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The retailer's optimal procurement quantity and the number of transfers from the warehouse to the display area are determined when demand is decreasing due to recession and items in inventory are subject to deterioration at a constant rate. The objective is to maximize the retailer's total profit per unit time. The algorithms are derived to find the optimal strategy by retailer. Numerical examples are given to illustrate the proposed model. It is observed that during recession when demand is decreasing, retailer should keep a check on transportation cost and ordering cost. The display units in the show room may attract the customer.

The management of inventory is a critical concern of the managers, particularly, during recession when demand is decreasing with time. The second most worrying issue is of transfer batching, the integration of production and inventory model, as well as the purchase and shipment of items. Goyal [

The aim of this paper is to determine the ordering and transfer policy which maximizes the retailer’s profit per unit time when demand is decreasing with time. It is assumed that on the receipt of the delivery of the items, retailer stocks some items in the showroom and rest of the items is kept in warehouse. The floor area of the showroom is limited and wellfurnished with the modern techniques. Hence, the inventory holding cost inside the showroom is higher as compared to that in warehouse. The problem is how often and how many items are to be transferred from the warehouse to the showroom which maximizes the retailer’s total profit per unit time. Here, demand is decreasing with time. This paper is organized as follows. Section

The retailer orders

Initially, the inventory level is

Combined inventory status for items in the warehouse and showroom.

The differential equation representing inventory status at any instant of time

The total profit per unit time of a retailer is a function of three variables, namely,

Next, to determine the optimum cycle time for showroom, for given

If

Since

In this case, we made (

Since

There are three subcases.

The optimal transfer level of units in showroom is zero and there exists a unique

