600	400	0
Feb	1,600	1,600	0	1,600	400	0
Mar	1,800	1,600	0	1,600	200	0
Apr	2,200	1,600	320	1,920	0	80
May	2,200	1,600	320	1,920	0	280
Jun	1,800	1,600	200	1,800	0	0
Jul	1,800	1,600	200	1,800	0	0
Aug	1,800	1,600	200	1,800	0	0
Totals			1,240		1,000	360
Cost/ unit			$50		$20	$100
Cost			$62,000		$20,000	$36,000
						$118,000

This leads to a total cost of $118,000 as we can see.

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Option-2: Do overtime in periods prior to the stock-outs up to a stock build-up of a maximum of 400 ending inventory so as to ensure minimum stock-outs in the later stages.

Month	Demand	Production	Overtime	Total output	Ending Inventory	Stockout
					200
Jan	1,400	1,600	0	1,600	400	0
Feb	1,600	1,600	0	1,600	400	0
Mar	1,800	1,600	200	1,800	400	0
Apr	2,200	1,600	320	1,920	120	0
May	2,200	1,600	320	1,920	0	160
Jun	1,800	1,600	200	1,800	0	0
Jul	1,800	1,600	200	1,800	0	0
Aug	1,800	1,600	200	1,800	0	0
Totals			1,440		1,320	160
Cost/ unit			$50		$20	$100
Cost			$72,000		$26,400	$16,000
						$114,400

This leads to a total cost of $114,400 as we can see.

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As we can see, option-2 is providing a lower total cost. This is happening because we are using the overtime to build-up 200 units of additional stock in March which will be used to reduce the stock-outs from 360 units in option-1 to 160 units only. This is always beneficial because the combined cost of producing in overtime and carrying ending inventory is less than the cost per stock-out.

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Calculations:

B Demand Production D Overtime G Stockout 0 А 1 Month 2 3 Jan 4 Feb 5 Mar 6 Apr 7 May 8 Jun 9 Jul 10 Aug 11 Totals 12 Cost/ unit 13 Cost 1400 1600 1800 2200 2200 1800 1800 1800 1600 1600 1600 1600 1600 1600 1600 1600 0 0 320 320 200 200 200 =SUMD3:D10) 50 =D11 D12 E F Total output Ending Inventory 200 =C3+D3 =MAX(0,F2+E3-B3) =C4+D4 =MAX(O.F3+E4-B4) =C5+DS =MAX(0.F4+E5-B5) =C6+D6 =MAX(0.F5+E6-B6) =C7+D7 =MAX(0.F6+E7-B7) =C8+D8 =MAX(0.F7+E8-B8) =C9+D9 =MAX(0.F8+E9-B9) =C10+D10 =MAX(0.F9+E10-B10) =SUM(F3:F10) 20 =F11*F12 =MAX(0,B3-F2-E3) =MAX(0.B4-F3-E4) =MAX(0.B5-F4-E5) =MAX(0.B6-F5-E6) =MAX(0.B7-F6-E7) =MAX(0.B8-F7-E8) =MAX(0.89-FS-E9) =MAX(0,B10-F9-E10) =SUM(G3:10) 100 =G11*G12 =SUM(D13:13) 14 15 16 Month Demand Production Overtime 17 18 Jan 19 Feb 20 Mar 21 Apr 22 May 23 Jun 24 Jul 25 Aug 26 Totals 27 Cost/ unit 28 Cost 1400 1600 1800 2200 2200 1800 1800 1600 1600 1600 1600 1600 1600 1600 0 0 200 320 320 200 200 200 =SUM(D18:D25) 50 =D26*D27 Total output Ending Inventory Stockout 200 =C18+D18 =MAX(0.F17+E18-B18) =MAX(0.B18-F17-E18) =C19+D19 =MAX(0.F18+E19-B19) =MAX(0.B19-F18-E19) =C20+D20 =MAX(0.F19+E20-B20) =MAX(0.B20-F19-E20) =C21+D21 =MAX(0,F20+E21-B21) =MAX(0.B21-F20-E21) =C22+D22 =MAX(0.F21+E22-B22) =MAX(0.B22-F21-E22) =C23+D23 =MAX(0,F22+E23-B23) =MAX(0.B23-F22-E23) =C24+D24 =MAX(0.F23+E24-B24) =MAX(0.B24-F23-E24) =C25+D25 =MAX(0.F24+E25-B25) =MAX(0.B25-F24-E25) =SUM(F18:F25) =SUM(G18:G25) 20 100 =F26*F27 =G26*G27 =SUMD28:628) 1800 1600 29