(

Assign parametric values to

If

If

If

Set

Obtain

If

Compute

Increment

Continue Steps

Set

Obtain

If

Compute

Increment

Continue Steps

Set

Solve (

If

If

Solve (

If

Increment

Continue Steps

Consider the following parametric values in proper units: [

We apply Algorithm

[Variations for | ||||||

[Fixed values | ||||||

0.40 | 6 | 0.138 | 0.830 | 135.48 | 812.94 | 1635.60 |

0.45 | 6 | 0.136 | 0.817 | 132.85 | 797.11 | 1629.22 |

0.50 | 6 | 0.133 | 0.804 | 130.34 | 782.04 | 1622.94 |

[Variations for | ||||||

[Fixed values | ||||||

10 | 9 | 0.152 | 1.368 | 148.4932 | 1336.439 | 1600.113 |

20 | 7 | 0.151 | 1.057 | 147.5394 | 1032.776 | 1560.089 |

30 | 6 | 0.138 | 0.828 | 135.1126 | 810.6756 | 1490.671 |

[Variations for | ||||||

[Fixed values | ||||||

50 | 6 | 0.149 | 0.894 | 145.631 | 873.7861 | 1679.377 |

60 | 6 | 0.146 | 0.876 | 142.7661 | 856.5966 | 1669.339 |

70 | 5 | 0.144 | 0.72 | 140.8545 | 704.2727 | 1663.394 |

[Variations for | ||||||

[Fixed values | ||||||

150 | 6 | 0.138 | 0.830 | 135.48 | 812.94 | 1635.60 |

250 | 5 | 0.156 | 0.778 | 151.90 | 759.50 | 1636.67 |

350 | 5 | 0.156 | 0.778 | 151.90 | 759.50 | 1636.67 |

Consider the following parametric values in proper units: [

[Variations for | ||||||

[Fixed values | ||||||

0.4 | 10 | 0.151 | 1.508 | 148.43 | 1484.305 | 1746.88 |

0.425 | 10 | 0.149 | 1.487 | 146.14 | 1461.393 | 1743.27 |

0.45 | 10 | 0.147 | 1.467 | 143.94 | 1439.398 | 1739.70 |

[Variations for | ||||||

[Fixed values | ||||||

10 | 10 | 0.1508 | 1.508 | 148.43 | 1484.305 | 1746.88 |

12 | 9 | 0.1493 | 1.3437 | 147.0036 | 1323.032 | 1734.124 |

14 | 8 | 0.1479 | 1.1832 | 145.6471 | 1165.176 | 1719.14 |

[Variations for | ||||||

[Fixed values | ||||||

80 | 10 | 0.1548 | 1.548 | 152.3285 | 1523.285 | 1753.253 |

85 | 10 | 0.1528 | 1.528 | 150.393 | 1503.93 | 1750.13 |

90 | 10 | 0.1508 | 1.508 | 148.43 | 1484.31 | 1746.88 |

[Variations for | ||||||

[Fixed values | ||||||

100 | 22 | 0.099 | 2.185 | 98.31 | 2162.86 | 1715.17 |

150 | 10 | 0.151 | 1.508 | 148.43 | 1484.31 | 1746.88 |

175 | 8 | 0.170 | 1.358 | 166.76 | 1334.12 | 1748.55 |

200 | 8 | 0.170 | 1.358 | 166.76 | 1334.12 | 1748.55 |

Consider the following parametric values in proper units: [

[Variations for | |||||||

[Fixed values | |||||||

0.40 | 3 | 0.151 | 0.452 | 150.74 | 452.22 | 7224.91 | 0 |

0.45 | 3 | 0.145 | 0.436 | 145.16 | 435.47 | 7195.76 | 4.845 |

0.50 | 3 | 0.141 | 0.422 | 140.16 | 420.48 | 7167.68 | 9.840 |

[Variations for | |||||||

[Fixed values | |||||||

30 | 3 | 0.151 | 0.452 | 150.74 | 452.22 | 7224.91 | 0 |

20 | 3 | 0.137 | 0.412 | 138.01 | 414.02 | 7294.20 | 11.993 |

10 | 4 | 0.101 | 0.405 | 103.20 | 412.78 | 7381.82 | 46.804 |

[Variations for | |||||||

[Fixed values | |||||||

90 | 3 | 0.151 | 0.452 | 150.74 | 452.22 | 7224.91 | 0 |

95 | 3 | 0.153 | 0.459 | 152.87 | 458.60 | 7214.22 | 0 |

100 | 3 | 0.155 | 0.465 | 154.97 | 464.90 | 7203.68 | 0 |

[Variations for | |||||||

[Fixed values | |||||||

150 | 3 | 0.1508 | 0.452 | 150.74 | 452.22 | 7224.91 | 0 |

200 | 3 | 0.1502 | 0.451 | 153.04 | 459.13 | 7231.60 | 46.96 |

250 | 3 | 0.1496 | 0.449 | 155.38 | 466.13 | 7238.39 | 94.62 |

The following managerial issues are observed from Tables

Increase in demand rate b decreases

Increase in transferring cost from the warehouse to the showroom increases

Increase in ordering cost decreases cycle time in showroom and units transferred from warehouse to the showroom and retailer’s total profit per unit time. The cycle time in warehouse increases significantly.

Increase in maximum allowable number in display area increases

In this article, an ordering transfer inventory model for deteriorating items is analyzed when the retailer owns showroom having finite floor space and the demand is decreasing with time. Algorithms are proposed to determine retailer’s optimal policy which maximizes his total profit per unit time. Numerical examples and the sensitivity analysis are given to deduce managerial insights.

The proposed model can be extended to allow for time dependent deterioration. It is more realistic if damages during transfer from warehouse to showroom are incorporated.

The following assumptions are used to derive the proposed model.

The inventory system under consideration deals with a single item.

The planning horizon is infinite.

Shortages are not allowed. The lead time is negligible or zero.

The maximum allowable item of displayed stock in the showroom is

The time to transfer items from the warehouse to the showroom is negligible or zero.

The units in inventory deteriorate at a constant rate “

The retailer orders

The maximum allowable number of displayed units in the showroom

The inventory level at any instant of time

The demand rate at time

Constant rate deterioration,

The unit inventory carrying cost per annum in the warehouse

The unit inventory carrying cost per annum in the showroom, with

The unit selling price of the item

The unit purchase cost, with

The ordering cost per order

The known fixed cost per transfer from the warehouse to the showroom

The cycle time in the warehouse, (a decision variable)

The integer number of transfers from the warehouse to the showroom per order (a decision variable)

The cycle time in the showroom (a decision variable)

The optimum procurement units from a supplier (decision variable)

The number of units per transfer from the warehouse to the showroom,

The inventory level of items in the showroom regarding the transfer of

The authors are thankful to anonymous reviewers for constructive comments and suggestions.